fissuring groundwater withdrawal

Mechanisms of Earth Fissuring Caused byGroundwater Withdrawal

ZHUPING SHENG

Texas A&M University System, El Paso Agricultural Research and Extension Center,1380 A&M Circle, El Paso, TX 79927

DONALD C. HELM

JIANG LI

Department of Civil Engineering, Morgan State University, 5200 Perring Parkway, Baltimore, MD 21251

Key Terms: Aquifer Movement, Boundary ElementMethod, Driving Forces, Earth Fissures, GroundwaterWithdrawal, In Situ Stresses, Land Subsidence, SoilMasses

ABSTRACT

Earth fissures associated with groundwater with-drawal are complex products of both human activ-ities and natural forces, and they occur in definablegeological environments. In this paper, the authorsfirst characterize the driving forces for earth fissurescaused by groundwater withdrawal. Then, the effectsof various factors, such as stresses and pre-existinggeological structures, are examined using conceptualmodels. Numerical results show that the fissuringprocess is controlled not only by the inducedmovement at depth and pre-existing structures butalso by the in situ stress field. In addition, the degreeto which aquifer movement and pre-existing struc-tures actually trigger fissuring depends greatly on thein situ stress field. The authors conclude that earthfissuring related to groundwater withdrawal isa multi-step process that is influenced by a multiplic-ity of factors, one being the aquifer movement. Withgroundwater withdrawal, hydraulic and gravitationalforces tend to drive aquifer material to deform bothhorizontally and vertically. Cumulative deformationor strain results in movement. In turn, this aquifermovement results in differential displacements atdepth along planes of weakness, such as pre-existingfaults and material interfaces. This differentialmovement (both horizontal and vertical) then gen-erates tensile zones at depth. Once formed, sucha tensile zone may migrate upward, form a crack(fail) where the vadose zone is brittle, and eventuallyexpress itself as an earth fissure at the land surface inarid or semi-arid regions. In humid regions, the same

tensile zone (lateral stretching) at depth will simplyexpress itself as a transient sub-vertical plane ofenhanced porosity within and crossing the vadosezone.

INTRODUCTION

Earth fissures have been widely observed in thewestern United States, namely Arizona, California, Idaho,Nevada, New Mexico, Texas, and Utah (Holzer, 1984;Sheng, 1996). These earth fissures not only cause damageto utilities, structures, and buildings but also providea path for surface contaminants to move downward to anaquifer and pollute native groundwater (Doty and Rush,1985; Helm 2000). Therefore, it is extremely important tounderstand the physics of earth fissuring so thatapproaches can be developed and implemented tomitigate existing fissures and to prevent new fissures.

Historically, several mechanisms have been suggestedto explain earth fissuring and surface faulting induced bygroundwater withdrawal. These included capillary stressassociated with a declining water table, localized verticaldifferential compaction (abrupt tilt or a vertical slip), andregional differential compaction (bending beam) (Holzer,1984). Researchers also have suggested that earth fissuresrelated to groundwater withdrawal result from aquifermovement, especially from the horizontal movement(Lofgren, 1978; Helm, 1994a). In fact, artificial rechargeor aquifer storage and recovery (increase in localgroundwater hydraulic head) may cause earth fissures ifthe process is not designed correctly. Bell and Price(1991) examined the spatial relation between surfacefissures and pre-existing geological faults in Las VegasValley, Nevada. They found that geological structures do,indeed, control the location of fissures induced bygroundwater withdrawal, and they concluded that inLas Vegas Valley, these structures are the Quaternaryfault zones.

Environmental & Engineering Geoscience, Vol. IX, No. 4, November 2003, pp. 351–362 351

Earth fissures are products of human activities, such asgroundwater pumping, and of natural forces, such asgravity, and they occur in certain geological environ-ments. Earth fissuring is influenced by a multiplicity offactors, such as in situ stress, pre-existing geologicalstructure, and depth of an aquifer. Identification of thecontrolling factors in earth fissuring is a key step inimproving our understanding of the fissuring mechanismand in developing a mitigation strategy for earth fissuringand, hence, hazard reduction. How these factors influencethe initiation and development of earth fissures, however,is not well understood.

In this paper, the authors evaluate the effects ofdifferent factors on earth fissuring, identify key factorsthat control the earth-fissuring process, and develop a newunderstanding of the mechanisms for earth fissuring. Theauthors first identify the driving forces for earth fissuresrelated to groundwater withdrawal. Hydraulic forces tendto drive the aquifer material to move horizontally (Helm,1994a). In turn, the aquifer movement results indifferential horizontal and vertical displacements alongweakness planes, such as pre-existing faults andinterfaces. These differential movements also causea nascent tensile failure zone to develop at depth. Sucha tensile failure zone may develop further, migratingupward and eventually expressing itself as an earthfissure at the land surface. Subsequently, the role ofadditional factors, such as in situ stresses and pre-existinggeological structures, are examined using a numericalrepresentation of four basic conceptual models based ondistinct geological environments and hydrological con-ditions. Numerical results indicate that initiation anddevelopment of an earth fissure are more sensitive tocertain factors, such as pre-existing geological structuresand the in situ stress field. The authors also use oneconceptual model to illustrate the multi-step process ofearth fissuring and the roles that some factors play.

