Karst collapse related toover-pumping and a criterionfor its stabilityKeqiang He Æ Changli Liu Æ Sijing Wang

Abstract Karst collapse, caused by natural orartificial abstraction of groundwater, has been anenvironmental geological problem. The origin ofkarst collapse has been described by the potentialerosion theory and the vacuum absorption erosiontheory. However, a mathematical prediction criteri-on for karst collapse cannot be established by thesetwo theories. This paper, from a new perspective,attempts to explain the microcosmic mechanism ofkarst collapse on the basis of these two theories. At acertain point in the unconsolidated soil covered onkarst caves, when shearing stress surpasses shearstrength of the soil, it fails under the mechaniceffects of water and gas as well as gravity pressure.With an increase in damage points, a break planeappears and the soil overlying the karst caves iscompletely damaged and, thus, the ground surfacecollapses. On the basis of Mohr–Coulomb damagetheory and previous studies, a prediction criterion ofkarst collapse is presented. An example displays thecalculating process of the model and proves itsreliability by analyzing nine typical collapses causedby a pumping test in Guizhou Province, China.

Keywords Environmental geological problem ÆKarst collapse Æ Prediction criterion ÆShearing strength Æ Shearing stress

Introduction

Karst collapse is a kind of environmental and geologicalphenomenon of surface deformation or collapse, causedby the failure of soil because of non-equilibrium of allkinds of pressures induced by water and air, the soil’sdeadweight and other forces imposed on the loose soilcover of karst cavities. It mainly appears in the form ofcone-shaped slumping pits, which are different frominhomogeneous depressions caused by mining-out andlarge-scale ground settlement caused by pumpinggroundwater and dewatering soil. Natural karst collapse isgenerally small in scale, so it normally does not exert asudden serious effect on human life. However, karstcollapses caused by human activities, such as pumpinggroundwater for water supply and mine dewatering, aregenerally of large scale and paroxysmal. They often appearin a crowed area and can pose a serious threat to buildingsand human safety. The genesis of such karst collapses hasbeen described by the potential erosion theory and thevacuum suction theory. Recently, some researchers havemade semi-quantitative and quantitative stability predic-tions of the soil cover by progressive regression analysis ofmultivariate statistical analysis theory. They have consid-ered the cohesion angle of internal friction, thickness,water table and lowering of groundwater of the soil cover(Huang and others 1985). Some researchers have at-tempted to judge the possibility of collapse through eval-uating the collapse resistances and collapse-inducing force(Jiang 1998; Wang 1998). The analysis of the formationmechanism and inducing factors for karst collapse, com-bined with the theory of soil limit equilibrium, has led to anew prediction criterion for karst collapse. The reliabilityof the criterion is tested by the karst collapses thatoccurred in Guizhou Province, China.

A new view of the originof karst collapse

Basic conditions of karst collapseThere are three basic conditions for karst collapse:

1. The soluble bedrock has opening karst features, such asshafts, karst caves and deep karst cracks, whichfacilitate groundwater movement.

Received: 28 March 2002 / Accepted: 22 July 2002Published online: 18 September 2002ª Springer-Verlag 2002

K. He (&)Dept of Civil Engineering,Qingdao Institute of Architecture and Engineering,Qingdao, P.R. ChinaE-mail: keqianghe@sina.com

C. LiuInstitute of Hydrogeology and Engineering Geology,CAGS, Zhengding, P.R. China

S. WangInstitute of Geology, Chinese Academy of Science,Beijing, P.R. China

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720 Environmental Geology (2003) 43:720–724 DOI 10.1007/s00254-002-0669-x

2. The cover is loose soil or weak rock layer, which iscrucial to karst collapse; most collapse occurs in soiland some in weak rock layers.

3. The pressure and action of water and air caused by thefluctuation of the water table and infiltration of surfacewater induce karst collapse.

Analysis of the mechanisms of karst collapsesThere are several traditional theories to explain karstcollapse (Li and Wang 1990), but two of them are moreinfluential. One is the potential erosion theory. This theoryemphasizes that the erosional ability of groundwater in-creases as the water table is decreased as a result of natureor human factors. The groundwater outwashes, erodes,scours and carries soil particles over time to form a soilcave at the interface between the soluble bedrock andcover. The increasingly enlarged cave may lead to twopossibilities. If the soil cover is thick and competent, anatural balanced arc will be formed in the soil and the cavewill not collapse without other inducing factors. If the soilcover is thin and less competent, the soil cave will continueto enlarge and cut through the soil layer, thus forming acollapse pit. The other theory of karst collapse is thevacuum absorption erosion (Lu 1986), which focuses onthe relatively airtight confined karst water. Whengroundwater suddenly falls by a large amplitude and thewater table drops below the floor of the cover, thegroundwater will change from confined water to uncon-fined water, and a cave with a low air pressure inside willoccur between the water table and the floor of the cover.The formation of the ‘‘vacuum cave’’ has two effects: thesuction-erosion of the floor of the soil cover and the‘‘punching’’ of the surface of the cover caused by the at-mospheric pressure outside the cave. Under the combinedaction of ‘‘suction inside the cave and pressure outside thecave’’, paroxysmal collapse takes place. The relationshipbetween karst collapse and the groundwater table isshowed in Fig. 1.The potential erosion theory and the vacuum absorptionerosion theory can explain some origins of karst collapsemacroscopically. Because the two theories do not give agood description of the process of collapse and its mi-cromechanism, a prediction criterion cannot be estab-lished on the basis of these two theories. No matterwhether it is caused by the potential erosion or by thevacuum suction erosion, all collapses are the result of soilfailure due to the unbalance of forces. The generation and

