Info 13E for pdf - Startsida - SGI · also in complicated soil profiles and loading sequences. ... - Creep parameters 5. Behaviour of soft soils - ... The presentation was made in

LINKÖPING 1997

STATENS GEOTEKNISKA INSTITUTSWEDISH GEOTECHNICAL INSTITUTE

Inform

ation 1

3E

Prediction of settlements of embankmentson soft, fine-grained soils.Calculation of settlements and their course with time.

ROLF LARSSON

PER-EVERT BENGTSSON

LEIF ERIKSSON

Prediction of settlements of embankments on soft, fine-grained soils. 1

STATENS GEOTEKNISKA INSTITUTSWEDISH GEOTECHNICAL INSTITUTE

Information 13E

LINKÖPING 1997

Prediction of settlements of embankmentson soft, fine-grained soils.Calculation of settlements and their course with time.

Rolf LarssonPer-Evert BengtssonLeif Eriksson

SGI Information 13 E2

Swedish Geotechnical InstituteSE-581 93 Linköping

Swedish Geotechnical InstituteLibraryPhone: Int +46 13 20 18 04Fax: Int +46 13 20 19 09E-mail: [email protected]: http://www.swedgeo.se

0281-7578SGI-INF--97/13E--SE

Rolf LarssonPer-Evert BengtssonLeif Eriksson

19604183

Swedish Geotechnical Institute

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This publication contains a recommendation forthe way in which prediction of settlements of

embankment fills on soft, fine-grained soils should beperformed, together with part of the background forthe described method. The method is limited tocalculation of one-dimensional consolidation.

Calculation of settlements and their course withtime for embankments on soft fine-grained soils,primarily clay, has been a major area for research anddevelopment at the Swedish Geotechnical Institute(SGI) since the Institute was founded in 1944.The first instrumented test embankment was con-structed in 1945, and this and several other morerecent fills and instrumented parts of road embank-ments have been studied since then. At the same time,new techniques and equipment for field testing,instrumentation and sampling as well as testing in thelaboratory have been developed.

The results from these investigations, togetherwith experience from consulting activities and fromother institutions, have provided a good insight intothe processes taking place in soils during consolidationfor applied loads.

In parallel with this, new calculation models andtechniques have been developed, which enable anaccurate prediction of the consolidation processesalso in complicated soil profiles and loading sequences.

The research results have been continuouslyreported in the Institute’s series of reports and ininternational publications and conference proceedings.They have also been continuously incorporated in thework and calculation practices of the institute.

This publication is a digest of the technique forinvestigations and calculations recommended forprediction of settlements of embankments.

Information 13 is addressed to those who performor use this kind of prediction. It also describes thebackground to the EMBANKCO computer programme,which has been developed for this purpose in co-operation between the Swedish National RoadAdministration and SGI. Paragraphs that are directlyrelated to this programme have been marked speciallyin the text.

The publication has been written by Rolf Larsson,Per-Evert Bengtsson and Leif Eriksson at the SGI.

Preface



Contents

1. Introduction ...............................................6

2. General requirements on calculationsand calculation data .................................9

3. Investigations and samplingin the field .................................................10- Sounding- Pore pressure measurement- Sampling

4. Laboratory investigations .....................12Determination of consolidation characteristicsby oedometer tests- Compressibility parameters- Permeability parameters- Creep parameters

5. Behaviour of soft soils -empirical experience .............................15

5.1 General ........................................................155.2 Laboratory tests ...........................................15

- Secondary compression- Swelling- Swelling in oedometer tests- Swelling in practical cases of unloading in the field- Reloading- General model for moduli and the time dependence of the compressibility- Simplified model for moduli and the time dependence of the compressibility- Modulus of elasticity- Permeability- Pore pressure generation at loading

5.3 Field tests ....................................................26- Pore pressure generation- Apparent preconsolidation pressure- Deformations- Excess pore pressure dissipation- Development of apparent preconsolidation pressures and undrained shear strengths

- Conclusion- Natural apparent overconsolidation

5.4 Influence of time dependence of the com-pressibility on the size of the settlement .....28- Larger settlements- Complication of the general picture by apparent overconsolidation

5.5 Examples of measured and calculatedsettlements ...................................................29- Case 1: Test fill at Lilla Mellösa- Case 2: Embankment on Road E4- Case 3: Embankment on Road E3

6. Calculation of stress distributionat loading ..................................................35Estimation of stress distribution by using charts- Examples of calculations of stress distribution- Influence of dry crust- Limited depth to firm bottom- Simplified methods- Submersion below the ground water level

7. Calculation of initial deformations ....39

8. Calculation of the course ofsettlements in one-dimensionalconsolidation ............................................41

8.1 Principle of calculation of the course of theconsolidation process ..................................41- Calculation for a single layer with constant parameters- Calculation for multi-layer systems- Calculation with consideration to varying parameters

8.2 Modern calculation methods .......................44- The EMBANKCO calculation programme- Conditions for the calculations- Course of the calculations

9. Literature .................................................50


The prediction of settlements and their course withtime is a central problem in geotechnical

engineering. Many structures that are built are verysensitive to settlements and calculations are thenmade in order to check that the settlements are notbecoming so large that reinforcing measures such aspiling or installation of lime/cement columns arenecessary. For other constructions, such as road andrailway embankments, large settlements can often beaccepted provided that the settlements are even andthat their course with time can be predicted. Thedemand for even settlements then applies both alongand across the embankments and is fulfilled byadjustment of the geometry of the embankment andthe density of the embankment fill material withregard to the properties of the underlying soil.

A good prediction of the consolidation process isrequired also in cases where the settlement of theembankment is to be taken out in advance bypreloading, with or without the use of vertical drains,and when the embankment for stability reasons is tobe constructed in stages to utilize the increase instrength during consolidation.

DETAILED KNOWLEDGE OFTHE SOIL PROFILEA good prediction of the settlements and their coursewith time demands a detailed knowledge of theunderlying soil profile concerning stratification andcompression characteristics of the different soil layersand also the in situ stress situation and the porepressures, as well as the natural variation of the latter.Furthermore, knowledge is required about the drainingproperties in different seams, varves and layers withinthe compressible soil as well as in the dry crust and theunderlying firmer bottom layers.

In soft soils with low permeability, such as clayeysilt, clay and gyttja, the consolidation process is veryslow and normally the consolidation properties cannot

therefore for practical reasons be determined by insitu tests. Undisturbed samples then have to be takenand the consolidation properties determined byoedometer tests in the laboratory.

CLASSICALONE-DIMENSIONAL THEORYThe results from tests on small specimens in thelaboratory must then be transferred to in-situ conditionsin the settlement prediction. In this process, verysimple assumptions have previously been employed.In the classical one-dimensional consolidation theory,developed by Terzaghi in 1923 [1], it is assumed thatthe relation between applied stress and compressionafter consolidation, i.e. when all excess pore pressurescreated by the load increase have dissipated, is aunique relation which is independent of time anddrainage conditions. In calculation of the consolidationprocess, it is also assumed that both the compressionmodulus and permeability are constants throughoutthe process without regard to the changing stress leveland that the pores in the soil are compressed.

The coarseness of the assumption of a uniquerelation between applied load and final compressionindependent of time can readily be observed inlaboratory tests on high-plastic clays which exhibitlarge creep effects. Numerous observations have alsobeen made in the field of settlements that continue inspite of the fact that all excess pore pressures havedissipated. Long-term observations in the field alsoshow settlements and pore pressures that widely deviatefrom the classical consolidation theory both regardingtheir size and their course with time. This is also validin cases which have taken into account changes inmodulus related to the stress level alone and changesin permeability during the consolidation process.

CHAPTER 1.

Introduction


TIME-DEPENDENT COMPRESSIBILITYThe time-dependent relation between effective stressand compression has been given many names, such ascreep, secondary compression, time resistance andrate effects, all of which are used to describe the samephenomenon. Many different approaches have beenused to take these time effects into consideration in thecalculation of settlements. In the simplest approach,classical consolidation theory has been assumed to bevalid until all excess pore pressures have dissipated,whereupon secondary compression has commenced.This latter compression has then proceeded at acontinuously decreasing rate, because secondarycompression is assumed to be a linear function versusthe logarithm of time. This division has appeared to beapplicable to the results of small scale oedometer testsbut is inconsistent with long-term observations in thefield.

Taylor’s laboratory modelThe first theory where time effects were at least partlyincorporated in the consolidation processes waspresented by Taylor in 1940 and was followed twoyears later by a model for a general variation ofcompression with effective stress and time [2,3]. Themodel was mainly valid for results from oedometertests.

Suklje’s general modelA more general model was presented by Suklje in1957 [4]. In this model, no separation is made betweenthe processes during pore pressure dissipation andthereafter, except for the hydrodynamic delay of thesettlement process during the first and more rapidphases of the consolidation process. In the model, therelation between effective stress and compressionchanges continuously with the rate of deformation.

The so called “secondary consolidation” is thusnot a separate phenomenon which is added after a“primary consolidation”. On the contrary, the entirecourse of stress-deformation is time dependent. Thedevelopment of this time dependent process is furtherregulated by the permeability of the soil and thedrainage paths since a corresponding volume of waterhas to flow out from the soil in order to allow thesettlements to occur.

Bjerrum’s geological modelAnother presentation with a corresponding modelwas made by Bjerrum (1967 and 1972) with the

purpose of illustrating the influence of time onsettlements under loads that act for a long time [5,6].The presentation was made in order to explain apparentoverconsolidation effects in natural soils because ofgeological “ageing” and to explain why settlementsmay occur under structures in spite of the fact that theapparent preconsolidation pressure has not beenexceeded.

Bjerrum´s presentation is well suited for illustratingprocesses that continue for a very long time, where theinfluence of the hydrodynamic delay of the settlementprocess has been equalised. In the shorter timeperspectives that are considered in normal predictionof settlements, the influence of the permeability andthe drainage paths has to be taken into account. Thiswas also pointed out by Bjerrum, but is often notevident in later presentations of the model.

Bjerrum’s model also includes time-dependentincrease in shear strength, because the relation betweenthe undrained shear strength and the apparentpreconsolidation pressure is assumed to remain thesame also when the apparent preconsolidation pressureis increased by time-dependent settlements at constantload.

The two latter models have been shown to agreevery well with the observations of the consolidationprocesses that have been made both in the field and inthe laboratory.

EMPIRICAL KNOWLEDGEIn calculation of settlements, a relevant model isrequired of what occurs in the soil during the consol-idation process apart from the vertical compression.Empirical knowledge about this has been obtainedfrom a large number of field tests, in which the porepressure build-up during loading and the pore pres-sure dissipation thereafter have been studied. Further-more, the elastic deformations during loading and thehorizontal movements occurring thereafter have beenstudied, together with the distribution of settlementswith depth in the soil profile. In some cases, also theshear strength increase has been studied [7].

In the laboratory, empirical knowledge has beengathered concerning the compression and swellingcharacteristics of different soils together with the timedependence of these properties and the relation be-tween compression and permeability. Simultaneous-ly, new test methods and equipment have been devel-oped, enabling a careful determination of the com-pression characteristics of the soil and its permea-


bility as a function of the compression. From observa-tions in the field, it has also been possible to calibratethe apparent preconsolidation pressures evaluatedfrom the laboratory tests against those stresses in thefield at which the behaviour of the soil is significantlychanged, [8,9]. It has also been possible to calibratethe initial permeability determined in the laboratoryagainst field tests.

In this way, it has been possible to create a methodfor transferring the results from small scale oedometertests in the laboratory to the conditions that apply infull scale loading cases in the field.

SETTLEMENT CALCULATIONSIn calculation of settlements, the soil between twodraining layers has often been simplified to a singlehomogeneous layer. This has been done in order tofacilitate hand calculations but involves considerableerrors. Alternatively, the soil has been divided into alimited number of layers and the calculation of theconsolidation process has been performed using agraphical procedure. Using the latter method alsopotentially makes it possible to take into accountvarying moduli and permeability as well as timeeffects. This is done by calculating the consolidationprocess for a limited time interval with constantparameters. Thereafter, new parameters are selectedwith regard to the deformation that has occurred andthe excess pore pressure is adjusted with regard to thetime dependent changes in the compression charac-teristics that have occurred during the elapsed time.The consolidation process is then calculated for a newlimited time step and the procedure is repeated. Forpractical reasons, the number of layers and time stepsin this procedure are limited in calculation by hand.