CONCEPTUAL MODELS

Characterization of Earth Fissures Related toGroundwater Withdrawal

An earth fissure is a tensile-dominated failure ingeological masses; that is, the opposing sides havea major displacement component that involves movementperpendicular to the plane of failure (Figure 1). The earthfissures discussed here are primarily related to humanactivities (i.e., groundwater withdrawal and injection).Therefore, aquifer movement caused by groundwaterflow is a principal factor in triggering the initiation andgrowth of earth fissures. This movement is expressed aspart of the boundary conditions of the numerical modeldiscussed in the next section. In addition, the materialproperties of an aquifer, such as Young’s modulus and

Poisson’s ratio of an elastic porous structure, as well asthe strength of soil help to determine the characteristics ofthe earth-fissuring process (Helm, 1994b; Li, 1994; andSheng, 1996). Furthermore, earth fissures occur in certainfavorable geological environments. Hence, geologicalenvironments, in situ stresses, depth of aquifer, andproperties of faults or interfaces are factors that maycontribute to or stop the initiation and development of anearth fissure. In this paper, effects of the mechanicalproperties of aquifer material, depth of an aquifer, in situstresses, and pre-existing planes of weakness (e.g., faults)on the earth-fissuring process are analyzed.

Driving Forces

Forces that drive, trigger, or prevent fissuring can bedivided into two types: non-hydraulic forces, such asgravity, changes in surface load (dr), and tectonic forces;and hydraulic forces, such as changes in static pore-waterpressure (Helm, 1987), dynamic forces associated withchanges in groundwater flow (Li, 1994; Li and Helm,1998), and capillary forces related to desiccation cracks.Some fissures may be directly induced by hydraulicforces, whereas others are directly related to non-hydraulic forces but indirectly triggered by hydraulicforces.

What are the contributions of these forces to aquifermovement and earth fissuring? Lofgren (1978) usedvertical and horizontal seepage stresses to explain groundmovement caused by groundwater withdrawal. Helm(1994a) demonstrated that Lofgren’s seepage forces arepart of a more general hydraulic driving force for viscousflow that acts on the saturated skeletal frame. Helmemphasized the role of hydraulic driving forces coupledwith material heterogeneities in generating localizedfissures at depth. For pumping an aquifer, this hydraulicforce reduces to the gradient of the excess pore-waterpressure. Li and Helm (Li, 1994; Li and Helm, 1998)established a general relation between driving force anddrag force for both dynamic and viscous pore-water flow.They also demonstrated the contribution of these forcesto aquifer movement. Following the approach of Sheng(1996), Helm’s general hydraulic driving force iscombined in the present paper with conceptual andnumerical models of failure and crack propagation.

The hydraulic driving force on the saturated skeletalframe can be expressed in the form of a body force vector(H~) (Helm, 1987, 1994a, 1994b):

~HH ¼ ~FFb þ qg~rrh ð1Þ

where h is the hydraulic head; q is the density of water; gis the gravity acceleration term; qgr~h is the seepage forceper unit volume, the negative value of which drives water

Sheng, Helm, and Li

Environmental & Engineering Geoscience, Vol. IX, No. 4, November 2003, pp. 351–362352

past the skeletal frame; and F~b is the driving force perunit volume on the entire bulk material (skeletal frameand pore water), or

~FFb ¼ ðqg=��KK�KKÞ~qqb

where

~qqb ¼ n~vvw þ ð1� nÞ~vvs

and ��KK�KK is the hydraulic conductivity tensor of the aquifer,n is the porosity of the saturated aquifer material, v~w andv~s are velocity vectors of water and the solid particles thatcomprise the skeletal frame, and n(vw � vs) is specificdischarge in accordance with Darcy’s law.

These forces are used in later sections to configure theconceptual models and to define the boundary conditionsof the numerical model.

Conceptual Models

An aquifer system is a complex combination of fluidflow, skeletal frame definition, and geological setting.Conceptual models help people to visualize a phenome-non that cannot be directly observed microscopically but

for which macroscopic responses can be observed andmeasured. Several basic conceptual models have beenestablished (Sheng, 1996). Figure 2 shows the four basicconceptual models used in the current analysis.

Conceptual Model 1 is an aquifer containing horizon-tal planes of weakness (Figure 2A). In stratified material,the interfaces between beds are planes of weakness. Withgroundwater pumping, horizontal hydraulic forces in theaquifer may induce shear stress and shear displacementsalong these weakness planes. If shear stresses increase upto shear strength, a shear failure will occur. At a distance,however, shear may dissipate and stop, because shearstress becomes lower than the shear strength ofsedimentary material. At this point, a tensile failuremay occur if the tensile stress is eventually built up highenough to exceed the tensile strength of soil (point A inFigure 2A).

Conceptual Model 2 is an aquifer containing a fault(Figure 2B). Because faults often are poorly permeablediscontinuities in alluvial aquifers, vertical compactionand horizontal displacement of the aquifer materialcaused by pumping wells may induce differentialdisplacements on the two sides of the fault. Suchdifferential displacements can trigger re-shearing oropening of the fault or even generate a new sub-verticalcrack. As pumping continues, this sub-surface crack maymigrate upward and express itself as an earth fissure atthe land surface.

