CLUSTER BEHAVIOR OF THE GROUND DURING ITS … · the moving ground passes through itself the energy of ground pressure, thermal energy, and ... (Kumsar et al., 2016), civil engineering

Acta Geodyn. Geomater., Vol. 14, No. 4 (188), 445–462, 2017

DOI: 10.13168/AGG.2017.0025

journal homepage: https://www.irsm.cas.cz/acta

ORIGINAL PAPER

CLUSTER BEHAVIOR OF THE GROUND DURING ITS IRREVERSIBLE MOVEMENT

Victor NAZIMKO * and Ludmila ZAKHAROVA

Institute for Physics of Mining Processes NAS, Ukraine,2A, Simferopol St., Dnieper, Ukraine, 49005

*Corresponding author‘s e-mail: [email protected]

ABSTRACT

Irreversible behavior of the ground or a rock mass encompasses both the transition of the groundover a peak strength and further development of the nonreversible movement and deformation.The irreversible ground movement is traditionally considered as the transition to chaos. Howeverthe moving ground passes through itself the energy of ground pressure, thermal energy, andexchanges by substances with surrounding rock mass. According to thermodynamics ofirreversible processes, such a non-equilibrium ground behavior may create dissipative structuresthat are the embodiment of self-organization. The paper describes the results of the structuresinvestigation, which have been unveiled with incremental fields of the irreversible groundmovement during a landslide development and underground roadway maintenance. Thesestructures were evolving from close interaction of the separate blocks or fragments of the groundand distant cooperation of the short-lived clusters that were periodically rearranging in time andspace as the irreversible ground movement started and progressed. Extant techniques restrainbasically one prevalent component of the irreversible ground movement. The other two collateraltransversal components were usually ignored. However, blocking of these transversecomponents can prevent the development of a dangerous irreversible movement of the groundand a rock mass.

ARTICLE INFO

Article history:

Received 25 June 2017 Accepted 9 October 2017 Available online 26 October 2017

Keywords: Irreversible ground movement Cluster Structure pattern Vortex Close and distant interaction

demonstrated by Grenon et al., (2017) despite thegenerally accepted theory separates process to elastic(Devies and Selvadurai, 1996) and post-peak stages(Jaeger and Cook, 1969). Therefore the irreversibleground movement is inherent in many geomechanicand geologic processes and plays the important role insafety maintenance and formation of the complexstructures and their evolution. That is why theirreversible behavior of the ground and rock masses isof constant interest for researches.

Any irreversible process reflects a specificbehavior of a thermodynamic system (Kondepudi andPrigogin, 2015). The irreversibility involves theaccumulation of the entropy. If a thermodynamicsystem is open – namely exchanges by energy andsubstance with its surrounding – it becomesdissipative and tends to form a structure or to transferto the self-organized state. According to Kondepudi etal. (2015), certain structure might emerge as thedissipative system when the excess of entropyproduction is negative. The ground and a rock massare the typical thermodynamic systems. Theirstructure might appear in different patterns: theseismic waves during an earthquake, specificallyoriented fracture systems (Jaeger et al., 1969), thefolds as a result of the Earth crust flow (Bigoni andGourgiotis, 2016), and thin details of the strain facies,which Tikoff and Fossen (1999) demonstrated.Seismologists developed a set of experimental andnumerical methods to visualize the seismic waves that

1. INTRODUCTION

Investigation of irreversible behavior of theground and rock masses is an important part ofgeomechanics (Kumsar et al., 2016), civil engineering(Bloodworth, 2002) and structural geology (Wilson etal., 2016). In contrast to elastic behavior, thenonreversible movement and deformation may causedisintegration of a rock mass (Malinowska andHejmanowski, 2016), damage of a support and evenfailure of an underground or a civil structure, andtrigger landslides. For instance, a roof fall in anunderground opening is preceded with the irreversiblemovement of the roof rock layers. Nonreversibledeformation of a dam foundation after itsconsolidation deteriorates stability of the dameventually. A dangerous landslide evolves after theaccumulation of irreversible ground deformations.

On the other hand, the irreversible rock massmovement is the natural process that follows roofweighting in an advancing longwall face. Garvey andOzbay (2013) illustrate that delay of the roof cavingcauses a danger of a catastrophic roof bump.Therefore a rock irreversible movement may bedesirable in this case. Also, the irreversible flow of theEarth crust was the main process which has formedthe modern rock mass structure during certaingeological periods (e.g. Wallis et al., 2015), sogeologists use this structure to investigate geologicalprocesses. Furthermore, the irreversible deformationof a rock mass accumulates long before its collapse as

Cite this article as: Nazimko V, Zakharova L: Cluster behavior of the ground during its irreversible movement. Acta Geodyn. Geomater., 14,No. 4 (188), 445-462, 2017. DOI: 10.13168/AGG.2017.0025

V. Nazimko and L. Zakharova

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Researchers have not emphasized on the ground self-organization. The most probable reason is this statehas been overlooked in spite of the numerous set ofsophisticated methods and technologies for moni-toring of irreversible processes of the ground and rockmass movement. Hence the choice of a relevantmethod may assist detecting of a new feature of self-organizing behavior in addition to apparent folding,fracture system generating, or strain facies emerging.Investigation of the ground irreversible movement anddeformation can help to find additional patterns ofself-organization and to develop specific measuresthat reduce negative effects or amplify positivefeatures of self-organized states during irreversiblemoving and deforming of the ground and the rockmass.

The aim of this paper was to demonstrate thatirreversible ground movement may self-organizeproducing complex dissipative structures. In thispaper, we accomplished such tasks: (i) We made theoretical consideration of a possible

self-organization of the ground and a rock massduring their irreversible moving and deforming.

(ii) Chose a relevant method for monitoring of theground irreversible movement and deformationfor detection of the structures and self-organizedstates.

(iii) Investigated process of irreversible moving anddeforming and find new patterns of self-organization.

(iv) Developed specific measures that reducenegative effects or/and amplify positive featuresof self-organized states during non-reversiblemoving and deforming of the ground and rockmass.