The calculation of the distribution of stress in-crease in the soil because of the applied load has alsooften been simplified in hand calculations. The sim-plifications have seemingly not involved very largedifferences in additional stresses but, because of thevariability of the soil and its non-linear compressi-bility, the differences in calculated settlements can bevery large.

No need for simplified assumptionsWith access to modern calculation aids, such aspersonal computers with large computational capacity,there is no need for simplified assumptions andcalculation procedures. The soil profiles can be dividedinto a large number of layers and the time steps in the

calculations can be made very short. Likewise, thecalculation of stress distribution can be performedutilizing all the possibilities provided by the theory ofelasticity. This theory is not perfect but is the best ofits kind that is available today.

Experience from this type of calculation is thatthe results agree far better with what in realityoccurs in the soil in the field, concerning bothsettlements and settlement rates anddevelopment of pore pressures and increase inundrained shear strength.


CHAPTER 2.

General requirements on calculationsand calculation data

In order to obtain a sufficiently accurate predictionof settlements and their course with time, the

following requirements must be fulfilled:

• The stratification of the soil profile and the drainagepaths must be known in detail.

• The in situ pore pressures must be measured andthe seasonal variation must be prognosticated.

• Undisturbed samples must be taken in all com-pressible layers to such an extent that the com-pressibility characteristics of the soil and theirvariation in different layers and with depth can beestablished.

• Compression tests in oedometers must be per-formed to a corresponding extent. The tests can beperformed as constant rate of deformation tests(CRS-tests) or as incrementally loaded tests,[10,11]. Alternatively, a combination of both typesof tests can be used for a more complete determi-nation of all parameters. In both types of tests, it isimperative to follow the Swedish standard con-cerning both the performance of the test and theinterpretation of the results. Otherwise, the re-sults must not be used in the model and calculationmethod described in this publication, and a corre-sponding procedure which is suited to the testingmethod used has to be applied.

• The calculations must take into account the factthat the compression parameters and the permea-bility change when the soil is compressed and thatthe compressibility is time dependent.

• In non-saturated soil, the effect of gas in the poresmust be taken into account. This problem isnormally negligible in Swedish clays.

• The elastic initial deformations must be calculated.

• In the calculations, the soil must be divided into alarge number of layers in order to obtain anacceptable accuracy of the prediction.

• The stress distribution in the soil must be calculatedaccurately. Simplified methods, such as the 2:1method, are not accurate enough.

• The loading sequence must be modelled accurately.Any later changes in load, such as adjustments ordecreases in effective load because of massesbecoming submerged below a ground water tableclose to the ground surface during the consolidationprocess, must also be taken into account.

The requirements for accuracy in the settlementpredictions for road embankments are mainly governedby the demands on the function of the road specifiedby the owner of the road. If the requirements listedabove are fulfilled, an acceptable agreement betweencalculated and actual settlements can be expected.However, perfect agreement cannot be expected. Thisis mainly because of limitations in the amount ofinvestigation that can be performed for each separatecase. The calculation model also involves certainsimplifications with a separation of the deformationsinto initial “elastic” deformations followed by one-dimensional vertical consolidation. The agreement isalso affected by external factors, for example the loadapplication in the field seldom follows any simplepredetermined pattern because of restraints andproblems at the site. Seasonal variations in the climatehave also been shown to affect the course of thesettlements. The influence of these external factorsdiminishes with time and normally they do not haveany practical significance for the long term settlementprocess.


CHAPTER 3.

Investigations and sampling in the field

The first condition for accurate prediction ofsettlements is that the underlying soil must be

thoroughly investigated concerning stratification ofthe soil profile and properties of the different soillayers. The natural stress situation in terms ofoverburden pressure and pore water pressure mustalso be clarified.

The field investigations must yield a detailed pictureof the stratification in the soil down to firm bottomboth across and along the projected embankment. Aclassification of the different soil layers must beobtained with respect to soil type, compressibility anddrainage properties. A possible occurrence of thindraining layers must also be registered together withprevailing pore pressure conditions.

SOUNDINGThe soil stratification is investigated by differentsounding methods. Previously, weight sounding testsor total pressure soundings were often used to deter-mine the stratification in compressible soils. The soilclassification then demanded that at least disturbedsamples were taken in the different layers. Thinnerlayers could not be registered by these methods andalso the registered stratification in terms of thickerlayers was relatively coarse. The possibility of effi-cient determination of the required parameters hasbeen increased considerably by the introduction ofthe cone penetration test CPT with simultaneousmeasurement of the pore pressures and the dilatome-ter test [12.13]. The former enables, a very gooddetermination of the stratification of the soil andthe occurrence of draining layers or seams. Further-more, the in situ pore pressure can be determinedefficiently in permeable layers and the need forfurther pore pressure measurements can be mini-mized.

By using parallel dilatometer tests, an improvedsoil classification and estimate of the soil density can

be obtained together with an improved estimation ofthe strength properties and stress conditions in the soilprofile. Furthermore, a good determination of thecompressibility of layers of coarse silt and sand can bemade.

In layered soil profiles and other profiles contain-ing overconsolidated soil and silt and sand layers, therequired compression parameters for these zones andlayers can thus often be obtained efficiently by usingmodern in situ methods. Elastic properties and com-pressibility of overconsolidated cohesive soils arenormally estimated by using empirical relations withthe undrained shear strength, and a measure of thelatter property is obtained from both CPT and dilato-meter tests. Dilatometer tests in coarse silt and sandyield moduli which can be used in the same way as theoedometer moduli from laboratory tests. An “oedo-meter modulus” can also be estimated from the resultsof CPT tests, although its practical use is restricted tonormally consolidated sand.

The need for supplementary sampling can therebybe minimized and in principle be limited to layersconsisting of clayey silt, clay, gyttja and possibly peatin which undisturbed samples have to be taken fortesting in the laboratory.

PORE PRESSURE MEASUREMENTFor registration of thinner seams and layers, soundingswith measurement of the sounding pore pressure arerequired. The pore pressure soundings can also beused for measurement of the in situ pore pressures byhalting the penetration in permeable layers andallowing the excess pore pressure to dissipate. Aregistration of the pore pressure dissipation versustime during such temporary stops can also be used fora coarse estimate of the draining properties of thelayer.

Pore pressure measurements must be performedby the installation of piezometers at different levels in


the profile. The extent of these installations dependson factors such as the extent to which equalized porepressures have been measured in the soundings. Themeasured pore pressures must be linked to nearbyobservation points in the national ground water networkfor an estimation of normal ground water conditionsand possible variations.

The piezometers can also be used in tests fordetermination of the in situ permeability as a comple-ment to the oedometer tests in the laboratory.

SAMPLINGSampling in soft, fine grained soils is performed witha sampler yielding undisturbed samples of high quality.In Sweden, the Swedish standard piston sampler isused, except in peat where a special peat sampler isused [14].

Repeated investigations have shown that highquality samples can be obtained in most compressiblesoils with the Swedish standard piston sampler. Acondition for this is that the recommended samplingprocedure is followed [15]. This involves, amongother things, that the punching stroke in the samplingoperation is performed evenly and very slowly, that awaiting time of 5 to 10 minutes is allowed between thecutting of the sample and the start of extraction of thesampler and that the extraction is performed slowlyand smoothly. All vibrations should be avoided andshutters should be applied only in exceptional caseswhere these have proved necessary in order to obtainsamples.

The sampling equipment must be in perfect condi-tion with a sharp and undamaged cutting edge, sam-pling tubes that are not excessively worn, well func-tioning mechanisms and no binding parts.In the St 1 equipment type, the locking of the releaseband (or rod) and the breaking mechanism must alsofunction properly.

When sampling in profiles with stiffer soil overlyingweaker soil, the stiff soil must be pre-drilled. Thismust always be done through the dry crust and thestiffer soil directly below.


CHAPTER 4.

Laboratory investigations

Calculations of settlements in cohesive soils arenormally based on results from oedometer tests.

These can be performed as incrementally loaded testsor as continuously loaded CRS tests, which arenowadays more common.

DETERMINATION OF CONSOLIDATIONCHARACTERISTICS BY OEDOMETERTESTSThere are a number of methods of performing andinterpreting oedometer tests, which all yield differentresults. A condition for the results to be applied in thecalculation model described in this publication is thatthe tests must be performed and interpreted in accord-ance with the recommendations given in SwedishStandard SS 02 71 29 or SS 02 71 26 for incrementallyloaded tests and CRS-tests respectively, [10, 11].*)

The parameters required for a settlement calculationare primarily:

Compressibility parameters:

M0 = Constant modulus at stresses below theapparent preconsolidation pressure

σć = Apparent preconsolidation pressure

ML = Constant modulus for stresses just above theapparent preconsolidation pressure

σ´L = Limit pressure ( > σć ) at which the modulusstarts to increase

M´ = Modulus number, ∆M / ∆σ´ for stresseslarger than σ´L

Permeability parameters:

ki = initial (natural) permeability

βk = coefficient of change in permeability withcompression ( = -∆logk / ∆ε )

Creep parameters:

αs(max) = coefficient of secondary compression( =∆ε / ∆logt ) at the apparentpreconsolidation pressure

βα s= coefficient of change in coefficient of

secondary compression with compression,(∆αs / ∆ε)

For more complicated loading cases involvingboth loading and unloading, there is also a need forparameters describing the swelling properties of thesoil.

The most efficient method of determining thecompression characteristics is the CRS-test, whichyields continuous relations for the compressibilityand permeability properties. Creep parameters andswelling characteristics can normally be estimatedwith sufficient accuracy by using empirical relations.

In the normal test procedure, the modulus M0 isestimated from empirical relations for both types ofoedometer tests. In those cases where a more accuratedetermination of the modulus at low stresses ( < σć)is required, incremental tests with loading, unloadingand reloading are performed according to the standard.

When this is necessary, more accurate determi-nations of the creep parameters and the swellingcharacteristics can also be obtained by using incre-mental oedometer tests.

For peat, incrementally loaded oedometer tests arenormally performed, [14].

_


The compression characteristics evaluated fromoedometer tests performed and evaluated accordingto the Swedish standard are representative for a rate ofrelative compression of αs·5·10-6 1/s. This rate is a

parameter that is used in the subsequent calculationswhere the time (or rate) dependence of the compressioncharacteristics is taken into account [7].

*) Oedometer tests according to the Swedish standard areperformed on 20 mm high specimens. Incrementally loadedtests are performed with a doubled load in each incrementand the load increments are applied for 24 hours. Drainageis provided at both ends of the sample. CRS-tests areperformed with a constant rate of deformation and withdrainage at one end and pore pressure measurement at theother end. The rate is adapted to the type of soil in such away that the pore pressure at the undrained end neverexceeds 15 % of the total applied vertical stress.• For incrementally loaded tests, the apparentpreconsolidation pressure is evaluated by plotting the 24-hour readings of strain versus the logarithm of the appliedstress and using the Casagrande construction.

Determination of the apparent preconsolidationpressure according to Casagrande.

The stress-strain relation is also plotted with the stressin a linear scale in order to verify that there is a significantbreak in the stress-strain relation at the apparentpreconsolidation pressure and to enable an evaluation of thecompression modulus. The modulus is evaluated as a tangentmodulus at the straight portion of the stress-strain relationjust after passing the apparent preconsolidation pressure,ML, and at a number of points along the curved part of therelation at higher stresses.

The evaluated moduli are then plotted versus the effectivestress at which they were evaluated and the modulus numberM´ = ∆M / ∆σ´ is evaluated from the straight line relationfor high stresses.