Conceptual Model 3 is an aquifer above a bedrockridge (Figure 2C). There are two distinct mechanisms:first, bending or draping of horizontal bedding planesover the ridge by differential vertical compaction and,second, tensile failure at depth along the top of the ridgecaused by horizontal movement of the aquifer in at leastone direction away from the ridge. The first mechanism(bending or draping) has been studied by Jachens andHolzer (1982). The vertical compaction at some distancefrom the ridge causes the overlying beds on one or bothsides of the ridge to drape or rotate in opposite directions.Differential vertical compaction near a stable bedrockridge may result in horizontal stretching of aquifermaterial over the ridge and formation of a tensile zonewhere the aquifer material is the thinnest. The secondmechanism is based on the horizontal movement of anaquifer that is partly or entirely truncated by the bedrock.This represents a new driving force for initiation anddevelopment of an earth fissure. This horizontal move-ment can also induce tensile failure at depth. Such failurecould occur in the material adjacent to the ridge in thedirection of pumpage, but it could also occur just abovethe top of the ridge, where the aquifer material on bothsides moves away from the ridge if two pumping centersare located on each side. Any such failure may eventuallyprogress upward and initiate a crack in overlyingmaterials as the lateral aquifer movement progresses.

Figure 1. An earth fissure caused by the groundwater withdrawal in the

Las Vegas Valley, Nevada, in which a pen shows the dominant

movement direction of two faces of the earth fissure (taken by Z.

Sheng).

Earth Fissuring Caused by Groundwater Withdrawal


Under some hydrological conditions, a combination ofmechanisms may co-exist.

Conceptual Model 4 is an aquifer containing hetero-geneities (Figure 2D). In this model, aquifer heterogene-ity refers to an abrupt change in the thickness of anaquifer or in beds within an aquifer. Such variations inthickness may result in rotation, vertical shearing, andeven horizontal extension at depth (Helm, 1994a). Forexample, the magnitude of vertical compaction isdifferent on each side of a geometric heterogeneity.Localized differential vertical displacements in compact-ing intervals that contain a geometric abnormality migrateupward into the overlying, non-compacting interval andinduce tilt and shear at the land surface. On the otherhand, localized differential horizontal displacements maygenerate an extensional zone at depth and induce an

opposite direction of rotation as well as fissures at theland surface.

NUMERICAL MODELS AND SENSITIVITYANALYSES

Numerical Models

Even with the simplification of conceptual modelswhen compared to real-world situations, complex bound-ary conditions still exist within each model. Hence,simplified mathematical models are not easily estab-lished, and analytical solutions are not easily evaluated.To examine the effects of different factors on the fissuringprocess using the conceptual models just described, weshall employ a well-established numerical computer

Figure 2. Conceptual models for earth fissuring.

Sheng, Helm, and Li


code. One of the boundary element approaches, namelythe displacement discontinuity (DD) method, is applied tothis study (Crouch, 1976; Crouch and Starfield, 1990; andSheng 1996) to analyze how the induced stresses anddisplacements specified along aquifer boundaries causedby the previously calculated aquifer movement (Helm,1994b; Sheng, 1996) redistribute themselves into result-ing stresses and displacements within the aquifer materialfor the specified conceptual models. One can specifyboundary stresses, boundary displacement, or a combina-tion and then calculate what has not been specified. TheDD method is based on the analytical solution to theproblem of a constant DD over a finite line segment in aninfinite, linearly elastic body (Crouch, 1976). The DDmethod is based on displacement potentials that allowone to compute the stresses and displacements for anelasticity problem by differentiating displacement poten-tial functions.

In the boundary element method, a boundary isrepresented by a set of boundary elements. The boundarystresses or displacements are specified along thoseboundary elements. Once boundary stress or displace-ment conditions are defined for a mechanical model, thedisplacements or stresses inside the domain and along theremainder of the boundary can be calculated using theprinciple of superposition (see the Appendix for details).In this study, those faults and other weakness planesalong which the boundary conditions of stress ordisplacements have not been prescribed are representedby Mohr-Coulomb elements. A Mohr-Coulomb elementis an element for which the total shear stress cannotexceed the shear resistance, and it is allowed to undergoa certain amount of inelastic deformation, or permanentslip, in the transverse direction. The relative displace-ments within an aquifer or along a crack or otherweakness planes that are prescribed (i.e., known) arerepresented by either crack elements or seam elements(Crouch and Starfield, 1990). A seam element representsa crack with a compressible filling. The thickness of theseam element is negligible compared to its lateral extent,and each element acts as a simple spring with specifiednormal and shear stiffness.

The horizontal hydraulic force on the submergedaquifer matrix (i.e., solids) at depth in response togroundwater withdrawal (Helm, 1994a) tends to induceshear displacements and shear stresses along theinterfaces between the aquifer and the overlying andunderlying confining layers. An imposed distribution ofshear displacements and shear stresses along theseinterfaces is applied as a boundary condition to themodel to represent the previously calculated, hydrauli-cally induced horizontal displacements and stresses(Helm, 1994b; Sheng, 1996; and Burbey, 2003). Verticalmovement of aquifer material is expressed in terms of animposed change of vertical displacements or normal

stresses along these boundary elements. Conceptualmodels are simplified as a half-space plane strain problemin the numerical analysis (see the Appendix for details).

Evaluation of Potential Tensile Failures

As mentioned, an earth fissure is a tensile-dominatedfailure. The goal of the current numerical modelingexercises is to identify any likely tensile failure zonecaused by aquifer movement that may develop in theaquifer and the overlying layers. For the four conceptualmodels, different boundary conditions are imposed, andcorresponding, distinct results are obtained. For eachconceptual model, the following conditions are applied:two pumping patterns, namely one pumping center andtwo pumping centers, and three cases of aquifermovement, namely horizontal movement only, verticalmovement only, and a combination of both horizontaland vertical movements. Self-weight and confiningstresses are considered in the calculation. Aquifermovement is imposed along specified interior aquiferboundaries by displacement discontinuities (both verticaland horizontal displacements).