2. THEORETICAL CONSIDERATION OF A POSSIBLE SELF-ORGANIZATION OF THE GROUND AND A ROCK MASS DURING THEIR IRREVERSIBLE MOVING AND DEFORMING

Let us consider a ground volume, thethermodynamic state of which is far out fromequilibrium. The main peculiarity of such system isthe possibility to form an ordered in time and spacestructures using external energy from the surrounding.These structures can persist only due to the externalenergy flow that allowed calling these systems as‘dissipative’. According to Glensdorf and Prigogine(1971), such self-organization of ordered structures ispossible only if there is a cooperation of system’scomponents. Haken (1981) pointed out that thesecomponents feel mutual influence.

Giving (Glensdorf et al., 1971), the thermos-dynamic system will evolve in self-organized state if

dŚ/dt=∫I(dX/dt)dv≤0 (1)

where Ś is the entropy production, t is time, I and Xare thermodynamic flow and force in that order, v isan elementary volume of the system through whichthe integration accomplished.

Let us consider a ground body or a rock massvolume that surrounds an underground roadway. Theirreversible behavior of a continuum ground starts

decay due to irreversible processes in the crust. Thestructures of a deformed rock mass have beentraditionally investigated by geologists as a final“frozen” result of the crust flow during geologicepochs. However, a wide range of irreversibleprocesses in the ground and the rock mass remainsunexplored from the perspective of self-organizationstate investigation.

So far, evolution of the rock mass around anunderground excavation has been considered as therock and ground deterioration that follows withreduction of the rock strength and increase of theentropy. For instance Kumsar et al. (2016) associatedgrowth of the entropy with the rock collapse, andLombardo et al. (2016) related increase of entropy tothe triggering of a landslide. However, thisdeterioration leads to the chaos, whereas developmentof a structure contributes to an order. The seismicwaves and the ancient geological structures areapparent and easily attracted attention of researches.However, self-organized structures that might emergeduring progressive landslide development, groundsubsidence over extracted longwall panels, floor heavein an underground roadway, a pile driving, may bemore delicate and subtle. These structures may maskand do not express explicitly. An important questionis how do disintegrated fragments of the ground moverelatively each other? How do they coordinate theirmovement?

The traditional approach to consideration of theirreversible deformation relies on the selection ofa relevant constitutive model. It is believed that anappropriate constitutive model automatically providesreliability of the irreversible process expression asa whole. However, researchers apply the results ofrock samples testing to construct a constitutive model,whereas irreversible processes encompass much morevolume of a rock mass that disintegrates into myriadsof such samples or fragments, which cooperate duringirreversible movement. In addition, any constitutivemodel implies a certain deterioration of the rock. Howthis degradation may convert to self-organization ofthe structures? As Peng (2015) indicated, the problemof selection or development new constitutive modelsremains of vital importance despite the goodagreement between the model forecast and theexperiment. An important reason may be thedifference between the behavior of the rock sample ora fracture according to chosen constitutive model andbehavior of the rock mass as a whole body.Consideration of a possible self-organizing processduring the irreversible deforming of the rock massmay cover this gap. Furthermore, the theory ofirreversible thermodynamics implies a possible self-organization of a ground body or rock mass volumesthat pass through them the flow of ground pressureenergy, underground water or gas, and are in a non-equilibrium state of progressive moving and de-forming.

Therefore this paper presents a theoreticalassessment of a possible event in a form of self-organization of a ground body or a rock mass volumeduring their irreversible moving and deforming.

CLUSTER BEHAVIOR OF THE GROUND DURING ITS IRREVERSIBLE MOVEMENT .

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Fig. 1 Results of system solving: variation of active fractures and stress in time (a); phase portrait of the systemin s-f (b) and f’-f coordinates (c).

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local volume of a ground in the vicinity of theunderground opening.

Fracture area has the quadratic dimension. Itmeans the rate of AB density increment may beproportional to the square of the AB. On the otherhand, AB density reduces as the ground pressure risesbecause Coulomb friction prevents sliding and isproportional to the pressure. Such simple assumptionsyield first differential equation:

f'(t) = -s(t) + f(t)2 (2)

We also may assume that the rate of groundpressure is proportional to AB density because thehigher the pressure the more probable destruction ofthe ground or the rock mass in vicinity of theunderground excavation:

s'(t) = f(t) (3)

The system (2-3) has been solved for thesimplest initial conditions:

f(0) =1, s(0)=1 (4)

indicating, that active fractures were present whenanalysis of the irreversible process of the groundmoving and deforming had started.

Figure 1 demonstrates the solution and the phaseportraits of the system (2-3). Fragment (a) indicates tothe periodic variation of the fracture density andground pressure. Fragments (b) and (c) depict cyclesthat clearly demonstrate that the dissipative systemhas generated the time-dependent structure. However,the most reliable proof of the time and spacestructures rests in an experiment because significantlymore variables cooperate in reality and theirinterdependences are much more complex. 3. SELECTION OF A RELEVANT METHOD FOR

MONITORING OF THE GROUND IRREVERSIBLE MOVING AND DEFORMING FOR DETECTION OF STRUCTURES AND SELF-ORGANIZED STATES

The methods that structural geologists use torecover historically formed structures in the crust arenot applicable for the unveiling self-organization andnew patterns of a structure because only the final

from its disintegration. Any discrete body of a rockmass accumulates the irreversible deformation due toaperture variation of the existent fractures or slidingadjacent blocks along the boundaries of the fracturesand the gaps. The expansion and the sliding produceirreversible movement of the rock blocks and, asa consequence, irreversible deformation of the wholebody of the rock mass. When separate blocks ofa ground converge and the fractures or the gaps close,the domains or clusters composed of the consolidatedblocks moves and deforms as a monolithic body.

It should be stressed that the plastic irreversibledeformation occurs due to sliding along the shearbands (Bigoni, 2012) which are natural boundariesbetween separate clusters or elementary volumes ofthe plastic ground. These shear bands are the naturalboundaries between adjacent clusters. Let us call thefractures and the shear bands as ‘active boundaries’(AB for short) if they participate in the accumulationof the ground irreversible deformation. Elasticdeformation of the blocks and clusters are reversibleand do not contribute to the irreversible process.Therefore discrete blocks (in a discrete brittle rockmass) or discrete clusters (in a plastic ground) are thenatural components that comprise the ground volumeas a thermodynamic system. It does mean thatcooperation of these blocks and clusters is the way tocreate a well-organized in time and space structuredue to the irreversible moving and deforming of theground.