Evaluation of compression mudulusfrom oedometer tests

The limit stress σ´L , at which the modulus starts toincrease, is calculated by fitting in such a way that theequation

[ ]ε σ σ σ σ= − + − +' ''

ln( ' ( ' ' ) )L c

L

L

LM MM

M1 1

corresponds to the measured stress-strain relation for stresseshigher than the apparent preconsolidation pressure.


• In CRS-tests, the effective stress, σ´, is calculated from

σ σ' = − 23

ub

whereσ = applied vertical stressub= measured pore pressure at the undrained end

The effective stress is plotted versus the strain in linearscales and the apparent preconsolidation pressure isevaluated by using the Sällfors construction.

Evaluation of compressibility parametersfrom the CRS-test

The modulus ML is evaluated from the straight portionof the stress-strain relation for stresses slightly higher thanthe apparent preconsolidation pressure and the measuredstress strain relation is then corrected by subtracting a factor(c, kPa) from the stress in order to make the straight portionof the curve pass through the point where the apparentpreconsolidation pressure was evaluated. This correction isintended to be a correction for rate effects in the test. Themodulus-stress relation is evaluated and plotted continuouslyand the modulus number M´ is evaluated from this plot. Thelimit pressure σ´L is then estimated and fitted as above inorder to make the evaluated parameters fit the correctedstress-strain relation.

The permeability of the soil is continuously evaluatedfrom

kt

g huwb

= ∂ε∂

ρ 2

2

The logarithm of the permeability is then plotted versusthe relative compression and the initial permeability, ki, andthe coefficient of change in permeability with compression,βk, are evaluated.

Evaluation of permeability parametersfrom the CRS-test


CHAPTER 5.

Behaviour of soft soils– empirical experience

5.1 GENERALA large number of observations have been maderegarding the general behaviour of soil at loading.These observations constitute the basis for the empir-ical relations used for estimation of creep parameters,swelling characteristics, reloading moduli, moduli ofelasticity for calculation of initial deformations andgeneration of pore pressure changes at changes in theloading situation [7].

5.2 LABORATORY TESTS

Secondary compressionThe coefficient of secondary compression, αs, at anincrease of the load has been shown to be a functionof the compression of the soil, Fig. 1.

Fig. 1. The coefficient of secondary compression as a function of thecompression in Bäckebol clay at 8 m depth [7].


The coefficient has a very low value until a certaincompression has been reached, whereupon it rapidlyincreases to a maximum value and then slowly de-creases with further compression. In clay, the criticalcompression where s starts to rapidly increase corre-sponds to an effective stress of about 0.8·σć.

The value of the coefficient of secondary compres-sion at its maximum and at further compression isstrongly related to the void ratio of the soil, which canalso be expressed in terms of soil type and water

content. Maximum values of αs and the related watercontents for a number of Swedish soils are shown inFig. 2. The figure shows that there is a clear relationbetween water content and maximum value of αs butalso that this relation varies between different types ofsoil. It has also been shown that the decrease in αs atcompression corresponds to the simultaneous de-crease in water content and follows the same relationas for maximum values and water content.

Fig. 2. Relation between maximum coefficient of secondary compressionand natural water content in different soils [7].


The variation of αs at loading above the apparentpreconsolidation pressure can be written

α α β εε αs s smax( ) max= − ∆

whereαs max = maximum value of αsαs max(ε) = αs at compression ∆ε

βα s

= coefficient of change in coefficientof secondary compression withcompression, -∆αs / ∆ε

∆ε = relative compression between theactual compression and thecompression at αs max

Both αs max and βα s can be estimated from Fig. 2.

on the basis of soil type and natural water content.Values of the coefficient of change in αs with

compression, βα s, are obtained by a recalculation

using the density of solids in the soil and can beestimated from

β αα s s N Nw w≈ + −max ( . ) / ( . )0 37 0 25(clay and organic clay)

β αα s s N Nw w≈ − + −( . )( . ) / ( . )max 0 002 0 37 0 25(sulphide soil)

β αα s s N Nw w≈ − + −( . )( . ) / ( . )max 0 0145 0 5 0 2(gyttja)

Measured values in Swedish peat indicate that thecoefficient of secondary compression in this type ofsoil can be related to the degree of humification ratherthan water content and that the parameter βα s

isnegligible [17], Fig. 3.

As has been shown, the secondary compressionsare very small until the effective stresses approach theapparent preconsolidation pressure. In modelling thebehaviour of soil, it is therefore very important toconsider the stress and deformation history of the soilin situ (primarily the overconsolidation ratio) also indescribing the time dependence of the properties.

A table with guiding values has been developed forselection of empirical values of αs max and βα s

,Table 1, for use in the EMBANKCO programme.

Fig. 3. Maximum coefficient for secondary compression in peat as afunction of the degree of humification [17].


Table 1. Table with guiding values for use in EMBANKCO.

For peat, αs max = 0.025 and βα s= 0.000 are normally used.

with decreasing effective stress and becomes verylow at low effective stress.

• The swelling modulus Ms can be expressed as

M aS S= σ' /

where σ´ = effective vertical stressaS = swelling index

When a normally consolidated soil is subjected toa small load reduction, the secondary consolidationcontinues at a reduced rate. If the load reduction islarge enough, also the time dependent deformationchange direction to secondary swelling. The stresslevel at which this occurs can be written as b·σć ,where b is a load factor. The coefficient of secondaryswelling at stresses below b·σć can apparently bedescribed as c·S, where c is a constant and S is the totalswelling that has developed at the particular time.

Swelling in oedometer testsThe net effect of the processes described above duringa 24-hour interval for a load step in the oedometer isthat at small load reductions there will be a smallcompression in spite of the reduced load. Thecompression at the stress level b·σć is often almostidentical to the compression at the start of the unloadingand for larger load reductions the net effect becomesa real swelling, Fig. 4.

SwellingWhen the effective stresses in a soil without cemen-tation are decreased to a sufficient degree, the soilstarts to swell. In a clay which has only just consoli-dated for a stress above the previous apparent precon-solidation pressure (i.e. the excess pore pressureshave just dissipated) secondary compressions are inprogress at a relatively high rate. A small reduction inload will halt this compression for a certain period oftime and possibly there will be a slight swelling beforethe secondary compression commences at a reducedrate. If the load reduction is large enough, the second-ary compression stops permanently and for evenlarger load reductions the clay starts to exhibit second-ary swelling in addition to the “immediate” swelling.

Swelling is time dependent in the same way ascompression. At unloading, the pore pressure in thesoil decreases. A hydrodynamic delay of the swellingoccurs for a certain time, during which the rate of theswelling depends on the permeability of the soil andthe access to free water. After equalization of the porepressure, the secondary swelling proceeds and may befurther delayed if the supply of free water is cut off.Apart from the demand for access to free water to besucked up, the swelling process is in principle identicalto the compression process.

Oedometer tests with incremental loading andunloading show that the swelling or unloading modulusis very high for stresses close to the new apparentpreconsolidation pressure, but decreases successively

Clay and slightly organic clay Organic clay, gyttja, sulphide clay, calcareous clay

wN´ αs max βas wN´ αs max βas% %

25 0.000 0.000 25 0.000 0.00030 0.002 0.027 50 0.007 0.03040 0.006 0.031 75 0.016 0.03350 0.010 0.035 100 0.021 0.03560 0.014 0.039 125 0.026 0.03870 0.018 0.043 150 0.030 0.04080 0.021 0.046 200 0.036 0.04690 0.025 0.049 250 0.040 0.051100 0.029 0.053 300 0.044 0.055110 0.033 0.057 350 0.047 0.058120 0.037 0.061 400 0.050 0.061


where S = total relative increase in specimen heightaS = swelling indexσć = preconsolidation pressureb = load factorσú = stress after load reduction

This equation has been applied to results from testson a large number of soil types and has been found tocorrespond well to the results.

For clays, the swelling index aS has been found tovary between 0.007 and 0.012 and the load factor b tobe about 0.8. The index aS decreases with increasinggrain size and becomes about 0.001 in sand andgravel. The factor b increases with increasing grainsize to become about 1.0 for gravel. Values of aS fora number of Swedish soils as a function of averagegrain size are shown in Fig. 5. The upper part of thefigure also shows approximate values of the loadfactor b. Investigations in Swedish peat show that theload factor is about 0.8 also for this type of soil [18].

In clays, there is probably a correlation betweenthe parameters aS and b and the plasticity of the clay.Preliminary relations of this type are shown in Fig. 6.

According to the results obtained in Swedish soils,the swelling after 24 hours in incremental oedometertests can be expressed as

S a bS

c

u

= ⋅ln ''σ

σ

Fig. 4. Deformations at unloading in anoedometer test [7].

Figure 5. Swelling index as as a function of average grain size [7].

Swelling without secondary compressionNet effect of swelling and secondarycompression


α α σ σσεs s

c

c

bb

= −−max( )' '

( ) '1where

αs max(ε) = coefficient of secondaryconsolidation at first loading andcurrent compression

σ´ = effective vertical stress b = load factor σć = apparent preconsolidation pressure

The secondary swelling at effective stresses lowerthan b·σć can be assumed to be governed by

α s swelling c S( ) = − ⋅

where c = a constantS = total developed swelling

In the EMBANKCO programme, version 1, secondaryswelling is not taken into account. The swellingmodulus, Ms, is calculated by using a givenmultiplication factor as a direct function of theeffective vertical stress, Ms= a·σć. The factors 100for clay and organic soil, 200 for silt and 1000 forsand are given as guiding values for selection of themultiplication factor a.

ReloadingThe modulus at reloading after an unloading dependson how much swelling has developed during theunloading period. In cases where the unloading hasbeen small, no significant swelling will have occurredand the reloading modulus will be high.

A characteristic feature of specimens which haveswelled is that the compression modulus at reloadingup to the effective stress b·σć can be approximatedto a constant. The compression when this effectivestress has been reached will be the same as theprevious maximum compression. b is the same loadfactor which also signifies when the specimen starts toswell.

••••• The recompression modulus Mrl within the stressinterval σú to b·σć can be written

where σú is the effective vertical stress to which the

Swelling in practical cases ofunloading in the fieldThe method of calculating swelling described aboveis applicable to the sequence of events in oedometertests with a specific routine for loading and unloading.The deformations in a practical case in the fielddepend among other things on how long the soil hasbeen subjected to various loads and the size of the timedependent settlements that has developed before theunloading started, the unloading sequence, how muchtime dependent swelling has occurred and access tofree water.

Calculation of these deformations requiresknowledge of how the secondary deformation varieswith both stress and strain in the soil. Preliminarily,the coefficient of secondary consolidation αs can beassumed to decrease linearly with decreasing stresswithin the interval σć to b·σć according to

Figure 6. Swelling parameters as a function ofplasticity index [7].

claycoarser soil

claycoarser soil

0 50 100Plasticity index %

0 50 100Plasticity index %

b

1.0

0.5

0

aS%

1.5

1.0

0.5

0


specimen has been unloaded and as and b are theswelling index and load factor respectively. Theapplication of this formula is also limited to whathappens in incrementally loaded oedometer testsperformed according to the standard procedure.

More generally, the equation can be written

M bSrlc u= ⋅ −σ σ' '

where S is the total swelling strain that has developedduring the unloading.

The reloading modulus in soil which has beensubjected to only a small unloading to a stress higherthan b·σć is difficult to measure because of the creepdeformations taking place simultaneously. On theassumption that the soil in principle behaves in thesame way as at larger unloading, the modulus can inthese cases be written

Ma

brlu

su c≈ ≥ ⋅

σ σ σ'' '

The recompression modulus which is calculatedwithout regard to secondary swelling, apart fromwhat occurs during 24 hours in the oedometer tests,becomes a function of overconsolidation ratio, swellingindex and load factor. Recompression modulicalculated by using typical values for a high-plasticclay are shown in Fig. 7.

As is evident from the figure, the frequently usedempirical values for the recompression modulus of50·σ'c (or 250·τfu) are only coarse approximationsover a wide span.

The time effects during reloading vary. The sec-ondary swelling does not stop altogether as soon as asmall increase in load is applied, but continues withina certain stress interval at a reduced rate. This may tosome degree affect the net result of a small increase inload in such a way that no compression, or even aminor swelling, will be the final result.