To identify the potential tensile failure zone, we haveto compare the model-calculated stress with the strengthof the sedimentary material. As discussed, a primarycomponent of an earth fissure is the tensile failure;therefore, we chose the tensile stress as an index offailure. To simplify such a comparison, we introduce thestress/strength ratio (Rs) that clearly shows when thestress exceeds the strength of the sedimentary material:

Rs ¼ r3=rt ð2Þ

where r3 is the minimum principal stress (negative fortensile stresses) and rt is the tensile strength. Tensilestrength is considered to be positive. A negative value ofRs less than�1.0 means that tensile failure may initiate atthis location. A potential tensile zone can then be definedby a zone where Rs is less than�1.0, because the absolutevalue of the minimum principal stress in this zone willexceed the tensile strength of the sedimentary material.As a result, the tensile failure is most likely to occur inthis tensile zone, which will eventually develop into anearth fissure at the land surface. In the subsequentsensitivity analysis, Rs is chosen as a key indicator.

Sensitivity Analyses and Controlling Factorsfor Fissuring

Sensitivity analyses quantify the effects that changesin parameter values have on the results of the numericalmodeling. This process helps to determine the mostsensitive factors that control the initiation of a modeled



crack and its propagation. In the analyses, the results ofcase 3, in which both horizontal and vertical aquifermovements are implemented, will be used as a basicreference for each model. As a basic reference, themodeled aquifer is located at a depth of 200 m. The basicstrength parameters for soil masses are listed in Table 1(Conwell, 1965) and are used in the evaluation ofpotential failures. They are also used as the basic valuesfor parameters in the factor sensitivity analyses.

Sensitivity analyses are performed by changing oneparameter value at a time. The magnitude of change in Rs

from the basic solutions is a measure of the sensitivity ofRs to a particular parameter. Here, an increase in Rs

means that its absolute value decreases, because thetensile stress is negative. In this paper, sensitivityanalyses of several parameters (i.e., factors) are de-scribed, including change in strength of the weaknessplanes—namely cohesion (cf) and angle of internalfriction ( ff), geometry of pre-existing weakness planes,horizontal distribution of aquifer/aquitard thickness,depth of an aquifer, in situ confining stresses, and soon. Factor sensitivity analysis using the DD methodprovides an insight regarding factors that control theinitiation and propagation of a crack. Two or morefactors, as a group, may intensify or reduce theircombined influence on the fissuring process. In thispaper, factors are analyzed individually, not as a group.

For Conceptual Model 1 (Figure 2A), the overlyingand/or underlying weakness planes are parallel to thenearly horizontal aquifer. The effects of four parameters onRs—confining stress, Young’s modulus and Poisson’sratio of the aquifer material, and depth of the aquifer— areevaluated. As shown in Figure 3, Rs increases with anincrease in the lateral confining stress. It should be notedthat the horizontal/lateral component of stresses increasesor decreases in terms of the percentage of self-weight of theoverlying soil. Once the confining stress becomes tensile(i.e., the negative side of the x-axis), Rs changes rapidly.This means that when one of the pre-existing lateral stressfields is tensile, it is easier for the aquifer movement tocause tensile failure than when all pre-existing stress fieldsare compressive. With increase in Young’s modulus andPoisson’s ratio, Rs decreases linearly. Increase in depth ofan aquifer results in an increase of Rs. After an aquiferreaches a certain depth (220 m in this case, as the 10percent increase in Figure 3), no significant change is

observed in Rs with any further increase in depth of theaquifer. The results suggest that a shallow aquifer is morelikely than a deep aquifer to cause tensile failure inresponse to the same driving force or aquifer movementcaused by pumping. For this model, the confining stressand depth of the aquifer are two important factors thatrequire attention when one is concerned about possibledevelopment of an earth fissure within a shallow aquifer.

In Conceptual Model 2 (Figure 2B), an aquifer ispartly or wholly truncated by a pre-existing fault. For thismodel, changes are made in nine parameters: confiningstress, Young’s modulus and Poisson’s ratio of the aquifermaterial, cohesion and angle of friction of the fault,compressive modulus and shear modulus of the fault, dipangle of the fault, and depth of the aquifer. They all causechanges in Rs. The results indicate that Rs increases withan increase in confining compressive stress. After theconfining stress is increased to 10 percent of the self-weight of overburden, no significant change in Rs occurswhen confining stress is increased further (Figure 4A).With any decrease in the confining stress (i.e., thenegative side of the x-axis), Rs decreases approximatelylinearly. The angle of friction and dip angle of the faultcause great changes in Rs (Figure 4A). The results showthat Rs decreases approximately linearly with a decreasein the angle of friction of the fault before the frictionangle reaches 10 percent less than the basic value of 208.After that point, Rs decreases rapidly as the angle offriction decreases (Figure 4A), and at this point, the

Table 1. Basic parameters for soil masses.

Parameter Basic Value

Tensile strength 0.01 MPa

Compressive strength 0.20 MPa

Angle of friction of the weakness plane 258

Cohesion of the weakness plane 0.05 MPa

Figure 3. Effects of changes in parameters on stress/strength ratio Rs

for Conceptual Model 1.

