GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE · Micaceous silt 10 to 30 Mild steel 300 Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay I r varies between 10 and

GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE

Prof. J. N. Mandal

Department of civil engineering, IIT Bombay, Powai , Mumbai 400076, India. Tel.022-25767328email: [email protected]

Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay


Module - 9LECTURE - 47

Geosynthetics for ground improvement

Recap of previous lecture…..


Design chart with smear effect and well resistance

Instrumentation of embankment on soft sol with PVDs

Installation of PVD

Design example (partially covered)

Step 8: Calculated the shear strength (improved) in eachstage

.S.FxNc

strengthShear cfinalu)improved(

cu(final) = Cohesion after the improvement,Nc = Bearing capacity factor = 5.7, andF.S. = Factor of safety.

2)improved( m/t28.7

37.5x83.3strengthShear

2)improved( m/t3.9


Improvement in shear strength after stage I,

Improvement in shear strength after stage II


2)improved( m/t83.10


Improvement in shear strength after stage III,

Step 9: Determine the height of fill (that can be safelyplaced on soil) for the next stage by following equation.

embankment

stagepreviousin)improved(fill

strengthShearH

Hfill = Height of fill that can safely be placed over the soil,γembankment = Unit weight of embankment soil = 1.8 t/ m3

As the shear strength improved in first stage is 7.28 t/m2,7.28 41.8fillH m


Step 10: Check whether the shear strength of soil isgreater than the bearing capacity of soil (Determined instep 1) or not; if not, revise the days.

The settlement after N number of stages should alsobe greater than the settlement calculated by generalconsolidation theory in step 2.

In put Soil Properties

1 Thickness of compressible layer, H(m) 102 Maximum Height of Reinforced Earth wall, h1(m) 4.353 Live load equivalent to embankment, H1 (m) 2.74 Hence total height of embankment (m) 7.055 Density of embankment (T/cum) 1.86 Density of compressible soil (T/cum) 1.77 Initial void ratio 1.28 PI 279 Horizontal degree of consolidation (m2/day) 2.20E-02

10 Vertical degree of consolidation (m2/day)11 Initial Cohesion os soil (T/m2) 2.512 Compression Index of Soil 0.24313 Factor of safety for SBC 3

Design Go to main screen


Stage loading Calculation

Stage of Loading I II IIITime Days 30 10 5Total fill Ht. meter 3 4 5Degree of Consolidation % 0.91 0.55 0.33Initial Cohesion, C T/m2 2.5 3.834151 4.9Initial Shear Strength T/m2 4.75 7.284887 9.3Cohesion after consolidation T/m2 3.834151 4.9 5.7Shear Strength T/m2 7.284887 9.3 10.83 > 7.4 t/m2Total ht of fill can be placed meter 4.047159 5.2 6.016667Hence, Provide 4 5

Settlement mm 410 156 70

Total settlement 636 OK


Settlement calculation in stage I, S1 = (U%) x δI

)17.1(5

8.13)17.1(5log2.1110243.091.0

ppplog

e1HC91.0S 10

0

0

0

c1

S1 = 0.91 x 447.69 mm ≈ 410 mm

Settlement calculation in stage II, S2 = (U%) x δII

)8.137.05(

8.14)8.137.05(log2.1110243.055.0

ppplog

e1HC55.0S 10

0

0

0

c2

S2 = 0.55 x 284.35 mm = 156 mm

p0= H/2 x γeffective γeffective = (γsaturated - 1) = 1.7-1 = 0.7 t/ m3


Settlement calculation in stage III, S3 = (U %) x δ III

)8.148.137.05(

8.15)8.148.137.05(log2.1110243.033.0

ppplog

e1HC33.0S 10

0

0

0

c3

S3 = 0.33 x 213 mm = 70 mm


Results and Summary:Ist Stage IInd Stage IIIrd Stage

Total height of embankment (m)

3.0 4.0 5.0

Degree of consolidation (%)

91 55 33

Period (days) 30 10 5Settlement (mm) 410 156 70

Shear strength (t/m2) 7.28 9.3 10.83After IIIrd stage,

Total settlement = (410 + 156 + 70) = 636 mm > 563.49 mm (calculated in Step 2), and

Bearing capacity = 10.83 t/m2 > 7.4 t/m2 (required). So, it is O.K.