At further reloading, there will not be any significantcreep effects until the effective vertical stress reachesb·σć. At this stress level and the related compression,the coefficient of secondary compression starts toincrease rapidly, which is in concordance with thesequence of events at first loading in the oedometer,until a maximum value is reached which is equal to thevalue obtained at first loading at the correspondingcompression.

In the EMBANKCO programme the compressionmodulus M0 for loading up to the apparentpreconsolidation pressure is given as input.

In soft, normally consolidated clay, where theinfluence of this modulus on the total compressionis marginal, the modulus is often estimated frommore approximate empirical correlations of thetype mentioned above

M0 ≈ 150 · τfu for organic soil≈ 250 · τfu for high-plastic clay≈ 500 · τfu for low-plastic clay≈ 1000 · τfu for very silty clay/clayey silt

In cases where this initial modulus has a largerinfluence on the results of the calculations, morerelevant moduli can be estimated from the effectivestress in situ, the apparent preconsolidationpressure and the relations presented above.

In cases where the calculations wholly or largelyconcern compressions at stresses below theapparent preconsolidation pressure, the modulusM0 should be determined by oedometer tests withunloading from σć to σ´0 and reloading accordingto the standard procedure.

General model for moduli and the timedependence of the compressibilityA general model for variation of modulus and coeffi-cient of secondary consolidation during the loading,unloading and reloading sequences is outlined inFig. 8 and Table 2.

Figure 7. Calculated recompression modulusin high-plastic clay as a function ofthe overconsolidation ratio [7].


Figure 8 and Table 2. Schematic variation of compressibility (modulus) and time dependence(coefficient of secondary consolidation) at loading, unloading and reloading [7].

The model may at first sight appear very compli-cated. However, it is only a summary of the empiricalobservations of the behaviour of soil at loading in theoedometer. For determination of the various parame-ters in the model, it is normally sufficient for oedom-eter tests to be performed and existing empiricalrelations utilized. The exception is cases where thesecondary swelling has to be considered, because noempirical experience of this property is available.• The critical deformation εCR1, where the creeprate attains its maximum value, is calculated from

ε σ σCR

cM11 0

0= −' '

where σć1 is the natural apparent preconsolidationpressure in situ. σć2 is the new apparent preconsoli-dation which is created if the compression εCR1 isexceeded. σć2 is the effective vertical stress on theoedometer curve for the first loading that correspondsto the largest compression that has occurred. σć2thus increases with the deformations that occur atsecondary consolidation and is a so-called “quasi-


preconsolidation pressure” which is related to maxi-mum compression rather than maximum effectivevertical stress.

At unloading and renewed loading, the apparentpreconsolidation pressure increases as soon as thetotal compression because of the new loading exceedsthe swelling that occurred as a result of the unloading.The apparent preconsolidation can in this way increaseduring cyclic loading and as a result of time effects,even if the previous maximum effective vertical stressis not exceeded.

The deformation εCR2, where the coefficient ofsecondary consolidation after unloading and renewedloading returns to the maximum values at the particulardeformation can be calculated from

ε ε σ σ σσCR b c rl u ccb M when b2 2 22

1= + − < ⋅⋅ ' ' ( ) / ' '

and

ε ε σ σ σ σ σσCR c u s u u cua when b2 2 2= + − ⋅ ≥ ⋅' ( ' ' ) / ' ' '

All secondary compressions that occur at a higherrate of strain than αs·5·10-6 1/s are incorporated in thecompressions calculated by using the different moduliexcept for Ms in the stress interval ( σć2 - b·σć2 ) andMrl in the first reloading stress interval where secondaryswelling may occur.

For slower processes, the effects of secondarydeformations must be taken into account. In thosestress intervals where the deformations from moduliand the secondary deformations occur in oppositedirections, the deformations from moduli can beregarded as immediate apart from the hydrodynamicdelay. The time dependent process then continues asbefore the stress change but at a reduced rate.

Simplified model for moduli and the timedependence of the compressibilityIn most cases of embankments on clay, the loadingentails a large increase in vertical stress. A limitedreduction in load can then be obtained during thecourse of consolidation because some parts of theembankment or the upper soil layers are depressedand become submerged below the ground water table.In some cases, a temporary surcharge is also used inorder to speed up the settlement process and to enablea subsequent termination of in the ongoing settlementprocess by a sufficiently large load reduction. Usually,no significant swelling is expected, and particularlynot any secondary swelling.

In calculation of settlements of embankments onsoft, normally consolidated soils, the values of theparameters M0, Ms and Mrl are normally also oflimited importance. What is most important to considerin the soil model for this type of soil and calculationis

• At unloading, an “elastic” swelling occurs at ahigh swelling modulus.

• The modulus at loading and reloading is very highat effective vertical stresses below the apparentpreconsolidation pressure.

• When the effective vertical stress exceeds 0.8·σ'cand the rate of strain is lower than αs·5·10-6 1/s,significant secondary compression will occur.

• The coefficient of secondary compression willincrease to a maximum occurring at a compressioncorresponding to the compression at the prevailingapparent preconsolidation pressure.

• Thereafter, the rate of secondary consolidationdecreases with further compression.

• The coefficient of secondary consolidation rapidlydecreases if the effective vertical stress decreasesand stops altogether at an effective stress level of0.8·σ'c. (This must be considered).

In this model, no parameters apart from thosedetermined in ordinary oedometer tests are required.Normally, it is sufficient to perform CRS tests be-cause the time dependence (coefficient of secondaryconsolidation) and the moduli M0, Ms and Mrlcan inmost cases be estimated with sufficient accuracy fromempirical correlations.

The EMBANKCO programme, version 1, operates withthis simplified model.

Modulus of elasticityWhen a load of limited extension is applied to theground, horizontal deformations and associatedsettlements occur. These horizontal deformations andrelated settlements are calculated by using the theoryof elasticity, an estimated modulus of elasticity and anassumption of ν = 0.5. This calculation is considera-bly simplified because ν = 0.5 applies to fully saturat-


ed and completely undrained conditions, which inoverconsolidated soils is not relevant even during thetime for load application. Furthermore, the horizontaldeformations are assumed to be immediate and occurdirectly when the load is applied, whereas in realitythey continue during a large part of the consolidationprocess, even if they relatively rapidly decrease insize and importance with time. The modulus of elas-ticity E is normally estimated from empirical relationsbased on the undrained shear strength of the soil.Different values of E have been proposed rangingfrom E ≈ 80·τfu for organic soils to E ≈ 2000·τfu forlow-plastic clay.

However, the properties of soil materials are notlinear-elastic but the stress-deformation curves atshear exhibit more or less hyperbolic shapes. Thisentails that the higher the degree of the shear strengththat is mobilized, the lower the modulus of elasticitybecomes. According to laboratory tests, the modulusof elasticity can be expressed as

EF

Ifu

P≈

⋅ ⋅τ 215 ln

where τfu= undrained shear strength of the soilaccording to corrected vane shear testsand direct simple shear tests

F = calculated factor of safety againstfailure at undrained shear

IP = plasticity index in the soil

This formula takes account of the non-linearity ofthe elastic properties and the type of soil. In principle,it is in agreement with the different proposals thathave been made based on experience from earlierfield tests and also from recent results obtained fromthe Institute’s test embankments.

The deformations calculated in this way may beassumed to comprise both the initial horizontaldeformations and those that will develop later withtime.

As a rule, the settlements because of horizontaldeformations are small at normal safety against shearfailure. However, they increase in high plastic clayand particularly in organic clays, and they increasestrongly in all types of soil when the safety againstfailure is reduced.

PermeabilityThe permeability of a soil is a function of its void ratioand thereby also of its relative compression. It hasbeen shown that within the range of compressionwhich is of practical interest, the permeability can bedescribed with good accuracy by

log logk ki kε β ε= − ⋅

where kε = permeability at compressionki = initial permeabilityβk = -∆logk/∆ε

In homogeneous soft clays, there is normally nosignificant difference in horizontal and vertical per-meability. However, in many cases the clay containsvarious layers and variations in vertical permeability,which entails different conditions for vertical andhorizontal water flow. In soils with pronounced struc-tural anisotropy, i.e. where the uneven particles aremainly oriented in the same direction, there is adifference in permeability with direction also in thesmall scale. Clays which have been subjected to veryhigh vertical stresses often have a pronounced struc-tural anisotropy.

This is also valid for peat soils with low degrees ofhumification, where the horizontal permeability isoften considerably higher than the vertical. Thedifference decreases with increasing degree of humi-fication. A higher horizontal permeability has beenobserved also in gyttja with a clear preferred horizon-tal orientation of the organic particles.

Even very homogeneous clays have a naturalvariation in water content and void ratio and therebyalso in permeability. Considering the small specimensthat are tested in the oedometer tests, a variation inmeasured permeability of at least ±20 % must beexpected. This entails that either a large number oflaboratory tests or field tests involving a larger volumeof soil ought to be performed. In a homogeneous clayprofile, it may be assumed that a sufficient number ofoedometer tests at different levels will yield a goodpicture of the permeability and that the effect of thespread in the results will be evened out.

In layered soils, and particularly when the hori-zontal permeability is of interest, field tests ought tobe performed.


Pore pressure generation at loadingA number of methods have been proposed for calcu-lation of the development of excess pore pressures ina soil mass when the total stresses are changed underundrained conditions. Earlier methods were based ondifferent combinations of responses to changes inmean normal stress and in shear stress.

A more rational approach has become possible bytaking critical stresses into consideration. It has beenshown clearly that a natural clay has a continuouscombination of compressive and shear stresses creatinga so-called yield surface, at which the behaviour of theclay changes from being essentially elastic to becomeelasto-plastic with large plastic deformations, Fig. 9.

The shape and size of the yield surface can beestimated from the apparent preconsolidation pressureσć, the coefficient of earth pressure in normallyconsolidated soil Konc and the effective shear strengthparameters c´ and φ´.

In undrained conditions, the initial development ofpore pressure in principle is such that the meaneffective normal stress p´ remains constant

p´= (σ´1 + σ´2 + σ´3) / 3

When the increasing stresses reach a point on theyield surface, the development of pore pressurechanges and in principle becomes such that the yieldsurface is not passed but the stress path follows theyield surface until undrained shear failure occurs,Fig. 10.

For a point in the soil mass below an embankment,this entails that the increase in pore pressure will beless than the increase in applied vertical stress until theeffective vertical stress reaches the apparent precon-solidation pressure. Thereafter, the further increase inpore pressure will be equal to the further increase invertical stress (Curve A in Fig. 10). If the soil has anoverconsolidation ratio larger than about 2, the stresspath up to failure may be such that critical shearstresses are reached before the effective vertical stresshas reached the apparent preconsolidation pressure.In this case, the development of pore pressure changesand may become negative when the effective shearstrength parameters are mobilized, (Curve B inFig. 10).

Fig. 9. Schematic yield surface for a soft clay when the principal stresses arevertical and horizontal respectively [7].


5.3 FIELD TESTSThe development of pore pressures and deformationsunder a large number of embankments has beenstudied.

Pore pressure generationIn those cases where the soil has been slightlyoverconsolidated, it has been observed that the porepressure generation has been lower than that calculatedon the assumption of fully undrained conditions untilthe apparent preconsolidation is reached. For stresseswithin the elastic stress range where the compressionmodulus is high, a certain amount of consolidationand pore pressure dissipation can thus be assumed totake place within the normal time for load applicationat construction of an embankment.

For clays with overconsolidation ratios less thanabout 2.5, there is a radical change in the developmentof pore pressures when the effective vertical stressreaches the apparent preconsolidation pressure. Forfurther stress changes, the increase in pore pressuredirectly corresponds to the increase in vertical stressand the effective vertical stress is thereby preventedfrom exceeding the apparent preconsolidation pres-sure, Fig. 11.

Fig. 10. Typical stress paths in soft clay in triaxial tests performed withnormal rates of deformation [7].