Sheng, Helm, and Li


presence of a fault supplies a favorable condition for anaquifer to experience tensile failure both at depth and atthe land surface. The results also indicate that at a certaindip angle, a fault causes Rs to reach a minimum value. Inthis case (i.e., Conceptual Model 2), the critical dip angleof the fault for the minimum Rs is 608 (Figure 4A). Nosignificant changes occur in Rs that result from changes inYoung’s modulus and Poisson’s ratio, cohesion of thefault, or compressive and shear moduli of the fault(Figure 4B). Increases in depth of an aquifer also do notcause any significant change in Rs (Figure 4B). For thismodel, the confining stress still plays an important role.The angle of friction and the dip angle of the faultbecome important factors in triggering tensile failure.Some critical values for those two angles are favorablefor development of fissures. The most favorable dip angleof a fault for earth fissuring under the specified conditionsis 608. A critical angle of friction of the fault is 188. Asmall, confining compressive stress or tensile stressprovides a favorable condition for earth fissuring.Increase in the friction angle may prevent overlyingmaterials from tensile failure; any decrease in the frictionangle may help to trigger earth fissuring.

In Conceptual Model 3 (Figure 2C), a ridge of fixedbasement rock protrudes into the overlying sediments.For this model, effects of four parameters on Rs areevaluated: confining stress, Young’s modulus andPoisson’s ratio of the aquifer material, and depth of theaquifer. Figure 5 shows the results of the sensitivityanalysis for Conceptual Model 3. The value of Rs

increases in proportion to the confining compressivestress and decreases linearly with the increase in Young’smodulus and Poisson’s ratio (Figure 5). An increase inthe depth of an aquifer results in an increase in Rs. Afteran aquifer reaches a certain depth (220 m in this case, asthe 10 percent increase in Figure 5), no significant changeis observed in Rs with any further increase in depth of theaquifer. It should also be pointed out that a decrease indepth of the aquifer from its basic value of 200 m doesnot cause any significant change in Rs. For ConceptualModel 3, the change in depth of an aquifer may play animportant role in earth fissuring, at least within themodeled range (200–220 m in this case). It should also benoted that the critical depth of aquifer (200–220 m in thiscase) varies with geological environments and hydrolog-ical conditions. Confining stress plays the similar role as

Figure 4. Effects of changes in parameters on stress/strength ratio Rs for Conceptual Model 2.



Young’s modulus and Poisson ratio. Evidently, no strongfactor among these three parameters controls the fissuringprocess for Conceptual Model 3.

In Conceptual Model 4 (Figure 2D), an abrupt changein thickness occurs in the aquifer and the highlycompressible confining layer. For this model, changesare made in four parameters: confining stress, Young’smodulus, Poisson’s ratio, and depth of the aquifer. Thesechanges in parameters cause changes in Rs. Results showthat Rs increases with an increase in confining compres-sive stress. After the confining stress is increased to 10percent of the self-weight of overlying soil, however, Rs

decreases with the increase in confining stress (Figure 6).The value of Rs changes rapidly once the confining stressbecomes tensile (i.e., the negative side of the x-axis). Thismeans that when the pre-existing stress field is tensile, itis easier for the aquifer movement to cause tensile failurethan when only a compressive stress field exists. Thevalue of Rs decreases linearly with the increase inYoung’s modulus and Poisson’s ratio (Figure 6). Theincrease in depth of an aquifer results in an increase of Rs,but the decrease in depth of an aquifer from its basicmodeled value of 200 m does not cause any significantchange in Rs. The results indicate that a deep aquiferexhibits less possibilities of earth fissuring than a shallowone exhibits. For Conceptual Model 4, the confiningstress still plays a very important role in earth fissuring. Apre-existing tensile stress field or small in situ compres-

sive stress field favors the occurrence of earth fissuring. A

change in depth of the aquifer also plays an important

role in earth fissuring within the modeled range (200–220

m in this case). An increase in depth of an aquifer may

prevent overlying material from experiencing tensile

failure. It should be noted that the critical depth of an

aquifer (200–220 m in this case) varies with geological

environments and hydrological conditions.

In summary, the numerical model simulated well the

influence of different parameters on the initiation of earth

fissures under different geological environments. The

results of the sensitivity analyses indicate that some

factors control the initiation of a fracture at depth,

whereas others do not. A factor may play an important

role in one geological environment but not be a dominant

factor in another environment. Therefore, some of these

factors can be considered as key factors for earth

fissuring. They also likely are keys for the prediction

and control of earth fissuring in the field. The confining

stresses play a very important role in earth fissuring in all

geological environments. Tensile or lower compressive

confining stresses tend to favor the initiation of a fracture

at depth. The lower the strength of a soil mass is, the

more likely an earth fissure will occur. If a fault is

involved, its friction angle and dip angle are additional

Figure 5. Effects of changes in parameters on stress/strength ratio Rs

for Conceptual Model 3.Figure 6. Effects of changes in parameters on stress/strength ratio Rs

for Conceptual Model 4.

Sheng, Helm, and Li


controlling factors for initiation and growth of a newfracture. Some critical values for those two angles aremost favorable to the development of fissures. The mostfavorable dip angle of a fault for earth fissuring underconditions described in this paper is 608. A criticalfavorable angle of friction of the fault is 188. Two or morefactors may intensify or reduce their combined influenceson the fissuring process. In general, for the same pumpingstress, a shallow aquifer is more likely than a deep one toexperience tensile failure.

MECHANISMS OF EARTH FISSURING

Earth fissuring is a multi-step process that is influencedby a variety of factors. In this paper, Conceptual Model 4will be used as an example to show the initiation anddevelopment of earth fissuring. Factors that affect thebehavior of earth fissures will also be addressed for eachstep.