The process of AB evolution can be described interms of ground pressure s and AB density f because sis the thermodynamic force in the case and f isthe thermodynamic flow. Requirement f>0 is themandatory condition for active irreversible deformingof the whole ground body and irreversible moving anddeforming of the separate components (blocks andclusters). We will use ABs only in the case, whereasthose fractures and shear bands that are not in processof active deforming are excluded from consideration.The transition of AB in an active state and vice versameans that they may vary during irreversibledeformation of the ground. Variables f and s arefunctions of time (t) and will be analyzed in certain


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incremental attitude have been reported for differentcases (Bloodworth, 2002; Lia et al., 2016; Huang,2016). As was mentioned above, irreversible behavioris path dependent, therefore the incrementalmethodology is the best way to reveal this behavior indetails because individual increments of non-reversible movement may have opposite signs andthus annihilate each other.

The trial and error method has shown thatvisualization of the displacement field in a form ofincremental vectors is an appropriate technique tounveil the structure in the moving ground. However,unlike the distribution presented by Amitrano et al.(2007), time increment should be as small as possible,what assures that the finest details of the irreversiblemovements will not be lost. Practically, such methodis available for recovering of a structure on the groundsurface, for example on the roof of an undergroundroadway or on the landslide surface. Length l ofa vector is:

l=√(Δx2 + Δy2) (5)

where Δx=xt-1 - xt., Δy=yt-1 - yt;, x and y are thecoordinates of a fixed point on a plane. This planeshould approximate the surface of the ground onwhich displacements are monitored. Subscript tindicates the current state of the ground, whereasindex t-1 denotes its previous state.

Traditionally, points on the ground surface arefixed with monuments or benchmarks, and thecoordinates of these benchmarks are measuredgeodetically. In addition, modern applications inremote sensing such as synthetic aperture radars(Assilzadeh et al., 2010; Delbridge et al., 2016) maybe used. The time interval between successivemeasurements should be chosen in such a way that lwould be essentially more than error of measurement,for instance, more than three standards of the error.However, some important details of structuresevolution will be missed if the interval of durationgrowths.

Examples of the incremental analysis will bedemonstrated in the next paragraphs for the cases ofa landslide progress and displacement of surroundingrock mass in an underground roadway.

4. INVESTIGATION OF STRUCTURES

DEVELOPMENT DURING LANDSLIDE PROGRESS

Figure 2 demonstrates a steep shore near shallowinland Sea of Azov which is connected to the BlackSea (Nazimko and Nazimko, 2002b). A clay groundcomposed the coastline which is in the state of slowpermanent sliding similar to the mudslide reported byAmitrano et al. (2007). Slowly developed landslidesare typical phenomena as Zerath et al. (2016) stated.Sea waves deteriorate, dissolve the shore and absorbdiluted clay removing the retaining action thatsupports the steep ground. Eventually, this steep shoreloses stability and slides down to the sea. Theprobability of the landslides increases after a longperiod of precipitation. Massive landslides occur often

states of the structures are available in-situ. However,any irreversible process is path-dependent, thus thestructures might vary both in time and space duringtheir developing. Therefore the concrete path of theirreversible process or its history should be monitoredin order to reveal the structure dynamics andimportant details of the self-organization. This meansthe monitoring should be carried out continuously intime and in space. The most popular method thatsatisfies this conditions and requirements is micro-seismic monitoring (Lei et al., 2016; Yu et al., 2017).The micro-seismic monitoring provides continualregistration of the dynamic events that have beentriggered by the collapse of the ground or growth of afracture (Cui et al., 2016). The majority ofobservations have demonstrated that intensive micro-seismic events follow the sources of ground agitationby artificial or natural processes, for instance,underground roadway driving, a longwall faceadvance, pillars forming, injecting of fluids duringhydro-fracturing, landslides development. In spite ofthe fact the clouds of micro-seismic activity areapparently tied to these processes, development of theclouds occurs chaotically in a random manner. Atleast, experimenters have not noticed the signs of self-organization or certain obvious structures so far. Tosay otherwise, micro-seismic monitoring has nothelped to reveal the cooperation among the blocks orclusters during active irreversible deforming, sliding,or moving of the ground.

Registration of the blocks movement and clustersdisplacement is another popular method that is usedfor monitoring of the irreversible ground movement.Amitrano et al. (2007) illustrated the results of suchmonitoring during a mudslide progress investigationin a mountainous region. They demonstrated integraldisplacement field and average velocity distribution ofground movement. Vectors of ground displacementreport obvious facts, namely the mud movesaccording to gravity gradient along ravine axis;moreover, the forefront outpaces the tail part of theslide that indicates to dilation of the mud body. Thisinformation does not add a new essential knowledgeand does not provide evidence concerning a possiblestructure formation. On the contrary, the distributionof the ground velocity demonstrates an unusualbehavior of the sliding ground. The average velocityof the central cluster of the mudslide is more than thevelocity of surrounding peripheral ground mass,although the central cluster is not the front-runner partof the slide.

It is evident that process of sliding is not assimple as the displacement field reported. Thisexperimental fact can be considered as a hint thatindicates to a complex hierarchy or a structure of thelandslide. However, this possible structure has beenhidden because integrating approach, namely the mudmovement was indicated as a total displacementduring 8-year period, and the sliding velocity wasaveraged. Therefore an incremental approach shouldbe used to recover the history of monitoredirreversible ground movement. The advantages of the


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sessions of geodetic measurements were accomplishedduring 44 days period.

Incremental displacements of the monumentswere determined as a difference between successiveand subsequent measurements. These data wereinterpolated and used to design the incremental vectordistribution (Fig. 3). The step of gridding wascomparable to the average distance between adjacentmonuments that prevented possible distortion ofexperimental results.

Field of displacements was apparently dividedinto clusters. It is possible to separate the groundsurface with several methods. To delineate theseclusters, we used different colors for upright, up left,down right and down left vectors. Such fistapproximation is relevant because it is impossible toexactly detect the defects that existed in the groundbefore the experiment. The whole area near the sea isin permanent slow movement and there was a greatnumber of fractures, shear bands, and the other defectsbefore the experiment started. Therefore a comparisonof the measured deformations and of the peak(allowable) deformation is not relevant in the casebecause any level of the deformation can beovercritical (irreversible).