Fig. 11. Typical pore pressure developmentat construction of an embankmentin the field [7].

The difference in maximum overconsolidationratio for this type of pore pressure development fromabout 2 in the fully undrained laboratory tests to about2.5 in the field tests depends on the partial drainageoccurring in the field.


Apparent preconsolidation pressureThe observed pore pressure development in the field,as well as observed settlements for approach embank-ments with a very gradual increase of the load, hasbeen used to calibrate the apparent preconsolidationpressures evaluated from the oedometer tests.

In this way, it has been possible to establish thatoedometer tests performed and evaluated accordingto the standard procedures yield apparent preconsol-idation pressures that correspond very well to theeffective vertical stresses in the field where largechanges occur both regarding pore pressure genera-tion and settlements.

From measurements of the horizontal movementsbelow the toes of the embankment slopes, it has alsobeen possible to establish that horizontal movementscorresponding to the vertical settlements will notoccur until the effective vertical stresses reach theapparent preconsolidation pressures. Only then will itbe relevant to assume fully undrained conditions andν = 0.5.

DeformationsLong-term observations of settlements for stresslevels below the apparent preconsolidation pressurehave only been performed in one case, but also thesemeasurements indicate that the secondary compres-sions start to become significant at a stress levelof about 0.8·σ'c and then increase with increasingstresses, Fig. 12.

Long-term field observations of settlementsdeveloping at loading to stresses above the apparentpreconsolidation pressure show that the settlementsbecome considerably larger and develop much morerapidly than those calculated without consideration totime effects.

The horizontal movements have proved to continuefor a long time after load application but decrease inrelation to the settlement and can from a practicalpoint of view be assumed to stop altogether after acertain period of time.

Fig. 12. 10-year settlements under buildings in Drammen as a function of thestress level in the upper high-plastic clay layer [7].


Excess pore pressure dissipationThe dissipation of excess pore pressures has beenfound to be a much slower process than that calculatedwithout regard to time effects on the properties.Considerable excess pore pressures remain when the“final” settlement calculated without regard to thetime effects has been reached and the settlements thencontinue without any tendency to slow down morethan the continuous decrease in rate because thesettlement is more or less linear against the logarithmof time.

Development of apparent preconsolidationpressures and undrained shear strengthsInvestigations of samples taken under the embank-ments show that quasi-preconsolidation pressures de-velop which are considerably higher than the largestvertical stresses that have occurred in the soil. Alsoshear strength tests performed under the embank-ments in the field show that undrained shear strengthscorresponding to these quasi-preconsolidation pres-sures develop.

ConclusionIn order to predict the observed development in thefield, a calculation model is required which takes intoaccount the time dependence of the soil compressi-bility.

Natural apparent overconsolidationAnother observation which has been made in the fieldis that natural soil deposits as a rule exhibit a certainoverconsolidation which has been created during thetime that has elapsed since the deposition by secondaryconsolidation for the soil´s own weight and climaticfactors. This apparent overconsolidation can varyfrom only a few kPa in the middle of thick deposits ofsoft “normally consolidated” clay which have neverbeen subjected to any extra overload and in whichvery slow consolidation processes continue, amongother things because of the ongoing land heave.Closer to draining layers, the overconsolidation ratioOCR (=σć /σ´0 ) increases to become normally at least1.25 at the drainage borders. For soils which havebeen subjected to real overloads and then beenreloaded, higher overconsolidation ratios normallyapply.

This overconsolidation, even when small, must beconsidered in calculations with time dependentparameters. Unless this is done, the calculated

secondary consolidation will begin immediately at amaximum rate at the start of the calculations even fora marginal increase in the load.

5.4 INFLUENCE OF TIMEDEPENDENCE OF THECOMPRESSIBILITY ON THESIZE OF THE SETTLEMENT

Many attempts have been made to create rules ofthumb for estimation of the additional settlementsbecause of creep effects. However, there is no simpleand general way of estimating the size of thesettlements at different times with respect to the timedependence of the compressibility and such a waycannot be found. A soil profile cannot be simplified toa few homogeneous layers with constant propertiesfor calculation of settlements. Even less can such asimplification be made in a comparison betweensettlements calculated with and without considerationto the time dependence of the parameters. This ispartly due to the fact that the relations between moduliand time dependence are not constant but depend onstress level and stress history and partly to the fact thatthe entire consolidation process is regulated bypermeability, drainage paths and the interactionbetween the different soil layers in the profile. Theinfluence of the time dependence of the compressibilityon the settlements and their course with time thereforebecomes a unique function for each specific loadingcase and soil profile.

Larger settlementsAttempts to obtain rough estimates of the size of thesettlements have been made [32]. As expected, theresults of these attempts show that the calculatedsettlements become larger throughout theconsolidation process when account is taken of thetime dependence of the compressibility and that therelative difference increases with time. It is commonfor the settlement calculated with time dependentparameters to be more than twice the settlementcalculated otherwise in clays with relatively highwater contents. The increase in the relative differencein calculated settlements with time occurs faster whenthe permeability of the soil is higher. Correspondingeffects can be observed in settlement observations inthe field.

In general, the relative difference in the calculatedsettlements increases when both the moduli (M) andthe time effects (αs) increase. A higher modulus gives


smaller settlements calculated without regard to thetime dependence and an increase in time effects giveslarger calculated additional settlements because ofthese effects.

Complication of the general picture byapparent overconsolidationIn normally consolidated soil, the difference betweenthe two types of calculation generally decreases withincreasing application of load. However, most soilprofiles are more or less overconsolidated, particularlyin layers close to the ground surface or drainageboundaries. This considerably complicates the picture.When the soil is sufficiently overconsolidated, thereis no significant difference in the calculated settlementswhether the time effects are observed or not. When thesoil is slightly overconsolidated, the difference incalculated settlement in a specific layer reaches amaximum when the sum of the initial vertical stressand the additional stress coincides with the apparentpreconsolidation pressure. For the soil profile taken asa whole, where both overconsolidation ratios andadditional stresses vary, the relative difference reachesa maximum at an additional load which can vary withboth the internal relations between the properties inthe different layers and the considered period of time.Also factors such as the geometry of the load, thethickness of the soil layers and the stress distributionwith depth, as well as the changes in load that occurduring the consolidation process, play significantroles for the calculation results.

A method for estimation of the influence of thetime dependence of the compressibility which is bothsimple and useful in practice cannot thus be created.The demand for such a method has also in practicebeen eliminated as a result of the development incalculation aids. Calculations which only a few yearsago demanded access to a large computer can today beperformed with ordinary personal computers.

5.5 EXAMPLES OF MEASURED ANDCALCULATED SETTLEMENTS

Investigations and prediction of settlements are per-formed by the Institute both for research purposes andin consulting projects. In many cases, the settlementsin the field are monitored for several years afterconstruction, enabling a comparison between predict-ed and actual settlements, see for example [7], [29],[30].

In this chapter, three examples of full scale casesin the field where the settlements have been monitoredare presented; one test fill which was constructed forresearch purposes and where the investigations arevery comprehensive, and two road embankmentswith a more normal extent of the investigations.

CASE 1:Test fill at Lilla MellösaThis test fill with a base of 30 x 30 metres wasconstructed on top of 14 m of soft clay in 1947. Thefill consists of 2.5 m of gravel with an original slopeinclination of 1:1.5. The load increase under the crestwas about 41 kPa. The settlements have then beenfollowed for almost 50 years and the observations arecontinuing. Detailed investigations concerning thedistribution of settlements with depth, remainingexcess pore pressures and changes in the soil propertieshave been carried out at different times.

Supplementary investigations concerning the soilproperties outside the loaded area have also beenperformed when new and better equipment andmethods have been developed.

Soil profileThe soil profile in the natural ground at Lilla Mellösais shown in Fig. 13.

On top of the profile was a 0.3 m thick layer of topsoil which was scraped off before the fill was applied.The dry crust is unusually thin and consists of organicsoil. The fissured and weathered part is only half ametre thick and overlies soft clay. The clay has anorganic content of about 5 % immediately below thedry crust. This content decreases with depth and is lessthan 2 % at depths greater than 6 - 7 metres. The watercontent is about equal to the liquid limit and decreasesfrom 130 % in the upper organic clay to 70 % in thebottom layers. Below 10 depth, the clay is varved. Thevarves are at first diffuse, but become more distinctwith depth. At 14 m depth there is a thin layer of sandon top of bedrock.


Fig

. 13.

So

il pr

ofil

e at

Lill

a M

ellö

sa [

7].


The undrained shear strength in the clay has aminimum of 8 kPa at 3 m depth and then increaseswith depth. The overconsolidation ratio in the softclay is fairly constant at about 1.2, which entails anoverconsolidation from only about 3 kPa at the top toabout 12 kPa in the lower part of the profile. The porewater pressure is hydrostatic from a ground waterlevel 0.8 m below the ground surface.

Measured and calculated settlementsThe settlement during the time for load application,which lasted for 25 days, amounted to 0.07 m. The

corresponding calculated settlement because of elasticdeformations was 0.1 m.

Fig. 14 shows the measured and calculatedsettlements together with measured distributions ofsettlements and excess pore pressures with depth. Theconsolidation settlements have been calculated withand without consideration to the time dependence ofthe compressibility. The parameters evaluated fromoedometer tests and employed in the calculations areshown in Fig. 15.

The “final settlement”, which is calculated withoutregard to the time effects, is just below 1.4 m. This

Fig. 14. Measured and calculated settlements at Lilla Mellösa [7].a) total settlementb) distribution of settlements and excess pore pressures in the soil profileat various times after load application.


CASE 2:Embankment on Road E4 betweenRåneå and StrömsundThe construction of Road E4 between Råneå andStrömsund was started in 1982. On the part of the roadin question, the road embankment is 9.5 m wide andthe 1.1 m high fill consists mainly of slag stone froman ironworks. The settlements are monitored inhorizontal flexible tubes under the embankment. Whenthe settlements were found to become larger thanexpected, the fill was adjusted within a year by anadditional 0.45 m of fill. The soil profile, the resultsof the calculations and the measured settlements forsection 4/720 - 5/180 are presented.

Soil profileThe soft soil consists of an approximately 9 m thicklayer of slightly organic clay coloured by sulphideoverlying coarser soil. The pore water pressure can beassumed as hydrostatic for a ground water level 0.75m below the ground surface and the clay is almostnormally consolidated from 4 m depth and below. Theundrained shear strength varies between 6 and 14 kPa.The soil stratigraphy and some of the calculationparameters are shown in Fig. 16.

settlement was reached after 19 years (1966). At thistime, the remaining excess pore pressures amountedto about 30 kPa and the settlements continued. In1979, 32 years after the load application, the settlementsamounted to 1.65 m and the remaining excess porepressures were over 20 kPa. The settlements in 1992amounted to 1.8 m and are still increasing.

From the results shown in Fig. 14, it is evident thatthe time effects on the compressibility have to betaken into consideration if a good prediction of thesize of the settlements and their course with time is tobe made. Otherwise, the real settlements in this casebecame twice as large as the calculated settlementsafter 10 years and onwards and with time the calculated“final settlements” were exceeded by a wide margin.The measured pore pressures show that none of thiscan be related to a more rapid excess pore pressuredissipation than calculated and it has been checkedthat it is not related to horizontal movements.

Fig. 15. Compressibility and permeability parameters at Lilla Mellösaevaluated from oedometer tests [7].


Fig. 16. Summary of the geotechnical conditions in Section 5/080on Road E4, part Råneå-Strömsund [29].

Measured and calculated settlementsFig. 17 shows the average of the measured settlementsin the centre line of the road together with calculatedsettlements with and without consideration to timeeffects on the compressibility. As is evident from thefigure, the actual settlement is much larger and occursmuch more rapidly than that calculated without regardto the time dependence of the parameters. After about

5 years, the measured settlements were more thantwice the settlements calculated in such a way, 0.75 mversus 0.33 m respectively, and the difference increaseswith time. Calculations taking the time dependence ofthe compressibility into account yield settlements andcourses with time that are in acceptable agreementwith the measurements.