First, as pumping begins, a hydraulic force drivesaquifer material to move horizontally and vertically(Helm, 1994a). This results in land subsidence at the landsurface. At the same time, aquifer movements alsoproduce differential displacement at locations where theoverlying clay layer exhibits abrupt changes in itsthickness. In turn, this may create tensile or shear zonesthat are in a pre-failure condition (Figure 7). At this stage,any decrease in the confining stresses, which may becaused by other pumping activities or tectonic movement,helps to initiate cracks or failures. Factor sensitivityanalyses also indicate that a deeper aquifer may pose lessrisk than a shallow one regarding initiation of an earthfissure if the same pumping stress is applied. Mechanicalproperties of the overlying clay will also determine thecharacteristics of failure. At this stage, if the pumpingstress is reduced, a pre-failure zone may not developfurther into cracks or express itself as an earth fissure atthe land surface.

Second, as pumping continues, a pre-failure zone mayextend further upward by the continued aquifer move-ment. As aquifer material cumulatively moves toward the

discharge well, an activated tensile zone may migrateinto overlying layers and form a crack where the vadosezones are sufficiently brittle, such as those in arid orsemi-arid regions (Figure 8). Such a crack may belocalized near pre-existing geological structures, such asan interface between the confining layer (clay) and theaquifer (sand). In humid regions, however, the sametensile zone (lateral stretching) at depth will simplyexpress itself as a transient sub-vertical plane ofenhanced porosity within and crossing the vadose zone.At this stage, the strength of the weakness plane playsa very important role in fostering or halting furtherdevelopment of the failure.

Third, once a sub-surface crack is formed at depth witha certain length and aperture opening, actual failure at theland surface can be triggered by a number of factors. Onesuch triggering force results from a possible suddenincrease of pore-water pressure in a pre-failure zone or ina sub-surface crack. The increase in pore-water pressuremight be caused by artificial recharge or by infiltratingprecipitation. According to field observations (Bell, 1981;Holzer, 1984), concealed or sub-surface cracks oftendevelop into fissures at the land surface during or shortlyafter a rainstorm. Another triggering force may resultfrom the aquifer movement caused by additionalgroundwater withdrawal from the same or a neighboringwellfield. Additional groundwater withdrawal results infurther horizontal movement within the aquifer. In turn,such movement might trigger a sub-surface crack topropagate upward and eventually manifest itself as anearth fissure at the land surface in arid or semi-aridregions. In humid regions, the sub-vertical zone ofenhanced porosity may eventually intercept the landsurface. It will probably remain undetected based onsimple visual inspection, even when such an upwardmigrating plane of enhanced porosity intersects the landsurface. One can, however, expect a highly enhancedvertical flow of water to cross the vadose zone locallyduring the next rain storm. At that time, both the earthfissure and the upward plane of enhanced porosity will

Figure 7. The first step of earth fissuring: A pre-failure zone formed at

depth driven by the aquifer movement.

Figure 8. The second step of earth fissuring: A crack or fracture formed

at depth.



provide a conduit for the runoff to carry surfacepollutants into the underlying aquifer and to degradethe native groundwater. At this stage, strength of theoverlying soil material may also become a dominantfactor in controlling or masking the sub-surface cracks.Finally, once the earth fissures form at the land surface,they may remain active in response to on-going pumpingpractices or become inactive because of release ofpumping stresses or the filling of loose, overlyinggranular material into the open space of fissures (Bell,1981; Carpenter, 1993; and Helm, 2000).

CONCLUSIONS AND DISCUSSION

Factor sensitivity analyses of the numerical modelindicate that some factors strongly influence the initiationof a fracture at depth but that others do not. A factor mayplay an important role in one geological environment butnot be a dominant factor in another environment.Therefore, some of these factors probably play animportant role in actual earth fissuring. They can alsobe considered as key factors for earth fissuring and likelyare keys for the prediction and control of earth fissuringin the field.

In situ confining stresses play a very important role inearth fissuring in all geological environments. Tensile orlower compressive confining stresses tend to favor theinitiation of a fracture at depth. An increase in depth of anaquifer may prevent overlying material from experienc-ing tensile failure. Therefore, a given induced aquiferdeformation is more likely to trigger tensile failure withina shallow aquifer than within a deep one. The lower thestrength of a soil mass, the more likely an earth fissurewill occur within the tensile zone. The effects of water onthe fissuring process, such as degree of saturation, depthto water table, influence of water on strength of soil, andso on, need to be studied for a better understanding of themechanism of fracturing in soil masses.

If a pre-existing fault is involved in the aquifermovement and development of earth fissures, its frictionangle and dip angle are controlling factors for initiation andgrowth of a new fracture in addition to the factorsmentioned above, namely in situ stresses and depth of theaquifer. Some critical values for those two angles are mostfavorable for the development of fissures. The mostfavorable dip angle of a fault for earth fissuring underconditions described in this paper is 608. A critical angle offriction of the fault is 188. If a bedrock ridge is involved, theeffect of the ridge on the initiation and development ofa fracture depends on the depth of an aquifer and theconfining stresses. The geometry of the ridge, lateralextension of an aquifer, distance between two pumpingcenters, and so on may also change the role of aquifermovements in the generation of fissures, which needs to be

studied. Although inter-relationships among factors andtheir combined effects on initiation and development ofearth fissures are not evaluated in this study, two or morefactors may intensify or reduce their combined influenceson the fissuring process. To predict and control earthfissuring, their combined relationships also require in-vestigation. A similar sensitivity analysis may also beapplied to test the effect of changes in parameter values oneffects other than Rs, such as displacement.