Excel Program


GEOSYNTHETIC ENCASED STONE COLUMNS

Load carrying capacity of the ground treated withgeosynthetic encased stone column may be obtained bysumming up the contribution of each of the followingcomponents under wide spread load such as tanks,embankments, pavements etc.

A] Capacity of the stone column resulting from theresistance offered by the surrounding soil against itslateral deformation i.e., bulging under axial load.

B] Capacity of the stone column resulting from the bearingsupport provided by the intervening soil.


C] Capacity of the stone column resulting from increasein resistance offered by the surrounding soil due tosurcharge over it.

D] Capacity of the stone column resulting from increasein resistance offered by the confining effect dueperipheral geosynthetics encasement.

Geosynthetics encased stone columnProf. J. N. Mandal, Department of Civil Engineering, IIT Bombay

[A] Load Carrying Capacity Considering Bulging Action

Bishop, Hill and Mott (1945) provided a theoreticalrelationship between limiting pressure (σrL) and shearstrength (Cu) as,

u

surL C12

ELn1C

Gibson and Anderson (1961) incorporated the effect oftotal initial lateral stress (σho) in an elasto-plastic materialand modified the Bishop, Hill and Mott (1945) equation as,

u

su horL C12

ELn1C k CuhorL


σrL = limit pressure in a pressure meter,Es = the elastic modules of soil,

Cu = undrained shear strength of soil, and

µ = Poisson’s ratio

1C2ELn1k

u

s

Based on the field records, Hughes and withers (1974)demonstrated that the limit pressure (σrL) may beapproximated to an acceptable solution replacingrigorous analytical solution as follows.

OuhorL Uk C Uo = initial excess hydrostatic pore water pressure


Considering that the loaded pile behaves as a pressuremeter (Hughes et al. 1975) and the granular materials inthe pile approaches shear failure as well as bulgingoccurs near top of the pile, the ultimate yield stress (qult)on stone column is as follows.

rLpuhopult KC k'Kq

Uo = 0 allowing full drainage in the stone column

The above equation is interdependent on the values of (a) Coefficient of passive earth pressure (Kp)(b) Total in-situ initial effective radial stress (σ'ho), and(c) Coefficient, k


(a) Coefficient of passive earth pressure, Kp

2/'45tanK 2p

ɸ' refers to angle of internal friction for compactedgranular fill in the stone column. It can be taken in therange 45°-55°, say 55° for rammed stone columns(Nayak, 1985)

(b) Total in-situ initial effective radial stress, σ'ho

'K' vooho


σ'vo = Effective vertical stress at depth ‘Z’ = γsub x Z

Z = 4 x Diameter of stone column (i.e. at critical length ofstone column)

Ko = Average coefficient of lateral earth pressurecorresponding to undisturbed state of soil i.e. at restcondition,

Soil type Ko RemarksGranular, Loose 0.5 to 0.6 Thus for granular materials,

an average value of Ko = 0.5 and that for soft clays

0.9 may be taken for design purpose

Granular, Dense 0.3 to 0.5Soft clay 0.9 to 1.1Hard clay 0.8 to 0.9


Total initial effective radial stress (σ'ho) can be consideredequal to 2Cu or can be obtained from limiting pressure-strainrelationship achieved form in-situ pressuremeter tests(Hughes et al., 1975).

(c) Coefficient, k

}1{C2Eln1k

u

s rIln1k

Ir = Rigidity Index (Vesic, 1972)

Medium Rigidity Index, IrRock 100 to 500Sand (loose to dense ) 70 to 150Saturated clay (soft to stiff) 10 to 300Micaceous silt 10 to 30Mild steel 300


Ir varies between 10 and 300 for cohesive soil. The valueof ‘k’ will be between 3.33 and 6.7. Therefore, ‘k’ valueappears to be reasonable for design purpose.The ultimate yield stress on stone column is given by,

usubopult C 4 Z KKq

- If some part of the column is not submerged, use bulkdensity for calculations.