Maximum movement of the ground was 49 mm.An experimental area separated to 15 apparent clustershaving dimensions from 2 to 10 m. Cluster 1 slippedto the right-hand ravine and cluster 2 moved to theopposite direction that resulted in the divergencebetween these clusters. In Figure 3, the empty arrow

in spring periods. The climate at the area is dry andintensive precipitations happen once during 5-10years. Therefore activation of the landslides followsthese periods of ground wetting. Monitoring ofa slowly developed landslide is the best way tocapture the ground structures in details.

The total height of the shore above the sea leveltypically ranges between 20 m and 30 m. The averageslope of the shore is 200 but sometimes reaches 300

and more. Fine homogeneous brown clay havingdensity from 1850 to 2040 kg/m3 represents ground atthe site. This clay becomes a perfectly plastic materialwhen saturated with water. Uniaxial compressivestrength (UCS) of a dry sample that contains 4 % ofwater was approximately 18 MPa and collapse of thesample occurred at a strain level of 0.018. After thiscollapse, the resistance of the sample reduced quickly.After absorption 33 % of water, the clay barelyresisted to compression at the level of 1 MPa andmaximum resistance occurred at a strain level of 0.05.Approximately the same level of the resistance keptup to the strain of 0.2 what demonstrates perfectplastic properties of the clay ground. Limit of tensionvaried in the range from 0.35 to 0.55 of UCS.

We monitored geodetically irreversible sliding ofa crag that was surrounded with two deep ravines. Thestandard error of displacement measurement was2.1 mm. We installed sixty-five monuments on thesurface of the landslide area approximately 40 m by30 m (Fig. 2b). The average distance between adjacentmonuments varied between 3 m and 5 m. Two

Left hand ravine

Right hand ravine

Crag

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Fig. 2 View of the progressing landslide (a) and layout of the monuments (b).


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accelerate the process of modeling, vibrationtechnique has been employed. The power of a vibratorwas 50 W, frequency and magnitude of vibration were50 Hz and 0.5 mm. The vibrator has been fixed to thebottom of the model.

Subsidence of the model surface has beenmeasured by a ruler with standard error of ±1.5 mm.Displacements in the horizontal plane (X and Y –displacements) were registered by a digital cameraand processed by special software. One pixel ina picture corresponded to 0.56 mm in the model.Errors of measurement of X and Y–displacementsregistration was ± 2.35 pixels or ± 1.32 mm with theconfidence of 95%. Pictures of the model were madeevery time when apparent modification of the modelstate has been registered during consecutive stages ofthe landslide development. This helped to assemblemaximum information concerning the complexbehavior of the ground during generation anddevelopment of the landslide. We have made 32pictures during the experiment and chosen 17 picturesto create the incremental fields of ground deformation.

Stages 1 through 8 reflected an incubation periodduring damage accumulation and preparation toground separation development. Figure 5ademonstrates the typical patterns of groundincremental movement during 7th stage. Themovement generated clusters divergence, their countermotion, mutual sliding and the creation of vortexeslike those registered in situ. The ground massorganizes itself into clusters that interact and rearrangeduring the ground sliding.

Even after sufficient destruction and separation,ground and rock blocks should adjust their mutualmovement, rotating, changing the velocity of theirmovement and even its direction. The vortex patternof incremental movement is the most probablebetween the adjacent clusters moving with differentvelocity or in opposite directions. That is why weregistered both in situ and in physical model complexcluster organization, vortexes and unusual behavior ofground clusters including short-term incrementalmovement in the direction that is opposite to slidingof the whole body of the ground.

Such complex behavior occurs at initial stages ofthe landslide development when there is not sufficientspace for the movement. The pattern of ground self-

indicates a fracture fragment that emerged betweenthese clusters. While cluster 2 moved to the west,cluster 8 displaced to the opposite direction. Clusters3 and 4 separated from the other ground and are goingto fall down. Clusters 6, 7, and 15 drifted into a left-hand ravine. Pairs of clusters 12, 15 and 9, 10 createdtwo clockwise vortexes.

Therefore despite the general trend of the slidemovement to the sea, forty-four-day incrementaldisplacements demonstrated different directions ofclusters’ movement and their unusual behavior. Thelandslide separated into clusters and developedthrough their asynchronous movement. The directionof separate cluster incremental displacement does notconcord with the general direction of the landslidedevelopment (to the sea). Some clusters convergedwhereas other diverged. Groups of selected clusterscreated vortex structures. Apparently, adjacentclusters cooperated that promoted self-organization ofthe ground movement.

Physical modeling helped to study the landslidein more details. The landslide was investigated in thephysical model in geometric scale 1:200. Dimensionsof the model were 8 cm left height, 7 cm right height,34 cm width and 20 cm length (Fig. 4). Therefore themodel represented the behavior of the seashore alongthe distance of 68 m. Slight gradient from the left tothe right, viewing from the seaside, reflected realinclination of the land in situ.

Dynamic scale factor may be calculatedaccording to the formula:

Fn/Fm = (200/1)•(γn/γm) (6)

where Fn and Fm have force or stress dimension andare physical parameters of natural ground and modelsynthetic material; γn and γm are correspondingdensities.

Synthetic material was composed of fine sand(grain size <0.8 mm), cement, gray clay and water inproportion 94:3:1:2. This mixture has been poured bylayers into a box having sidewalls and back wall andconsolidated by the pressure of 15 kN. Density of thismixture after compression was 1550 kg/m3. To satisfythe dynamic scale factor, UCS of the syntheticmaterial should be in the range from 0.072 to0.004 MPa. To simulate deterioration of the groundstrength due to its saturation with water and to

a b

Fig. 4 View of the model front (a) and top (b).


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development that energy spent for this process wouldbe minimal or, in other words, the same amount ofenergy produces minimum entropy. It does mean thatprocess of ground sliding combines the rock blockdestruction, the clusters rearrangement and theirrecombination in time and in space to dissipate thedifference of the potential energy due to loss of theheight level.

There is another peculiarity of this pattern ofground self-organization: adjacent blocks and clusterspromote their cooperation giving the way one after theother, moving in turn, alternatively. Next paragraphsexplain this behavior.

5. SHORT INTERACTION OF ADJACENT

FRAGMENTS OF THE GROUND

Alternative irreversible movement of theadjacent ground blocks has been investigated in anunderground head entry at the depth of 540 m. Thehead entry provided fresh air for a longwall face thatretreated with the rate of 3.1 m per day and extracted1.8 m coal seam which had UCS of 20 MPa. Sectionof the entry was of arched shape and had the area of13.7 m2. The entry has been supported by fullyencapsulated rock bolts, 5 bolts in a row and 1 mbetween the rows.