Earth fissuring is a multi-step process that is controlledby a variety of factors, as discussed in this paper. First,the aquifer movement relative to the fixed boundariesinitiates a pre-failure tensile zone at depth. This pre-failure tensile zone extends upward and eventuallyintercepts the land surface. Under conditions that causea brittle vadose zone, such as those in arid or semi-aridregions, an upward-migrating tensile zone may developinto a fracture or crack at depth and finally express itselfas an earth fissure at the land surface. Understanding howpre-failure tensile zones are initiated and migrateprovides a great opportunity to control or reduce the riskof earth fissuring in arid and semi-arid regions. In morehumid regions, it also provides a similar opportunity tocontrol the tendency of vertical zones of enhancedporosity at depth to migrate upward across the vadosezone. When such a vertical zone of enhanced porosityintercepts the land surface, one can expect a highlyenhanced vertical flow of water to cross the vadose zonelocally during rainstorms, streamlining the path of anysurface pollutants to the underlying aquifer.

ACKNOWLEDGMENTS

This research is supported by the Las Vegas ValleyWater District, the Nevada Bureau of Mines andGeology, and the State Water Research Institute Program.This project is also supported in part by the Massie Chairof Excellence program of the U.S. Department of Energy,the Hatch Project of the U.S. Department of Agriculture,and the Texas Agricultural Experiment Station. Theauthors thank Michael S. Bonkowski of Bonkowski andAssociates, Inc., Dr. Thomas J. Burbey of Virginia Tech,Dr. Ari Michelsen of Texas A&M University, Dr.Jonathan G. Price of the Nevada Bureau of Mines andGeology, and the anonymous reviewer for their construc-tive comments to improve this manuscript.

REFERENCES

BELL, J. W., 1981, Subsidence in Las Vegas Valley: Nevada Bureau ofMines and Geology Bulletin 95, 84 p.

BELL, J. W. AND PRICE, J. G., 1991, Subsidence in Las Vegas Valley,1980–91: Nevada Bureau of Mines and Geology Project Report.

BURBEY, T. J., 2003, personal communication. Department ofGeological Sciences, Virginia Tech, Blacksburg, VA 24061.

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CARPENTER, M. C., 1993, Earth-Fissure Movements Associated withFluctuations in Groundwater Levels near the Picacho Mountains,South-Central Arizona, 1980–4: U.S. Geological Survey Pro-fessional Paper 497-H, 49 p.

CONWELL, F. R., 1965, Engineering Geology and Foundation ConditionSurvey of Las Vegas, Nevada. Unpublished report to the USDepartment of Energy: John A. Blume and Associates, 49 p.

CROUCH, S. L., 1976, Solution of plane elasticity problems by thedisplacement discontinuity method: International Journal Nu-merical Methods Engineering, Vol. 10, pp. 301–343.

CROUCH, S. L. AND STARFIELD, A. M., 1990, Boundary ElementMethods in Solid Mechanics with Application in Rock Mechanicsand Geological Engineering: Unwin Hyman, London, 322 p.

DOTY, G. C. AND RUSH, F. E., 1985, Inflow to a Crack in PlayaDeposits of Yucca Lake, Nevada Test Site, Nye County, Nevada:U.S. Geological Survey Water Resources Investigation Report84-4296, 24 p.

HELM, D. C., 1987, Three-dimensional consolidation theory in terms ofthe velocity of solids: Geotechnique, Vol. 37, No. 3: pp. 369–392.

HELM, D. C., 1994a, Hydraulic forces that play a role in generatingfissures at depth: Bulletin Association Engineering Geologists,Vol. 31, No. 3, pp. 293–304.

HELM, D. C., 1994b, Horizontal aquifer movement in a Theis-Thiemconfined system: Water Resources Research, Vol. 30, No. 4, pp.953–964.

HELM, D. C., 2000, Fissures in Yucca Flat dry lake bed, Nevada testsite. In Looney, B.B. and Falta, R.W. (Editors), Vadose ZoneScience and Technology Solutions: Battelle Press, Columbus,OH. CD-ROM.

HOLZER, T. L., 1984, Ground failure induced by groundwaterwithdrawal from unconsolidated sediments. In Holzer, T. L.(Editor), Reviews in Engineering Geology, Vol. VI: GeologicalSociety of America, pp. 67–105.

JACHENS, R. C. AND HOLZER, T. L., 1982, Differential compactionmechanism for earth fissures near Casa Grande, Arizona:Geological Society America Bulletin, Vol. 93, pp. 998–1012.

LI, J., 1994, Fundamentals of Aquifer Multiphase Flow in Response toInertial and Viscous Forces: Unpublished Ph.D. Dissertation,University of Nevada, Reno: 566 p.

LI, J. AND HELM, D. C., 1998, A general relation of viscous drag anddynamic driving force within an aquifer and how they reduce toDarcy’s law: Water Resources Research, Vol. 34, No. 7, pp.1675–1684.

LOFGREN, B. E., 1978, Hydraulic stresses cause ground movement andfissures, Picacho, Arizona: Geological Society America AbstractsPrograms, Vol. 10, No. 3, p. 113.