From the yield stress obtained above, safe load capacity of the column may be determined using factor of safety = 2 (D = Diameter of stone column)

Therefore,

4D

S.FqQ

2ult

1


[B] Bearing Support Provided By the Intervening Soil

Bearing capacity of soil is given by, qult2 = cNc

For clays (ɸ = 0), Nc = 6. Therefore, qult2 = c x 6

Therefore,S.F

qq 2ult2safe

Factor of safety = 2 (B.I.S, 1997) is consideredadmissible in view of the strength gained in case oftanks, embankments, sub-grades etc.

Safe load taken by surrounding soil, s2safe2 AqQ

As = actual area of the soil surrounding a stone column


Let’s consider triangular pattern of stone columns havingspacing ‘S’ between them.

2e S 0.866 S 60 sin SA

Area of intervening soil for each column is given by,

4D -S 866.0A

22

s

Therefore, safe load is calculated as,

4D S 866.0qQ

22

2safe2

Ae = total influence area including the column


[C] Surcharge Effect

Due to load when stone column dilates, some part of loadwill be shared by the surrounding soil.

Consideration of soil under this load results in the increaseof its strength providing additional lateral resistance againstbulging of stone column.

The analogy for expansion of cylindrical cavity (Vesic,1972) and bulging failure phenomenon of granular pile in ahomogeneous, isotropic and infinite soil mass has been usedto find increase in capacity due to additional soil resistance.


Increase in mean radial stress (Δσr')

o2safe

r K 21 S.F

q'

Increase in ultimate cavity expansion stress,

'F K q rpro

Fq' is the Vesic’s (1972) dimensionless cylindrical cavity

expansion factor. It depends upon ϕ and reduced rigidityindex.

For ϕ = 0o, Fq' = 1 (Vesic, 1972)

Therefore, increase in Yield stress,

column stone of area c/s q ro3ult


Allowing a factor of safety = 2 to account for variation inKo, Cu and cross-sectional area, the increase inpermissible load of column,

4D

S.Fq

Q2

3ult3

[D] Effect of Geosynthetics Encasement

- Geosynthetics encased stone columnanalogues to thin cylinder

D = internal diameter, t = thickness, and L = lengthp = internal pressure intensity


Let us consider a longitudinal section XX through axisdividing the shell into two halves A and B.

Let us consider two elementary strips subtending an angleδθ at the centre at an angle θ on either side of the verticalthrough the centre (Ramamrutham and Narayanan, 2008).


The normal force acting on each strip is given by,δpn = p r δθ L

Resultant of the two normal forces on the two elementalstrips acting vertically i.e. normal to XX is,δp = 2 p r δθ L cosθ

Total force normal to XX on one side of XX= Total bursting force

p Lr 2

Cos Lr p 2P0

P = Projected area x Intensity of radial pressure


Let F1 is the intensity of tensile stress induced inGeosynthetics material across section.

Then resisting force offered by section = F1 x 2 x L x t

Equating the bursting force to resisting force,F1 x 2 x L x t = 2 x r x L x p

t2D pF1 D

F t 2p 1Hoop stress,

Longitudinal stress is given by (For Geosynthetic casing, F2 = 0)