The angle of inclination of the strata was 60. Theimmediate roof of the coal seam consisted of 10 to12 m of sandy shale having UCS of 30 MPa. This wasoverlain with a competent thick layer of sandstone.The immediate floor of the coal seam was representedwith 1 to 1.5 m sandy shale having UCS of 27 MPaand followed by 2 m sandstone with UCS of 50 MPa.Three-meter shale layer followed this sandstone.

Non-reversible roof movement has beenmonitored on a set of 9 rock bolts. Plan view of the setdepicted in the fragment (c) of Figure 8. Dimensionsai were parallel to the entry center line, moreover a2-5

and a5-8 coincided with it, whereas intervals bi werenormal to the axis. The distance between adjacentbolts was about ai = bi = 1 m. Distance ai and bi

organization evolves from a complex versatile andclearly expressed set of bocks, clusters, and vortexesduring landslide development to a simple picture ofstraightforward flow in the slide direction, whendisintegrated ground accumulates sufficient degree offreedom and dilation. In fact, variogram analysis ofthe nearest neighbor statistics (Noel, 1991) hasdemonstrated that complete spatial randomness of theincremental vector length and direction were decayingas the landslide has developed (Fig. 6). The higherClark-Evans index (Clark and Evans, 1934) orHopkins-Skellam factor (Hopkins and Skellam, 1954)the more probability that there is an aggregation of thevectors. All diagrams in Figure 6 quantitativelycorroborated that self-organization process subsidesactually because these indexes decreased steadily.

The cluster organization is manifested not onlyin the mutual arrangement of the movement but alsoin involving of hierarchy (Fig. 7). For instance, tocontinue the process of sliding, the clusters at stage 7should rearrange and give origin to new clusters atstage 8. Meantime, some clusters existing at stage 7should collide at stage 8. The majority of theantecedent clusters mentioned above should collide tocreate large clusters-offspring at the 9th stage ofsliding. Hence we may notice the hierarchy of solidblocks – clusters. Blocks create short-lived clustersthat disintegrate to produce new clusters. Thusa cluster may split into clusters and blocks eventually.Rearrangement of the clusters might be followed bycutting of the ground or rock blocks because theboundary of a cluster-ancestor may not coincide withthe boundary of the cluster-offspring. Sliding maydevelop only if the separated blocks will adjust theirmutual movement, rotating, changing velocity anddirection of sliding, and organizing into clusters of theblocks. These clusters obey the hierarchy thatdemands them to reunite during sliding.

Figure 7 can illustrate this conclusion wheremosaics of the clusters at stages 7, 8, and 9 have beenoverlapped. The nature chooses such a way of slide

Fig. 6 Decay of spatial randomness of incremental vectors.

R² = 0,9074

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possibility of plane strain state in vertical section ofa long underground horizontal roadway. For example,56 mm expansion and 75 mm contraction of theroadway axis on the basis of 1 m do not allowconsidering its vertical section in plane strain statewhich is usually implied to employ a 2-dimensionalcomputer model: variation of axial strain from -0.056to +0.075 is much more than error of measurement.

Subsidence of the experimental bolts reflectedthe same anti-phase behavior (Fig. 9). Leveling of thebolts started earlier than monitoring of the distancesbetween them; therefore the time scale does notcoincide in Figures 8 and 9. However, right ends ofthe time scale matched actually. Bolts 4, 5, 7, 8, and 9accelerated their subsidence at the moment I, whereasbolt 6 ceased to move actually.

At the moment II, vice versa, the five leadingbolts delayed their downward movement, and bolt 6speeded up the sagging over 50 mm. In addition, thefinal incremental subsidence of the bolts wasessentially different. Furthermore, the greaterincremental subsiding was experienced by bolts 5 and9 which terminated their movement at the previousstage.

and subsidence of the experimental bolts weremonitored periodically during retreating of thelongwall face. The standard error of the measurementswas ± 1.9 mm. The monitoring started when thelongwall face was at the distance of 93 m from thenearest experimental bolt and finished when the faceapproached the experimental site. Fragment (a) and(b) in Figure 8 demonstrate the variation of ai and bi

respectively. An anti-phase pattern of incremental bolt

movement prevails and is the most importantpeculiarity of the irreversible behavior of the rockmass in this experiment. When one pair of the boltsdiverged, adjacent pair converged to yield room forthe first pair. This behavior is apparent at the momentsof 28, 37, 43, 63, and 66 days in fragment (a) ofFigure 8 as well as on 37, 59, 64, and 66 days inFigure 8b. This behavior is typical and representativebecause the other pairs of the dimensions between theadjacent bolts demonstrated the same pattern ofcooperation: the rock blocks gave the possibility toexpand one after the other.

Such alternative and asynchronous deformationof the rock mass in horizontal plane eliminates the

Fig. 8 Variation of the distance between adjacent rock bolts along the head entry (a) and inits cross section (a); fragment (c) indicates to layout of the monitored bolts.


453

Fig. 9 Variation of the incremental subsidence of the monitored rock bolts.

depth of the extensometer installation. The deepestextensometer in the roadway roof has been positionedat 13.9 m, in the sidewalls at 7.45 m and 10.2 m, inthe floor at 7.9 m. Initial zone of damaged rock massaround the roadway was registered with the specialoptical device. The extensometers were installedbefore extraction of an adjacent panel.

Extraction of the coal in the 3rd east panelincreased ground pressure and induced activation ofrock mass movement around the experimentalroadway. Figure 11 demonstrates strain of the groundafter the longwall face of the 3rd east panel passed bythe monitored site to the distance of 25 m and 182 m.The strain of the ground is indicated in mm/m andcritical level of the tensile strain was 5 mm/maccording to the rock samples testing. The tensilestrain has a negative sign. Noticeably, the groundmovement activation has been registered in the sidesand the floor of the roadway during the initial stage ofdeformation, while the competent sandstone remainedstable. Eventually, damage of the ground expanded tothe roof (Fig. 11b) after withdrawal the face to 182 m.It is important to notice that compression zoneemerged behind the tensile fronts of the overalldamaged zone. This effect is natural and coincideswith the coordination of tension-contraction of theintervals between adjacent bolts in Figure 8. Thecompression zone provides a room for dilatation offorefront sectors of the ground that follow theboundaries of damaged zone around the roadway.