SHENG, Z., 1996, Conceptual and Numerical Models for the Mechanicsof Fissuring Caused by Groundwater Withdrawal: UnpublishedPh.D. Dissertation, University of Nevada, Reno: 308 p.

APPENDIX: NUMERICAL MODEL ANDSENSITIVITY ANALYSIS

Numerical Model and Boundary Configurations

The boundary element method (BEM) solves bound-ary problems by making approximations along theboundary of the problem domain. The boundary isrepresented by a set of boundary elements. Eitherboundary stresses or displacements can be specifiedalong those boundary elements. Once boundary stressesor displacement conditions are defined for a mechanicalmodel, the displacements and/or stresses inside thedomain can be calculated using the principle of

superposition. At points where stresses are specifiedalong the boundary, displacements are calculated, andvice versa. In this study, the displacement discontinuity(DD) method (Crouch, 1976; Crouch and Starfield, 1990;and Sheng, 1996), which is one approach of the BEM, isemployed to examine the conceptual models that areintroduced in the paper. The DD method is based onanalytical solutions to the problem of a constant DD overa finite line segment in an infinite, linearly elastic body(Crouch, 1976). The DD method is a method based ondisplacement potentials that allow one to compute thestresses and displacements for an elasticity problem bydifferentiating displacement potential functions. It is usedhere to analyze the induced stresses and displacementsalong aquifer boundaries that are associated with aquifermovement and to calculate the resulting stresses anddisplacements in the host material for the specifiedconceptual models (i.e., for the specified boundarygeometry).

The numerical procedure for the DD method consistsof placing N displacement discontinuities of unknownmagnitude along the boundaries of the domain to beanalyzed, then setting up and solving a system ofalgebraic equations to find the discontinuity values thatproduce the prescribed boundary tractions or displace-ments (Crouch, 1976; Crouch and Starfield, 1990).

A discrete approximation to the continuous distributionof DD is made by referencing to the N subdivisions of thecrack. Each of these subdivisions is a boundary elementand represents an elemental DD. There are several kindsof boundary elements, such as crack element, seamelement, and Mohr-Coulomb element (i.e., fault element).In this study, the relative displacements within an aquiferor along a crack or other weakness plane that areprescribed (i.e., known) are represented by either crackelements or seam elements (Crouch and Starfield, 1990).A seam element represents a crack with a compressiblefilling. The thickness of the seam element is negligiblecompared to its lateral extent, and each of the elementsacts as a simple spring with specified normal and shearstiffness. The pre-existing faults and other weaknessplanes, on which the boundary conditions (i.e., the knownspecified stress or displacements) are not prescribed, arerepresented by Mohr-Coulomb elements. A Mohr-Coulomb element is an element for which the total shearstress cannot exceed the shear resistance, and it is allowedto undergo a certain amount of inelastic deformation, orpermanent slip, in the transverse direction.

Conceptual models are simplified as a half-space planestrain problem in the numerical analysis. Stresses anddisplacements in the plate are found by summing theinfluence of individual boundary elements on all otherelements. Self-weight and distributed confining stressesare also applied. The horizontal hydraulic force on thesubmerged aquifer matrix (i.e., solids) at depth in



response to groundwater withdrawal (Helm, 1994a) tendsto induce shear displacements and shear stresses alongthe interfaces between the aquifer and the overlying andunderlying confining layers. An imposed distribution ofshear displacements and shear stresses along theseinterfaces is applied to the model to represent thehydraulically induced horizontal displacements andstresses. Vertical movement of aquifer material isexpressed in terms of an imposed change of verticaldisplacements or normal stresses along these boundaryelements. Figure A1 shows some examples of theimposed boundary conditions in terms of displacementdiscontinuities. A positive vertical displacement Dn

means that an aquifer material is compressed during thegroundwater withdrawal. Figure A1a shows two patternsof the vertical displacement discontinuities. Figure A1band c show relative horizontal displacement discontinu-ities Ds for the overlying weakness planes and underlyingweakness planes during the groundwater withdrawal.

Sensitivity Analyses

The initiation of a crack is dependent on the appliedload, geometry of the crack, strength of the aquifermaterial, local boundary conditions, and other factors.Each factor plays a different role in the initiation and

propagation of a crack. To determine the roles of each,factor sensitivity analyses were conducted for severalfactors.

Sensitivity analyses are performed by changing oneparameter value at a time and observing the changes in Rs

as defined in this paper. The value of Rs is a ratio of theminimum principal stress and the tensile strength ofsedimentary material of the aquifer. The magnitude ofchange in Rs from the basic solutions is a measure of thesensitivity of Rs to a particular parameter. Here, anincrease in Rs means that its absolute value decreasesbecause the tensile stress is negative. In this paper,sensitivity analyses are conducted for following factors:strength of weakness planes (i.e., cohesion cf and angle ofinternal friction ff), geometry of pre-existing weaknessplanes, horizontal distribution of aquifer/aquitard thick-ness, depth of an aquifer, confining stresses, and so on.The value of Rs is used to quantify the tensile zone, andthe failure is directly related to tensile zone. Therefore, Rs

is used to quantify the failure and to determine the mostsensitive factor that controls the initiation of a modeledcrack and its propagation. To compare effects of differentfactors on Rs, the percentage of changes in each factorfrom its basic value is used in analysis. In general, a steepslope shows a sensitive factor, and a gentle slope denotesa non-sensitive factor.

Figure A1. Displacement discontinuities Dn and Ds of the boundary elements.

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fissuring groundwater withdrawal

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