Figure 17. Time-settlement curves for part 4/750-5/180 on Road E4, part Råneå-Strömsund [29].


Fig. 19. Course of settlementswith time in Section20/800 on Road E3, partV. Åby-Adolfsberg [30]

Fig. 18. Summary of thegeotechnicalconditions inSection 20/800 ofRoad E3, part V.Åby-Adolfsberg[30].

CASE 3:Embankment on Road E3between Västra Åby and AdolfsbergThe embankment is on a stretch of motorway betweenMariestad and Örebro. Road E3 has here dualembankments, each with a crest width of 12 m. Thecentral dividing strip has a width of 16 m and theheight of the embankments is 1.4 m. The section inquestion, 20/800, was constructed without any soilimprovement but is located relatively close to a sectionwhere vertical drains and surcharging have beenapplied. The sequence of load application duringconstruction is not known in detail but the firstapplication of fill started in July 1979 and the road wasopened for traffic 2 years later. The settlements arebeing followed by measurements in horizontal flexibletubes under the embankments.

Soil profileIn the particular section, a 5.5 to 7 m thick clay layerlies on top of coarser soil. A firm dry crust with a

thickness of about 1m has developed. The pore waterpressure is hydrostatic from 1 m below the groundsurface and the clay is slightly overconsolidated withapparent preconsolidation pressures about 10 kPahigher than the in situ vertical stress from 2 m depthand below. The undrained shear strength variesbetween 10 and 18 kPa. The stratigraphy and some ofthe calculation parameters are shown in Fig. 18.

Measured and calculated settlementsThe measured and calculated settlements in the centreline of the embankment are shown in Fig. 19. Thesettlements calculated on the assumption of a smoothand even load application correspond poorly to whatwas measured in the field during the time forconstruction and directly thereafter. However, thelong term observations clearly show that the timedependence of the compressibility has to be taken intoaccount if a good correlation between predicted andactual settlements is to be obtained.


CHAPTER 6.

Calculation of stress distribution at loading

A careful calculation of the distribution of additional stresses in different parts of the soil mass

below an embankment is of very great importance forpredictions of both the maximum size and the rate ofthe settlements and also for the distribution ofsettlements across the embankment.

These calculations are made on the basis of thetheory of elasticity which, in spite of the fact that a soilmass does not directly correspond to the assumptionsof an isotropic, ideal elastic and weightless material,is the most developed method available at present.

Calculation of vertical stresses under embankmentswith arbitrary cross sections is performed by integrationof the Boussinesque solution for stresses caused bystrip loads on a semi-infinite, homogeneous andisotropic mass [19], Fig. 20.

ESTIMATION OF STRESS DISTRIBUTIONBY USING CHARTSIn calculations by hand, it is possible to use one of thecharts which have been constructed for this purpose,e.g. the Osterberg chart [20], Figs. 21 and 22.

The Osterberg chart is used in such a way that theinfluences of several loads with the given shape areconsidered and the influence factors are summated.

Fig. 21. The Osterberg influence chart forestimation of stresses underembankments. The chart isconstructed by using the solution forthe influence of a triangular load ofinfinite length [20].

Fig. 20. Designations in the Boussinesquesolution for stresses caused by striploads on a semi-infinitehomogeneous isotropic mass.


Fig. 22. Equations used in the construction of the Osterberg chart [20].

Example C: Calculate the additional vertical stress at apoint under the centre of the slope shown in Fig. C. Thestress caused by the triangle abc is equal to the stresscaused by the imaginary triangle cde. Hence, the additionalstress can be calculated from the influence factor from aload with a/z = 1 and b/z = 2.5. The additional verticalstress is sz = 0.492·q.

Example B: Calculate the additional vertical stress at thepoint outside the loaded area shown in Fig. B. Firstdetermine the influence factor for the embankment togetherwith the dashed imaginary part (a/z = 1, b/z = 4, I = 0.499)and then deduct the influence value from the dashedimaginary part (a/z = 1, b/z = 1, I = 0.455). The additionalvertical stress is sz = 0.044·q.

EXAMPLESof calculations of stress distribution

Example A: Calculate the additional vertical stress at thepoint under an embankment shown in Fig. A. At the lefthand side, a/z = 1, b/z = 0.5 and the corresponding I = 0.397is obtained from the chart. For the right hand side,I becomes 0.478 and the total influence factor is 0.397 +0.478 = 0.875. The additional vertical stress is sz = 0.875·q.


Example F: The load is divided into two parts and animaginary part is added. I = 0.08·1/4 + 0.474 - 0.203·3/4.sz = 0.302·q.

Example D: The chart can also be used for evenlydistributed loads. The additional stress at the point shownin Fig. D is calculated using the limit value for a/z = 0.01. Theerror because the real value of a/z is 0 becomes a 4 % toohigh influence factor when b/z = 0.1, 2 % too high whenb/z = 0.3 and 1 % when b/z = 0.5. For higher values ofb/z, the error becomes negligible. The influence factors inthe example become b/z = 0.5, I = 0.278·0.99 = 0.275 andb/z = 1.0, I = 0.410·1.00 respectively. The additionalvertical stress becomes sz = 0.685·q.

Example E: b/z = 0, a/z = 1, I1 = I2 = 0.25. sz = 0.5·q.

Influence of dry crustThe calculations according to the theory of elasticityoften have to be modified with consideration to thefact that the soil in the profile often cannot be simplifiedto a semi-infinite medium with ideal elasticity. Whensoft clays are covered by a firm dry crust, this affectsthe stress distribution. The type and extent of thiseffect depend on the character of the crust. In astrongly fissured crust, no spreading of the loadoccurs and in calculation of the stress distribution atgreater depths, the load can be assumed to be appliedat the level where the wide open cracks disappear.

The depth to this level is normally very limited.For estimation of the influence of a more homogeneousdry crust on soft soil, an analogy can be made in whichthe crust is assumed to act as a beam with a certainstiffness against deflection. The dry crust can then bereplaced by a layer with the same modulus of elasticityas the underlying soil, but with the fictitious height he

he = 0.9h(E1 / E2)1/3 [21]

where 0.9 = empirical correction factorh = actual thickness of dry crustE1 = modulus of elasticity in dry crustE2 = modulus of elasticity in underlying

soil

The calculation of stress distribution is thenperformed as for an ideally elastic soil but with thedepth in the dry crust corrected according to z = z1·he/hand in the underlying soil corrected according toz = z1 + he - h.

The soil can be divided into several layers accordingto the same principle, provided that the stiffnessdecreases with depth.

Limited depth to firm bottomWhen the depth to firm bottom is limited, also thiscircumstance affects the spreading of the load effectsand the stress distribution. When there is a firmbottom at a limited depth (hf) below the compressiblesoil, the additional stresses can be calculated by acorrection of the depth in the calculations according tothe theory of elasticity for a semi-infinite medium.The influence of the stiff base extends upward toabout half the depth, (0.5·hf). From this level, theadditional stress is calculated both for depth z and forthe corrected depth 0.75·z. The additional stress atdepth z in the lower half of the compressible layer is


then calculated by interpolation between these valuesaccording to

σ σ σ σ= + −−

z z zf

f

z hh

( )...0 750 50 5

Also in cases where the stiffness of the soil increasesrapidly with depth, similar but more limited stressconcentrations may occur. The additional stresses canthen be calculated in accordance with the type ofgeneralized Boussinesque solution presented byFröhlich [22] among others.

Simplified methodsThe type of simplified approximate methods that havebeen presented, such as the 2:1 method, cannot beused to calculate the stress distribution across thesection and should also be avoided in calculations ofsettlements on the whole. Because the original in situvertical stress, the overconsolidation ratio, the apparentpreconsolidation pressure and the compressibility allvary with depth, a relatively small change in calculatedadditional stress can result in large differences incalculated settlement.

Accurate determination of the existing in situvertical stresses and the pore pressures is as importantas correct calculation of the additional stresses.

Submersion below the ground water levelWhen the settlements cause a depression of the uppersoil layers and/or parts of the embankment below ahigh free ground water level, the load intensity q isreduced by

∆q s m w= ⋅ − +( )γ γ γ

where q = load intensity, kPas = total settlement, mγ = unit weight, kN/m3

γm = unit weight of water saturatedmaterial, kN/m3

γw = unit weight of water, kN/m3

The EMBANKCO programme uses the theory ofelasticity and the Boussinesque solution for stressescaused by strip loads on a semi-infinitehomogeneous isotropic mass. Corrections areapplied for limited depth to firm bottom and forsubmersion below the ground water table.


CHAPTER 7.

Calculation of initial deformations

At loading of a limited area of the ground,shear deformations will occur. The

settlements in an embankment resulting fromso-called elastic shear deformations, wherehorizontal movements occur under the toes ofthe slopes and corresponding vertical move-ments occur in the embankment, are calculat-ed by using the theory of elasticity. It isnormally assumed that these deformationsoccur in a fully undrained mode, ν = 0.5, andin spite of the fact that these deformations arepartly time-dependent, they are calculated asif they occurred at the same rate as the load isapplied.

The elastic settlements are usually smallwhen normal safety against shear failure isapplied but may be considerable at low factorsof safety and in organic and high-plastic soil.In calculation of the initial settlements, theloaded area is divided into rectangular parts,each with one corner at the point for which thesettlement is to be calculated [23], Fig. 23.

On the assumption that ν = 0.5, thesettlement at the corner point is then calculatedfor the four rectangles as

S q bE

Fc = ⋅ ⋅ ⋅0 75 1.

The factor F1 for l/b = ∞ is obtained from Fig. 24.The calculated settlements for the common corner

in the four rectangles are then summed up in order toobtain the settlement at this particular point.

The division into rectangles can be further elabo-rated in cases where the geometry and the load inten-sity vary.

The curves shown in Fig. 24 are only valid for longembankments and loads with similar geometry. Inprinciple, the method can be used for all types of

Fig. 23. Division of an embankment into rectangularload areas.

geometry and ν-values, but with different functionsfor the influence factors. These can be studied in, forexample, SGI Meddelande No. 10 from 1972 and thehandbook BYGG from the same year [24].

It has to be taken into consideration that the modulusof elasticity varies between different layers. At alimited depth (d/b ≤ 3), the influence factor increasesapproximately linearly with depth and a characteristicmodulus of elasticity can then be chosen as a harmonicmean value over the entire depth.


Fig. 24. Chart for estimation of factor F1 when l/b = ∞∞∞∞∞.

dE

hE

hE

hE

hE

n

n= + + + +1

1

2

2

3

3.........

At greater relative depths and in more carefulcalculations, the settlement is calculated by asummating the settlement in the various layers as

S q b F FE

FEc

i i

ii

n i

nn= ⋅ ⋅ − ++

=

−∑0 75 1

1

1. ( ( ) )

where Ei = modulus of elasticity in layer iFi = influence factor at depth di, which is

equal to the distance from the groundsurface to the upper edge of layer i.

Calculation of initial deformations because ofhorizontal movements is normally not included incalculation programmes for one-dimensionalconsolidation; instead, these settlements must becalculated separately. This is the case also in theEMBANKCO programme. In more careful predictionsand where the size of the initial settlement is ofimportance, the initial deformations are calculatedbeforehand. The subsequent calculation of theconsolidation process is then performed with a loadand a geometry which have been adjusted withconsideration to the initial settlements.


CHAPTER 8.

Calculation of the course of settlementsin one-dimensional consoladition

8.1 PRINCIPLE OF CALCULATION OFTHE COURSE OF THECONSOLIDATION PROCESS

The calculation of the consolidation process forembankments on soft soils is based on the fact that thepore water pressure increases because of the appliedload and the resulting pressure gradient gives rise toa flow of water out of the soil. This flow of water isnormally assumed to take place only in the verticaldirection. When draining layers are embedded in thesoil profile, the water flow is assumed to be verticalbetween these layers.