This experiment demonstrated that the adjacentrock blocks alternated their horizontal movement andsubsiding in turn giving the way one after other.Should the adjacent blocks do not cooperate theywould not move or their movement would be blockedessentially. This behavior causes an important effectthat will be discussed in the next paragraph.

6. SEQUENTIAL DEVELOPMENT OF THE

DAMAGE ZONE AROUND AN UNDERGROUND OPENING

The alternative irreversible movement of theadjacent blocks describes a close interaction of thethermodynamic components of the ground. However,these interactions can generate a distant effect in theground body as a whole as a result of the self-organization. This effect has been registered in a caseof underground roadway maintenance (Nazimko et al.,1997). The main entry was driven in the 2.0 m shalelayer at the depth of 820 m. The floor of the roadwayconsisted of 10.5 m argillite, and roof has beenpresented with competent 11 m sandstone overlainwith a coal seam which has been extracted witha longwall face (Fig. 10). Plan view of mine map isshown in Y0X plane (fragment (a)) and verticalsection of the strata is in Z0Y plane in fragment (b).Mechanical properties of the surrounding rockspresented in Table 1.

We monitored the evolution of the damage zonearound the roadway using multi-point boreholeextensometers. Fragment (c) of Figure 10 depicts the

-250

-200

-150

-100

-50

0

50

60 70 80 90 100

Incr

emen

tal s

ubsid

ence

, mm

Time, day

6789123

1

6

7

9

8

2

3

1 2

3 6

7

8

3,9

7,9

6

8


454

Table 1 Mechanical properties of the rocks around the roadway.

Rock UCS, MPa Tensile Elasticity Peak strength strength module, at confined stress

MPa GPa 10 MPa 20 MPaSandstone 63.0 3.0 23.0 290 360 Shale 48.1 0.5 13.0 117 133 Argillite 51.7 2.7 29.8 285 353

2nd east panel

3d east panel

Entry

MPBEx

a

b

c

Fig. 10 Layout of the experimental site.

dissipative structures that emerge discontinuously too(Glensdorf et al., 1971; Haken, 1981). Factually, thecluster mosaic bifurcates under random fluctuations ofground pressure, strength of the rock mass, itshumidity, or temperature.

Paradoxically, these bifurcations occur duringcontinuous changing of the irreversible groundmovement as in kaleidoscope, incessant rotation ofwhich produces images that replace each otherdiscontinuously. Therefore, velocity of the groundmovement as its derivative cannot serve as anindicator of the bifurcation. We found empirically thatonly monitoring of incremental irreversibledisplacement in diapason between 2 and 10 standarderrors of measurement provides reliable unveiling ofthe dissipative structures.

Szafarczyk and Gawalkiewicz (2016) publishedresults of landslides monitoring that may serve asa good independent confirmation of this diapason(Fig. 13). Standard error of the ground strainmeasurement was 0.28 mm/m and maximumregistered strain was 0.7 mm/m or 2.5 times more.The arrow indicates general direction of the gravitygradient. It can be seen that there is not apparentcorrelation between the directions of maximal tensilestrain and the gradient of the gravity. It means thatPolish authors could delineate a ground clustersstructure using incremental vectors of groundmovement.

Figure 12 demonstrates the evolution of thedamaged zone which expanded consequently in timeand space. Position 1 indicates the zone boundarybefore the influence of the adjacent longwall.Dimensions of the damaged zone were 2.9 m in thefloor, 2.7 m in the left side and the roof of theroadway, and 1.3 m on the right side. The adjacentlongwall had disturbed stress state of the rock massthat induced consequent development of the damagedzone to the floor and to the right side of the roadway(position 2) then to the left side (position 3) andfinally to the roof that indicated with position 4.Therefore rock mass self-organized the process ofirreversible movement in the form of groundcompression-tension (close cooperation) andsequential expansion of the damaged zone (distantcooperation) in time and space. Apparently, if thiscooperation were blocked, the dimensions of thedamaged zone would be smaller.

It is important that the patterns of the dissipativestructures succeeded each other discontinuously intime and in space. This significant peculiarity hasoccurred both during the landslide progress anddisintegrating zone development around theunderground opening. The cluster mosaic shiftedabruptly as indicated in Figure 7 likely the boundariesof the damaged zone, which expanded with discreteincrements (Fig. 12). Such irreversible behavior of theground is consistent with the bifurcations of


455

Scale

Dilatation Scale

a b

Compression zone

Fig. 11 Progress of surrounding rock deformation after withdrawal of thelongwall face to 25 m (a) and 182 m (b).

Scale

Maximum strain of 34 mm/m has been registeredduring another case of slow landslide monitoring thatwas conducted in approximately same geographicaland geological conditions. Strain distribution depictedin Figure 14 and demonstrates strong correspondencebetween directions of the strains and the gravitygradient because maximal strain is 121 times morethan error of measurements. Ground displacement wasintegrated during such a long period that hid possibledissipative structures.

7. DISCUSSION

Self-organization of the irreversibly movingground has theoretical and practical importance. Intheoretical aspect, we for the first time proved thateven deteriorating rock mass is capable to create thestructures which organize and facilitate theirirreversible movement to spend minimum potentialenergy for the same amount of the irreversible integralmovement of the rock mass. This condition isgoverned by the second law of thermodynamics. Put itsimply, the rock mass tends to move by the easiestway producing minimum excess entropy. Wediscovered specific patterns of the structures thatpromote transition to such the way, namely rock massdisintegrated into short-living clusters comprised rockblocks and fragments which converge, diverge, sliderelatively each other, and create vortex patterns duringthe irreversible movement of the ground. It was foundthat such pattern is mandatory condition fordevelopment of irreversible movement of a rock massor ground due to close interaction of the blocks andfragments and distant cooperation of the clusters.Therefore it is practically important that restriction ofsuch self-organizing behavior enforces the rock massto choose another and more energy-expensive way forthe irreversible movement.

Fig. 12 Successive development of damage zoneboundaries


456

There is a prevailing component of groundmovement usually. A sliding ground tends to movealong a maximal gradient of gravity. Surroundingunderground cavity rock mass moves into theopening: the roof moves along the gravity, the floorheaves in opposite direction, and the sidewalls movetransversely to the gravity.