t4D pF2


Greatest shear stress qmax is given by,

t2D p

2FF

q 21max

ncecircumfere Originalncecircumferein Changestrain tialCirumferen

ε1 = circumferential strain

1

D D D DD D

Also, Circumferential strain can be expressed as,

mEF

EF 21

1 E is Young’s modulus and 1/m isPoisson’s ration.


11

1

D2 t E

2 t ED

F pE

p

The developed resisting force for a given strain,

12 E Dfab

PPt

Therefore, safe load carried,

4D

S.FKP

Q p fab4

Factor of safety may be taken as 2.0


Total safe load carrying capacity of plane/ordinarystone column,

Qsafe1 = Q1 + Q2 + Q3

Total safe load carrying capacity of encased stonecolumn,

Qsafe2 = Q1 + Q2 + Q3 + Q4

Total number (N) of stone columns required,

safeQ load TotalN

The area per column is given by Nayak (1985),

Netc.) Embankment (Tank, Load of Area Column StonePer Area


Required spacing of stone columns for triangular pattern,

0.868Column Stoneper Area

Sreq

CU = 10 kN/m2

ɸ = 35ºSpacing = 1.5 mγsub = 5 kN/m3

BEARING CAPACITY OF PLANE & REINFORCED STONE COLUMNSTONE COLUMN DIAMETER IN M

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2Q1 kN 17.75 26.50 37.35 50.45 65.97 84.05 104.86 128.54Q2 kN 52.56 49.97 46.91 43.38 39.37 34.89 29.95 24.53Q3 kN 15.22 21.91 29.82 38.95 49.30 60.86 73.64 87.64Q4 kN 14.49 17.39 20.29 23.19 26.08 28.98 31.88 34.78Qsafe1 kN 85.53 98.38 114.08 132.78 154.63 179.80 208.44 240.71Qsafe2 kN 100.02 115.77 134.37 155.97 180.72 208.79 240.32 275.49

Design example:


ENCASEMENTS

Different types of encasements can be prepared usinggeosynthetic reinforcements.

Bamboo is easily available and cheaper in India withrespect to polyester geogrid and also environmentfriendly.

Natural bamboo geogrid encasements can beprepared to encapsulate the stone columns.

Narrow bamboo sticks of 10 mm width with properfinishing were collected to prepare bamboo encasements(Dutta et al., 2012).


(a) Bamboo encasement (b) bamboo made encasement wrapped with jute geotextile (c) Polyester geogrid

encasement (After Dutta et al., 2012)

(a) (b) (c)


Tensile strength of the bamboo geogrid was determinedaccording to ASTM D4595-11 specification for wide-widthstrip method.

Wide width specimens of 200 mm width and 100 mmgauge length were prepared by attaching the narrowbamboo strips from both directions with adhesive.

Wide width bamboo grid specimens (a) before tensile test (b) after tensile test (ASTM D4595-11)


Wide width tensile strength test of polyester geogrid (ASTM D4595-11)


0

20

40

60

80

100

120

0 1 2 3 4 5 6 7 8 9 10

Ten

sile

str

engt

h (k

N/m

)

Strain (%)

Bamboo geogrid

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30

Tens

ile s

treng

th (k

N/m

)

Strain (%)

Polyester geogrid

(a) (b)

Tensile strength versus strain curve of (a) bamboo geogrid (b) polyester geogrid


Material Properties ValueBamboo geogrid Mesh size 5 mm x5 mm

Ultimate tensile strength

110 kN/m

Ultimate stiffness 2200 kN/m

Polyester geogrid Mesh size 5 mm x5 mmUltimate tensile

strength32 kN/m

Ultimate stiffness 160 kN/m

Properties of geogrid


Axisymmetric finite element model (FEM) of encased stone column (After Dutta et al., 2012)


Effect of encasement stiffness on radial deformation:

0

50

100

150

200

250

300

350

400

450

500

0 4 8 12 16

Hei

ght (

mm

)

Radial deformation (mm)

OSC

ESC (160 kN/m)

ESC (2200 kN/m)

Radial deformation of stone column without and with encasement from finite element analysis

(After Dutta et al., 2012)

OSC = Ordinary stone column

ESC = Encased stone column

Bamboo geogrid = 2200 kN/m

Polyester geogrid = 160 kN/m


More uniform and minimum radial deformation isobtained with increasing stiffness of the encasements.

Ordinary stone column (OSC) fails by bulging withinalmost 2D length of the column with a significant radialdeformation of around 13 mm.

Using Polyester geogrid and Bamboo encasement radialdeformation reduces to 4 mm and 1.5 mm respectively.

Geogrid encasements provide excess lateral confiningpressure to the columns and prevent its radial deformation.

As the stiffness increases, more hoop tension getsgenerated in the encasement and it provides moreconfining pressure to the stone column.


Please let us hear from you

Any question?


Prof. J. N. Mandal

Department of civil engineering, IIT Bombay, Powai , Mumbai 400076, India. Tel.022-25767328email: [email protected]


Documents

GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE · Micaceous silt 10 to 30 Mild steel 300 Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay I r varies between 10 and