In cases where the loaded area is small in relationto the thickness of the compressible layers, theinfluence of the horizontal water flow cannot beneglected. This is particularly the case for circular andsquare footings. In the case of embankments, thehorizontal water flow apart from the flow in thedraining layers can normally be neglected. However,there is always a certain influence from the horizontalwater flow on the rate of the settlements in the outerparts of the embankment. The settlements in theseparts therefore become somewhat larger and occursomewhat more rapidly than those calculated on theassumption of one-dimensional consolidation.

Calculation for a single layer withconstant parametersIn calculation of the consolidation process withoutregard to time effects on the compressibility thefollowing equation is used [1] :

∂∂

∂∂

ut

M vz

= −

or

∂∂ ρ

∂∂

∂∂

ut

Mg z

k uzw

= −⋅

⋅ ( )

where u = excess pore pressurev = velocity of pore water flowt = timek = permeabilityM = oedometer modulusρw= density of pore waterz = distance from the draining surface to

the particular element (Fig. 25).

The calculation result in terms of degree ofdissipation of the excess pore pressure after a certaintime (degree of consolidation) becomes a function ofthe initial distribution of excess pore pressure withdepth, the drainage paths and the compressibility andpermeability of the soil. The time factor Tv is calculatedfrom

T k Mg

tdv

w= ⋅

⋅⋅

ρ 2

see Fig. 26.

Calculation for multi-layer systemsIn most cases, the soil in a profile cannot be simplifiedto a single layer with constant modulus and permea-bility, but has to be divided into several layers withdifferent properties. It is then no longer possible tosolve the equation analytically and a numerical proce-dure has to be applied. A method for this purpose, bywhich the consolidation process can be determinedthrough a graphical procedure, was presented byHelenelund in 1951, [27].

In this method, the soil profile is divided into anumber of layers in such a way that the product

k Mg w

⋅⋅ ρ


can be assumed to be constant. By choosing aconstant value for ∆Tv and calculating as if alllayers have a thickness of ∆z, it is possible tocalculate the remaining excess pore pressure aftera certain time starting from the excess pore pressureat time t = 0. The pore pressure at the centre of thelayer after time t + ∆t is obtained as the arithmeticmean of the pore pressures at the interfaces towardsneighbouring layers. Because of the constant valueof Tv, the thickness of the layers varies withconsideration to oedometer modulus andpermeability in such a way that

∆z F k Mn n n= ⋅( ) .0 5

where ∆zn= thickness of the layerF = a factor which is common for all

layerskn = permeability in the layerMn= oedometer modulus in the layer

When the permeability in the different layersvaries, the pore pressure gradients at the interfaceshave to be modified. The pore water flow is equalon both sides of the interface and according toDarcy´s law

k uz

k uzn n n n( ) ( )∂

∂∂∂

= + +1 1

A graphical construction of this kind is shown inFig. 27.

In the figure, the excess pore pressure at timet = 0 has been drawn as a function of depth z.Layers in which the product of k and M can beconsidered constant have been selected and thethicknesses of the layers (∆z) have been selectedwith consideration to the value of the square root of(k·M) in relation to the corresponding value for theother layers.

Auxiliary construction lines have been drawnat the centres of the layers and at distances of(kn+1 / kn) · (zn / 2) above the interfaces.

The excess pore pressures at the interfaces arecalculated for the time step ∆t and the average ofthe pressures at the interfaces for each layer isplotted at the centre of the layer. The excess porepressure profile at the interfaces is constructed byusing the auxiliary construction lines, whereby

Fig. 25. Distribution of excess pore pressure in aclay layer with single drainage at the topcaused by an applied surface load with alarge extent in relation to the thicknessof the compressible layer [25].

Fig. 26. Time factor based on the pore pressureequation for one-dimensional consolida-tion according to Terzaghi [25].


applied loads or load reductions. Such chang-es in applied load bring changes in theexcess pore pressures. When the compressions occur at suchslow rates and at such stresses that creepeffects occur, also the resulting changes incompressibility have to be considered. How-ever, also time dependent creep compres-sions require that a corresponding amount ofwater flows out of the soil and thereforethese effects in the short time perspectiveinstead result in a corresponding increase inthe excess pore pressure. Even if it is possi-ble to calculate the consolidation process fora short step in time with constant parametersand boundary conditions, it therefore be-comes necessary to update the parametersand conditions with regard to what has hap-pened during the elapsed time and to refor-mat the problem before a new calculationcan be made for the next step in time.

The load from an embankment is notapplied momentarily but gradually during acertain time for construction. This can betaken into account by using very short timesteps during this phase and updating the porepressures with regard to the applied load

during each time step. A graphical construction, whichhas previously often been applied for correction of theconsolidation process calculated on the assumption ofan instantaneous load application (broken line c1), isshown in Fig. 28.

Fig. 27. The Helenelund graphical method forestimation of the consolidation process [27].

tan α = (δu/δz)n and tan β = (δu/δz)n+1. This construc-tion ensures that kn· tan α = kn+1· tan β and therebyDarcy´s law is followed.

Thereafter, the decrease in pore pressure at thecentre each layer can be measured. This correspondsto the increase in effective stress and the compressionof the layer can be calculated by the oedometermodulus M.

Calculation with considerationto varying parametersA compression entails that both the properties of thesoil and the boundary conditions change. The com-pression brings a decrease in permeability and achange in the oedometer modulus which depends onthe stress level. The thickness of the soil layer and thelength of the drainage paths decrease. In addition, theapplied load may change during the course of consol-idation. This may be the result of an indirect stressreduction because parts of the upper soil layers and /or the fill material have been submerged under a highground water level or a direct change because of

Fig. 28. Graphical construction of theconsolidation curve in cases wherethe load is applied slowly accordingto Terzaghi [26].


of the one-dimensional consolidation processin multi-layer systems were developed in 1978[28]. By using these programmes, it has becomepossible to divide the soil profile into a largenumber of layers with varying properties anddegrees of saturation. Loads can be appliedgradually in different loading steps and withvarying geometry and the consolidationprocesses can be calculated in many small stepsin time, after which the properties and theboundary conditions are continuously updated.Compared to previous calculation methods withsimplified assumptions, the results from thenew type of calculations have in all respectsproved to correspond considerably better to theobservations that have been made in full scaleapplications in the field concerning courses ofsettlements and pore pressure dissipation [7,29, 30]. The new calculation method has also

been used as a standard procedure for several years incalculations of courses of settlements for roadembankments in Sweden.

The EMBANKCO calculation programmeWith consideration to the experience gained andparticularly to the demand for a more user-friendlyprogramme that can be used in the personal computersof today, the EMBANKCO programme has been devel-oped in co-operation between the Swedish NationalRoad Administration and SGI. The programme isbased on the theories and empirical experience thathave been presented in this publication.

Conditions for the calculationsIn the calculations, the somewhat simplified soilmodel described in Section 5.2, page 23, is used. Thesimplification mainly concerns the description of thecourse of swelling at unloading.

The compressibility of the soil is described by theparameters M0, σć, ML, σ´L, and M´, as evaluatedfrom oedometer tests according to Swedish standard.For soft normally consolidated and only slightlyoverconsolidated soils, the parameter M0 may beestimated by empirical correlations. The load factor bis normally assumed to be constant = 0.8.

The compressibility of layers of coarser soil maybe described by the compression modulus which isevaluated from results from in-situ methods, primarilydilatometer tests [13]. In these layers, M0 is given asthe evaluated compression modulus and the apparent

When the soil contains significant amounts of gas,the consolidation process changes. This, however, israther unusual in Swedish clay and gyttja. When theground surface is loaded, the increasing pore pressureresults in an immediate compression of the gas bubblesaccording to Boyle´s law and simultaneously acorresponding immediate compression of the soilmass occurs. As the excess pore pressure dissipates,the gas volume then increases, which entails that theoutflow of water thereafter occurs without a fullycorresponding settlement and excess pore pressuredissipation. Furthermore, the permeability changeswith the size of the gas bubbles, but this is moredifficult to take into consideration. The correspondinggraphical construction for correction of the calculatedconsolidation process is shown in Fig. 29.

8.2 MODERN CALCULATIONMETHODS

The accuracy with which the courses of the settlementscan be calculated depends on how well the soil and theboundary conditions can be described, how well thestress distribution can be calculated and how well thechanges in properties and boundary conditions thatoccur during this course can be taken into account.

The possibility of performing detailed calculationsby manual or graphical methods is for practical reasonsvery limited. With access to modern aids in terms ofcomputers and data processing technique this limitationhas virtually ceased to exist.

Advanced computer programmes for calculation

Fig. 29. Graphical construction of the consolidationcurve when the soil contains gas accordingto Terzaghi [26]. U0 = apparentconsolidation at time t = 0 because of thecompression of the gas bubbles.


preconsolidation pressure σć is set to σć> (σ´0+∆σ).If no tests have been performed in the coarser soil, arough estimate of the modulus number m can be madefrom empirical relations. M0 is then estimated from

M m00 1100 2

100≈ ⋅ + −( ' / )σ β∆σ

where m and β are obtained from Fig. 30 [31]. σć isgiven in the same way as > (σ´0+∆σ).

The permeability of the soil is described by itsinitial permeability ki and the index for change inpermeability with compression, βk ; both parametersnormally being evaluated from oedometer tests.

The creep properties of the soil (time dependenceof the compressibility) are described by the parametersαs(max) and βαs. These parameters are normallyestimated from empirical relations based on soil typeand natural water content.

The distribution of additional stresses in the soilcaused by the applied load is calculated according totheory of elasticity and the instantaneous increase inpore pressure at load application is calculated accordingto

∆u = ∆p when σ´v < σćand ∆u = ∆σv when σ´v = σć

In analogy with the observed pore pressure devel-opment, this entails that in undrained conditions theeffective vertical stress can reach but not exceed theapparent preconsolidation pressure.

(In non-saturated soil, the initial settlement be-cause of the compression of the gas bubbles is calcu-lated and the pore water pressures are modified ac-cordingly.)*

The time dependent consolidation processis calculated in analogy with the empirical modelsfor the time dependence of the compressibility.The applied oedometer moduli include all the timeeffects occuring at compressions at rates higher thanαs·5·10-6 1/s. This reference rate is compared to thecalculated rates of compression and when the latter

*) Operations within parenthesis are not included in theEMBANKCO programme version 1. In this programme, thesoil is assumed to be fully saturated. Elastic deformationsare calculated separately when required.

Fig. 30. Estimation of parameters m andfrom soil type and porosityaccording to Janbu [31].

become lower than the reference rate, time dependentcompressions are assumed to be added.

At compression, the time dependence leads to alarger compression than that calculated from thecompression moduli alone. A condition for this extracompression to occur is that the corresponding amountof water flows out of the soil. In turn, a condition forthis to occur within the same period of time as thecompression corresponding to the moduli alone is thata higher gradient exists in the pore water. Theimmediate effect of the creep tendency (or time effects)during a short time step is therefore an increase in porepressure, whose size is determined by the potentialcreep deformation and the compression modulus,Fig. 31.


The consolidation equation then becomes

where uct is the increase in pore pressure because ofthe creep effects. (When the soil is not fully saturated,this equation for excess pore pressure dissipation isfurther modified with consideration to the volumechange of the gas bubbles at changes in the porepressure.)*

As an example, a 1 m thick sub-layer can be studied.The dissipation of excess pore pressure during atime step is 2 kPa. Assuming that the oedometermodulus M is 500 kPa, the compression of the sub-layer during the time step is 2·1000/500 = 4 mm.During this time step, there would also haveoccurred a creep deformation ∆εc of 0.003 (= 0.3%or 3 mm) without consideration to the demand fora corresponding outflow of pore water. Instead, thepore pressure during the time step will become anincrease of ∆uct = 0,003·500 =1.5 kPa because ofthis creep effect. During the particular time step,there has thus occurred a compression of the sub-layer of 4 mm although the excess pore pressurehas decreased only by 0.5 kPa.

In the next time step, the pore pressure will be 1.5kPa higher than if no creep effects had occurred inthe previous time step. The rate of water flow andthereby the rate of compression of the soil will behigher because of the larger gradient and thesettlement that developes will be correspondinglylarger. If further creep effects occur during this timestep, the excess pore pressure dissipation will becorrespondingly lower, which in turn will affect therate of settlement in the subsequent time step, andso on.