The most attention is usually paid to preventgeneral trend of ground displacement in 3D space.However, the other two collateral directions areconsidered as minor or peripheral and remain

For example, the close interaction of the blocksand the distant cooperation of the clusters should berestricted to maintain the stability of undergroundconstructions or natural ground slopes. Technically,we should restrain the alternative movement ofadjacent blocks and clusters and prevent the sequentialdevelopment of the damaged zone around under-ground constructions forcing simultaneous andconcurrent expanding of the zones. To do this, weshould constrain all components or degrees of rockmass freedom.

Fig. 13 Distribution of incremental strain during a slow landslide progressing: case 1, (Szafarczyk andGawalkiewicz, 2016).


457

Fig. 14 Distribution of incremental strain during a slow landslide progressing: case 2, (Szafarczyk and Gawalkiewicz, 2016).

with three cable systems: cable system 1 orientedapproximately against the direction of integral groundmovement, whereas system 2 and 3 are transversal tothe system 1. Moreover, the all three systems of thecables are approximately mutually perpendicular toeach other. All cable bolts should be installed andfixed in the competent bed of the landslide and mustbe pretensioned. The long cables having a length of10 m and more exceed the average size of the groundblock by several times. Therefore the long cables canrestrain both close cooperation of the blocks anddistant interaction of the clusters because the setwhich consists of the three cable systems restrictsdegrees of freedom in 3-dimensional space.

All mentioned above reinforcing systems can beinstalled through the holes which are drilled from theground surface. However, an underground opening iscongested and crowded, hence there is not thesufficient room and possibility to reinforce thesurrounding rock mass is restricted. A way to restraindegrees of freedom in 3D space is to vary theinclination of the rock bolts (Naprasnikov et al., 1999)

unprocessed. Meanwhile, we should pay much moreattention for ground reinforcement in the transversaldirections. Soil nails, retaining walls, dowels,geotextile and other mechanical devices of groundreinforcement are oriented along the generalirreversible movement of the landslide and against themotion of the ground (Choi and Cheung, 2013). Thepiles are oriented mostly vertically and prevent groundmovement passively resisting shear deformation of theground (Hazarika et al., 2011). Rock bolts are orientedin the roof of an underground opening against thegravity or transversely to it against the sloughedsidewalls (Kent et al., 2014). Improving surface andsubsurface drainage, preserving vegetation and theother measures invest in resistance and blocking of thegeneral direction of landslides movement but do notrestrain the other two degrees of freedom that aretransversal to the first one.

Therefore we propose to restrict these degrees offreedom as much as possible. For instance, in the caseof a landslide, it is possible to restrain all threedegrees of freedom (Fig. 15a). This task can be solved


458

portions in space. Specifically, examination of micro-seismic events demonstrated that process of thedisintegration occurs by turn: it comes back to thepreviously fragmented rock clusters several times andrepeats crumbling of the rock blocks by pieces, oneafter other, what minimizes energy expenditure for thesame rate of rock mass disintegration. That directmanifestation of rock mass self-organization andforming of a structure in time and space is usuallyunnoticed because of strong stochastic noiseoccurrence.

There are other two theoretical issues whichwere raised. First, two-dimensional strain state of theground and rock mass is an ideal state which isimpossible to reach in reality because this state isextremely energy-expensive. The rock mass volumeor ground body will find a way to get out of this statethrough random fluctuation. Glensdorf et al. (1971)have proven that any thermodynamic system which isin the non-equilibrium state may bifurcate and shift toan essentially different state under triggering ofa subtle fluctuation. The real ground body or a rockmass has infinite sources of such fluctuation, namelydefects, fractures, inhomogeneity, non-uniformity. Itdoes mean that 2D modeling conceals an intrinsicerror which overestimates bearing capacity ofa system modeled. In reality, surrounding rock masscollapsed earlier under the same initial and boundaryconditions because there are more degrees of freedomin natural prototype in comparison to those simulatedon a computer in 2D state.

Second issue is less obvious but more importantfrom theoretical point of view. Is it applicable to usewell-known constitutive models for replication suchspecific irreversible behavior of the rock mass as thecluster interaction? This is discussion for anotherpaper but preliminary attempts, which we have made,demonstrated that popular models (for example finiteelement methods, finite difference methods) areinsensitive to the cluster behavior and cannotreproduce the close interaction of adjacent blocks orrock lumps and the distant cooperation of the clusters.This issue is very important because amount of energywhich irreversibly moving rock mass dissipates maydiffer several times depending on the way that itchooses. This theoretical issue generates a bigpractical effect, namely, using of the relevant methodsand specific technologies may change the way ofirreversible movement what essentially reducesconvergence of roof and floor in an undergroundopening or diminishes probability of a landslide.

Our findings open wide scope for prospectiveinvestigation of irreversible behavior of a discretemedium not only in rock mechanics, but inmetallurgy; mineral processing; transport, storageand warehousing of bulk cargo; micro-technology.For example we found that irreversible movementof metallic powder during pressing, extrusion ormetal microcrystals stirring during drawing wirethrough a die obey the same laws of cluster interaction(Nazimko et al., 2002a). Non-reversible clusterstructures of fine coal slime has been observed duringprocess of its dewatering in filter-presses (Garko-

or pretensioned cables with reference to the gravity(Fig. 15b). This technique may reduce the degrees offreedom and noticeably prevent close interaction ofthe blocks because the inclination of the bolts createscollateral tightening components which restricttransversal degrees of freedom for the rock mass.

The distant interaction of the clusters in the roofand floor of an underground opening can be restrainedwith the props that should be installed under heads ofthe selected rock bolts and cables, for example, thebolts that are installed at the centerline of a roadway.The best effect provides a combination of two or threerock bolts whose heads are close to each other andwhich are supported by the prop (Fig. 15c).

Pretensioned truss bolts are effective device torestrain degree of freedom along stratification (Cox,2003). However, the truss bolts create retaining forcesin vicinity of the ground surface, whereas distantinteraction of the clusters occur at least to the depth of10 m from a roadway lining. Kent et al. (2014)reported the successful experience of entry sidewallstabilization using webbing attachments that restrictedrelative movement of the rock bolt heads on the sidesurface of an entry. It is impossible to restrain theblocks and clusters interaction completely and inwhole volume of a ground where irreversibledeformations may occur but any intentional measurewill reduce the negative effect of their cooperation.

Requirement to restrain all degrees of freedom isabsolute and much more capacious, versatile andpotential than it appears at the first glance. Degrees offreedom should be restrained literally: translationaland rotational degree of freedom in all directions.Such terms provide a wide range of possible means,methods, devices and technologies that may facilitaterestriction of degree of freedom both along directionof active ground movement and in the collateral ortransversal directions. The moving ground usuallycontracts along the collateral directions what reflectsbalance of mass. This contraction provides additionaldegree of freedom that accelerates process ofirreversible ground movement in a back feed manner.Therefore designers should construct such gadgets,mechanisms and reinforcing systems which not onlyresist against active ground movement butcompensates collateral contraction of the movingground. For example, we developed a helicoidal rockbolt, which restricted both translational and rotationaldegree of freedom along direction of active groundmovement, and instantaneously, caused expansion ofthe borehole – and consequently rock mass – alongnormal to this direction. This effect assisted tomaintain lateral pressure in the moving rock mass andenhanced longwall entry stability (Nazimko et al.,2008). Importantly, the helicoidal bolts transform thepotential energy of ground pressure to generatecollateral expansion.

Another practical implementation of the newfindings concerns the cases when there is a need todisintegrate the rock mass, for example during itshydro-fracturing. This is out of the scope of this paperbut preliminary analysis indicated that surroundingrock mass disintegrates by separate stages in time and


459

Fig. 15 Reinforcement patterns that reduce degree of freedom for ground.

irreversible movement of the ground and the rockmass, what evolves the dissipative structures in timeand space. These structures facilitate the accumulationof degrees of freedom for a ground body to separatefrom the stable rock mass and develop a landslide orroof sag and even a fall in an underground opening.These patterns of nonreversible ground motion can beunveiled with incremental fields of ground movement.These increments should be as small as possiblehowever not to be less than the error of measurement.

The complete spatial randomness of theincremental vectors length and direction decayslinearly as process of the irreversible movementprogresses and the disintegrated ground accumulatessufficient degrees of freedom for dilatation.Eventually, versatile patterns of the dissipativestructures degrade to a simple picture of straight-forward flow of debris.

The patterns of ground irreversible movementand the dissipative structure vary in space and in time.The adjacent blocks and clusters promote theircooperation giving the way one after the other,moving in turn, alternatively. The anti-phase patternof incremental block movement prevails and is themost important peculiarity of the irreversible behaviorof the ground and a rock mass. A block delayed whenthe adjacent block accelerated and vice versa, whatdemonstrates the close interaction of the groundfragments. In particular, this close cooperation of theadjacent blocks makes impossible plane strain state invertical cross section of an underground elongatedroadway because random blocks displace along its

venko and Nazimko, 2003). Noticeably, we shouldsuppress the fragment and cluster cooperation whenthere is a need to increase stability of thedisintegrating medium and to the contrary, supportand promote the self-organization to activatedisintegration, nonreversible movement, and minimizeenergy consumption.

8. CONCLUSION AND FUTURE RESEARCH

8.1. NEW FINDINGS

It was for the first time proved that evendeteriorating, rock mass is capable to create thedissipative hierarchical structures which self-organizeand facilitate their irreversible movement duringaccumulation of the damage to spend minimumpotential energy for the same amount of theirreversible integral movement of the rock mass.These structures are triggered by random fluctuationsand are a product of both the close interaction ofadjacent blocks or ground fragments and the distantcooperation of the block clusters. The groundfragments create short-lived clusters that move asa whole aggregate body, which may eventuallyreintegrate into other clusters and blocks. The clusterpattern rearranges during progress of the irreversibleground moving. This process of the reorganizationmight be followed by cutting of the intact ground orrock blocks because the boundary of a cluster-ancestormay not coincide with the boundary of the cluster-offspring.

The blocks converge, diverge, slide relativelyeach other, and create vortex patterns during the

1

2

2

3

a

b

entry

Rock bolts

roof

floor

c

prop

Truss bolts


460

mass. It is necessary to restrain all degrees of freedomof the ground as much as possible including bothtranslational and rotational degrees.

Our findings open wide scope for prospectiveinvestigation of irreversible behavior of the groundand rock masses, its patterns, and their parameters,namely, sizes and dimensions of the clusters in 3Dspace, periods of patterns bifurcation, effects ofsupport type and its bearing capacity on theirreversible behavior of the dissipative structures,impact of stress and ground pressure level and its rate,for example speed of a longwall advance. In addition,new findings are the basis for reexamination of suchpopular technological process as hydro-fracturingwhich is widely used during extraction of oil, naturalgas, coal-bed methane, and shale gas.

ACKNOWLEDGEMENTS

The authors of this paper would like toacknowledge coal mine Pivdenno-Donbas’ka forproviding the experimental sites during experimentsand instrumental leveling of the rock bolt heads. Wealso extended our appreciation to our colleaguesViacheslav Sazhnev and Sergey Shakun for theirassistance during installation of BHMP extensometersand underground instrumental measurements.Investigation of the short interaction of groundfragments and distant cooperation of their clusters hasbeen accomplished under grant of NAS Ukraine III-2_2017.

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Lia, X.Y., Zhang, L.M. and Jiang, S.H.: 2016, Updatingperformance of high rock slopes by combiningincremental time-series monitoring data and three-dimensional numerical analysis. Int. J. Rock Mech.Min. Sci., 83, 252–261. DOI: 10.1016/j.ijrmms.2014.09.011

V. Nazimko and L. Zakharova: CLUSTER BEHAVIOR OF THE GROUND DURING ITS IRREVERSIBLE MOVEMENT

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bFig. 3 Distribution of incremental sliding.

Fig. 7 Overlapping of cluster distributions: red (1 – solid), blue (2 – intermitted) and black(3 – intermitted with point) boundaries correspond to 7th, 8th and 9th stages of modeling.

Fig. 5 Displacements distribution at stage 7 (a) and 10 (b).

0 20mm

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To the Sea

Fig. 3 Distribution of incremental sliding.

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CLUSTER BEHAVIOR OF THE GROUND DURING ITS … · the moving ground passes through itself the energy of ground pressure, thermal energy, and ... (Kumsar et al., 2016), civil engineering