The courses of consolidation calculated with andwithout consideration to creep effects are shownschematically in Fig. 32 and the calculated stress-strain relations followed during these courses arecompared to the oedometer curve in Fig. 33.

The time dependence of the compressibility mayentail that the pore pressure during a time step tendsto increase, in spite of the fact that no extra stress isapplied. In this case, the effective vertical stressdecreases, whereby the creep process decreases andafter a moderate decrease in effective vertical stress itstops altogether. When the pore pressure again startsto decrease and the effective stresses increase, thecreep process is resumed.

For a major part of the consolidation process, thecreep deformation in the soil is thus a self-restrainedprocess which cannot develop faster than permittedby the permeability of the soil and the drainage paths.The effects of the time dependence of the compress-ibility are that the excess pore pressures decreasemore slowly with time, the rate of settlement becomeshigher and the settlements never stop completelyunless an unloading is performed. However, withtime the rate of settlement will become so low that itspractical importance diminishes.

Course of the calculationsIn practice, the calculations are performed inaccordance with the flowchart in Fig. 34. The variationsin the soil properties with depth are described togetherwith the pore pressure profile. With consideration tothe variation in properties, the soil in the profile is thenautomatically divided into sub-layers with givenproperties and with thicknesses matched to facilitatea continuous calculation of the consolidation processin the profile in its entirety.

Thereafter, the load is described in terms of loadintensities, load steps and time for load application.(The elastic deformations at application of the loadare calculated first and after a possible adjustment of


Fig. 31. Influence of the time dependence ofthe compressibility during a short timestep [7].


Fig. 32. Schematic presentation ofcalculated courses of consolidation.

Fig. 33. Schematic presentation ofcalculated stress-strain relations

load and geometry the stress distribution and theexcess pore pressures are calculated. The elasticdeformations are calculated for the load step in itsentirety and are then distributed over the time for loadapplication.)*

(When gas is present in the soil, the initial com-pression of the gas bubbles is first calculated togetherwith the corresponding initial settlement and porepressure reduction.)*

The calculations of the consolidation process arethen made for very short time steps and on theassumption that the parameters remain constant duringthe time step, i.e. according to the simple consolidationtheory

∂∂ ρ

∂∂

∂∂

ut

Mg z

k uzw

= −⋅

⋅ ( )

The equation is solved by using finite differencesand the calculations are made with consideration tothe demand for continuity in the water flow across theinterfaces between the sub-layers, i.e. that accordingto Darcy´s law

k uz

k uzn n n n( ) ( )∂

∂∂∂

= + +1 1

After the calculations for the short time step, thecalculated pore pressure dissipation is corrected forpossible effects of gas bubbles and the settlement iscalculated. The rate of compression is then calculatedand compared to the reference rate, and the porepressure is adjusted for the creep process during thetime step. The thicknesses of the layers and theproperties of the soil are modified with regard to thecalculated compression.

Stresses and pore pressures are adjusted for possiblechanges in total applied load during the time step andin case the settlements have entailed that the effectiveload has been reduced because of a high ground waterlevel. (When the soil contains gas, the calculated porepressure changes because of creep effects are adjustedaccordingly and the corresponding initial deformationsbecause of the compression of the gas bubbles arecalculated)*. Thereafter, the consolidation process inthe following short time step is calculated, and so on.



Yes

No

Yes

Description of soil profile and properties

Division into sublayersand calculation of in situ stress conditions

Description of load; load steps,geometry, load intensity and time for load application

Calculation of elastic deformations for the load stepand distributionover the time for load application

Calculation of load change during the previous time step

Calculation of stresses and pore pressure

Calculation of initial settlement because of compressionof gas bubbles and correction of pore pressure

Calculation of consolidation during the time step t

Correction of pore pressure for gas bubbles

Calculation of settlement

Calculation of increase in pore pressure because of creep effects

End of calculation? Stop

Calculation of geometry and updating of the soil propertiesin the various sublayers because of compression

New load step?

Fig. 34. Flowchart for the calculations in a settlement prediction [7].


During the course of the calculations, a register hasto be kept of the stress and deformation history in thevarious layers and the rate effects that have been takeninto account. This is required for control of the creepprocess. The stress and deformation history is alsoused for updating the apparent preconsolidationpressure and the unloading and reloading moduli.


Literature

[7] Larsson, R. (1986). Consolidation of softsoils. Statens geotekniska institut. Rapport29. Linköping.

[8] Sällfors, G. (1975). Preconsolidation Pressu-re of Soft High Plastic Clays. Thesis. Chal-mers tekniska högskola, Institutionen förgeoteknik med grundläggning, Göteborg.

[9] Leroueil, S., Tavenas, F., Mieussens, C.and Peignaud, M. (1978). Construction porepressures in clay foundations under embank-ments. Part II: generalized behaviour. Cana-dian Geotechnical Journal, Vol. 15, No. 1.

[10] Swedish Standard SS 02 71 26 Geotechni-cal tests - Compression properties - Oedome-ter tests, CRS-tests - Cohesive soil. SwedishBuilding Standards Institution, Stockholm,1991.

[11] Swedish Standard SS 02 71 29 Geotechni-cal tests - Compression characteristics - Oed-ometer test, incremental loading - Cohesivesoil. Swedish Building Standards Institution,Stockholm, 1992.

[12] Larsson, R. (1995). The CPT test. An in situmethod for determination of stratigraphy andproperties in soil profiles. Swedish Geotech-nical Institut, Information Nr. 15, Linköping.

[13] Marchetti, S. (1980). In situ tests by flatdilatometer. ASCE. Journal of the Geotech-nical Engineering Division, No. GT3.

[1] Terzaghi, K. (1923). Die Berechnung derDurchlässigkeitsziffer des Tones aus demVerlauf der hydrodynamishen Spannungs-erscheinungen. Akademie der Wissenschaf-ten in Wien. Mathematisch-Naturwissen-schaftliche Klasse. Sitzungsberichte. Abtei-lung IIa. Vol. 132 No. 3/4. pp 125-138.

[2] Taylor, D. W. and Merchant, W. (1940).A theory of clay consolidation accounting forsecondary compressions. Journal of Mat-hematics and Physics, Vol. 19, Vol. 3, pp.167-185. (Massachusetts Institute of Techno-logy, Department of Civil and Sanitary Engi-neering, Serial 72.)

[3] Taylor, D.W. (1942). Research on consoli-dation of clays. Massachusetts Institute ofTechnology, Department of Civil and Sani-tary Engineering, Cambridge, Mass. Serial.82, 147p.

[4] Suklje, L. (1957). The analysis of consoli-dation process by the isotaches method. 4thInternational Conference on Soil Mechanicsand Foundation Engineering. London. Pro-ceedings Vol. 1, pp. 200-206.

[5] Bjerrum, L. (1967). Engineering geology ofNorwegian normally consolidated marineclays as related to settlements of buildings.7th Rankine Lecture, Géotechnique, Vol. 17,No. 2, pp. 83-118.

[6] Bjerrum, L. (1972). Embankments on softground. Proceedings of the Specialty Confe-rence on Performance of Earth and Earth-supported Structures, Vol. 2, Purdue Univer-sity, Lafayette, Indiana.


[14] Carlsten, P. (1988). Torv - Geotekniskaegenskaper och byggmetoder. Statens geo-tekniska institut, Information 6, Linköping.(In Swedish). Also in Carlsten, P. (1993).Peat - Geotechnical Properties and Up-to-Date Methods of Design and Construction.State-of-the-Art-Report. Swedish Geotechni-cal Institute, Varia 215, Linköping.

[15] Kallstenius, T. och Hallén, A. (1963). An-visningar för geotekniska institutets fältun-dersökningar, Del 2: Provtagning med stan-dardkolvborr St1. Statens geotekniska insti-tut, Meddelanden Nr. 6. Stockholm. (InSwedish). Swedish Committee on PistonSampling (1961). Standard Piston Sampling.Swedish Geotechnical Institute, ProceedingsNo. 19, Stockholm.

[16] Magnusson, O., Sällfors, G. och Larsson,R. (1989). Ödometerförsök enligt CRS-me-toden. (Oedometer tests, CRS tests). (InSwedish). Swedish Council for Building Re-search, Report R44:1989, Stockholm.

[17] Larsson, R. (1990). Behaviour of OrganicClay and Gyttja. Swedish Geotechnical Insti-tute. Report No. 38, Linköping.

[18] Inganäs, J. (1978). Vertikaldränering i orga-nisk jord. (Vertical drainage in organic soil).(In Swedish). Delrapport. Dnr 1-189/77.Swedish Geotechnical Institute, Linköping.

[19] Boussinesque, J. V. (1885). Application despotentiels à l’équilibre et du mouvement dessolides élastiques, Paris.

[20] Osterberg, J.O. (1957). Influence valuesfor vertical stresses in semi-infinite mass dueto embankment loading. Proceedings, 4thInternational Conference on Soil Mechanicsand Foundation Engineering, London,Vol. 1, p. 393.

[21] Burmister, D. M. (1943). The theory ofstresses and displacements in layered sys-tems and applications to the design of airportrunways. Highway Research Board, Procee-dings, Vol. 23, pp 126-144, Washington.

[22] Fröhlich, O. K. (1934). Druckverteilung imbaugrunde. Berlin.

[23] Steinbrenner, W. (1936). A rational methodfor the determination of the vertical normalstresses under foundations. Proceedings 1stInternational Conference on Soil Mechanicsanf Foundation Engineering, Vol. 2, Cam-bridge, Massachusetts.

[24] Hansbo, S. (1972). Deformationer och sätt-ningar. Handboken BYGG, Kapitel 173. ABByggmästarens Förlag, Stockholm. Också iStatens geotekniska institut, MeddelandeNo.10. (In Swedish). Based on [23] and Fox,E.N. (1948). The mean elastic settlement of auniformly loaded area at a depth below theground surface. 2nd Int. Conf. on Soil Mech.and Found. Engng. Proceedings, Vol. 1,pp. 129-132. Rotterdam.

[25] Hansbo, S. och Sällfors, G. (1984). Jord-mekanik (Soil Mechanics). (In Swedish).Handboken BYGG, Kapitel G05, Liber För-lag, Stockholm. Based on [26].

[26] Terzaghi, K. (1943). Theoretical SoilMechanics. John Wiley and Sons, NewYork.

[27] Helenelund, K. V. (1951). Om konsolide-ring och sättningar av belastade marklager.(Consolidation and settlement of layeredsoil). (In Swedish). Järnvägsstyrelsens geote-kniska sektion, Meddelande 3, Helsingfors.

[28] Magnan, J-P., Baghery, S., Brucy, M. andTavenas, F. (1979). Etude numerique de laconsolidation unidimensionelle en tenantcompte des variations de la perméabilité etde la compressibilité du sol, du fluage et dela non-saturation. Laboratoires des Ponts etChaussées, Bulletin de Liaison, No. 103, pp.83-94.

[29] Bergenståhl, L., Rogbeck, Y. och Eskils-son, S. (1988). Sättningsuppföljningar i lera- Jämförelse mellan beräkningar med ochutan krypning. (Settlements in clay - compar-ison between calculations with and withoutcreep effects). (In Swedish). X Nordc Geo-technical Meeting, Oslo, Artikler och poster-sammendrag, s. 320-323.


[30] Rogbeck, Y. (1989). Praktikfall 2 – Vägar-beten. (Settlements of road embankmentswith and without creep effects. A casestudy). (In Swedish). Grundläggningsdagen1989, Swedish Geotechnical Society, Stock-holm.

[31] Janbu, N. (1970). Grunnlag i geoteknikk.(Soil Mechanics). (In Norwegian). TapirForlag, Trondheim.

[32] Rogbeck, Y. (1991). Parameterstudie avse-ende sättningsberäkning i lera. (Settlementcalculations in clay – a parameter study).(In Swedish). Swedish Geotechnical Insti-tute, Varia 352. Linköping.

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