development of a collapse starts with a soil cave in thesoil cover with a certain thickness. When the water tablefalls quickly, and when the groundwater table falls to acertain level to form a relatively low-pressure cave, thedifferential pressure DP between the atmosphere pressureand the low pressure of cave acts on the soil cover. Be-cause of the lowering of the water table, the soil loses itsbuoyant support and the deadweight pressure of the soilincreases. Under the action of these forces, when a nor-mal plane shear stress of a point in soil is equal to theshear strength of soil (i.e., sf ¼ C þ tg/), the point startsto fail.After failure of the point, the stress acts on another point,and then that point fails. Developing in this way, thefailure points increase sequentially and connect to form acontinuous failure plane. Along this failure plane, the soilfalls or slides towards the cave and the soil is carried awayby flowing water, and thus a collapse pit finally occurs.

Criterion for karst collapse

According to the two traditional theories of karst collapse,in addition to the basic conditions, there are also otherfactors that affect collapse, such as the thickness (H) of thesoil cover, the strength index (C, /), the size (radius R) ofthe soil cave, the drawdown (Dh) of the water table, theflowing velocity(Uw), and the differential pressure DPbetween the atmosphere pressure P0 and the relative lowpressure P¢ in the soil cave, that is DP ¼ P0 � P0.To establish the karst collapse predication criterion, someassumptions are made as follows:

1. The failure of soil cover abides by the Mohr–Coulombcriterion and plastic equilibrium theory (Yang 1987):

r1 � r3 ¼ 2 sin /r1 þ r3ð Þ

2þ C

tg/

� �ð1Þ

where r1 and r3 represent the maximum and minimumprincipal stresses of a point in soil, and C and /represent the strength index.

2. The opening of a karst cave or the soil cave in the soilcover is circular in shape, and its radius is R.

3. The differential pressure DP ¼ P0 � P0 between atmo-spheric pressure and the pressure in the soil cave actson the soil cover, and the vertical compressive stressbelow the central point of soil can be calculated in

Fig. 1Diagrams showing the relationship betweenkarst collapse and groundwater table. ANatural state, B water-extraction state

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Environmental Geology (2003) 43:720–724 721

terms of the vertical compressive stress under theevenly distributed vertical loads based on the circulararea, which should satisfy the follow equation(Yang1987):

rz ¼ DP 1� Z2=R2

1þ Z2=R2

� �� �3=2

ð2Þ

where rz is the vertical compressive stress at the depthZ of soil, Z is the depth of a point, and R is the radius ofthe soil hole.

4. If the karst groundwater and the soil pore water arephreatic water relative to a unifying water table, thevertical compressive pressure after lowering the watertable and the action of flow velocity of the groundwaterare expressed as:

P ¼ cZ þ cwU2w=2g ð3Þ

If the karst groundwater is confined, the verticalcompressive pressure can be expressed as:

P ¼ cZ þ cw h0 � h1ð Þ þ cwU2w=2g ð4Þ

where cw is the unit weight of water, Uw is the flowvelocity of water, h0 is the initial level of the confinedgroundwater, h1 is the confined groundwater level afterpumping, �cw h0 � h1ð Þ is the buoyant support loss dueto the lowering of the confined karst groundwater table,and cwU2

w=2g is the kinetic pressure caused by the flowof groundwater, i.e., the erosion pressure to soil.

5. The lateral soil pressure coefficient is K0, thus thenormal compressive stress of a point at depth Z belowthe surface can be expressed as:

r1 ¼ rZ þ P ð5Þ

r3 ¼ K0r1 ¼ rZ þ Pð Þ � K0 ð6Þ

Substituting Eqs. (4) and (5) into Eq. (1), the followingequation can be obtained:

2Ccos/1� sin /ð Þ 1� K0ð Þ ¼ rZ þ P ð7Þ

Substituting Eqs. (2) and (3) into Eq. (7), the criterionof karst collapse under the condition of phreatic watercan be obtained as follows:

2Ccos/1�sin/ð Þ 1�K0ð Þ¼cZþcwU2

w

2gþDP 1� Z2=R2

1þZ2=R2

� �� �3=2

ð8Þ

Substituting Eqs. (2) and (4) into Eq. (7), the criterionof karst collapses under the condition of confined karstgroundwater can be obtained as follows:

2Ccos/1�sin/ð Þ 1�K0ð Þ¼cZþcw h0�h1ð ÞþcwU2

w

2g

þDP 1� Z2=R2

1þZ2=R2

� �� �3=2 ð9Þ

Let F represent the left side of Eqs. (8) and (9), and F¢represent the right. For the soil strata on a certain cave,F can be regarded as a constant. The stable coefficientof a karst collapse is defined as:

K ¼ F=F 0 ð10Þ

When K>1, the soil cover is stable; when K=1, the soilcover is in a state of limited equilibrium; if K<1, the soilis unstable and collapse is going to occur. Equations (8)and (9) are the criteria of karst collapses. Many factors,such as the thickness and strength of the soil cover, thesize of the karst cave and soil cave, fluctuations of thewater table, types of karst water, forces of erosion of soilcaused by the flow velocity of groundwater, and thevacuum negative pressure are all taken into account inthe criteria.

Analysis and evaluationof a karst collapse caseby means of the criterion

The karst collapse in Niuchang pumping test area (Fig. 2)of Guizhou Province, China, is taken as an example for theprediction by means of the criterion.The terrain of this area is flat and open, and the XimenRiver runs through it. It encompasses an area of about3.4 km2, which is mostly covered by Quaternary soil, andthe bedrock is only exposed along the Ximen River or inlocal places. The soil is generally 1.5–7.4 m thick. Thereare nine water supply wells and two coal pits. Sincegroundwater started to be pumped at the end of the 1970smany collapses have occurred. According to a survey,there are more than 70 collapse points, the biggest one ofwhich is 30 m long and 16.2 m wide, and the deepest one

Fig. 2Hydrogeological schematic map of the test area. 1 Quaternary andcarbonate rock aquifer; 2 broken bits clipping carbonate rock aquifer;3 watertight stratum; 4 water-resisting fault; 5 spring; 6 main hole andobservation hole of pumping test

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722 Environmental Geology (2003) 43:720–724

is more than 10 m deep. From 1985 to 1988, four watersupply wells were added. Because of over-pumping, large-scale collapses have taken place, especially around No. 4well. From 5–14 April 1985, a pumping test was carried outfor more than 180 h. The pump rate was 1,400 t/day with adrawdown of 6.8 m, but no collapse occurred. Later, from10 October 1986 to 20 February 1987, another pumpingtest was performed for 125 days and the pump rate was2,020 t/day. The amount of drawdown of water table in-creased from 8.4 m at the beginning to 15 m at the endand collapse occurred 24 m from the head of No. 4 well inthe first day of pumping. During the first 2 months of thepumping test collapses increased abruptly. During thisperiod, 38 collapse pits were formed. Most of them werewell shaped and some were pot or dish shaped.Well tests show that the Quaternary cover in this districthas a binary structure. The upper part of the upper stratais cultivated soil, 0.20 m thick, and the lower part is siltysandy loam, 0.8–1.10 m thick, with a unit weight ofc=16.4–18.6 kN/m3, the cohesion C=6–18 kPa, the angle ofinternal friction /=8.72–18.22�, and the lateral earthpressure coefficient K0=0.65. More detailed tests wereperformed on nine collapse pits caused by pumping ofNo. 4 well from 1986 to 1987, and the test data andevaluation results are shown in Table 1.According to the data in Table 1 and Eq. (8), F, F¢, cZ, andK can be obtained (Table 1). To complete the computationand evaluation on the nine karst collapse pits, someassumptions are made in handling the practical data.

1. For the shearing-strength indexes, C and /, theweighted mean thickness of the soil cover of eachcollapse cave is used.

2. For K0, the arithmetic average of 0.69 and 0.61, that is0.65, is used.

3. Because the vertical flow velocity of groundwater, Uw, is3.6·10–5 cm/s, cwU2

w=2g can be ignored in thecomputation.

4. In the item cZ of Eq. (8), Z is supposed to be the max-imum thickness of the cover, that is cZ ¼ c1Z1 þ c2Z2,and Z1 þ Z2 ¼ Z ¼ H, where c1 and c2 are the unitweights of the upper and lower layers of the cover, re-spectively, and Z1 and Z2 are the thickness, respectively.

5. The air pressure (P¢) of the soil cave is assumed to bezero and half an atmosphere pressure (P0), respectively,so the differential pressures DP is determined to be 100and 50 kPa, respectively.

In the process of calculating the most important indexes ofsoil affecting the karst collapse, such as the thickness ofsoil, the physical–mechanical properties, the structure ofthe soil, and degree of variation of the water table are alltaken into account. The results of the calculation showthat, among the nine collapse cases, except the sixth(138.17<141.57 kPa, that is F<cZ) the F values of the othereight collapse pits are >cZ, which indicates that the eightpits would not have collapsed if they had not been inpumping condition. Among the nine collapses, except theeighth (F=1.01), the K values of the other eight karst col-lapses are <1,which indicates that all karst collapses in thisarea resulted from sudden, large-amplitude lowering of thegroundwater table after pumping in No. 4 well.

Conclusions

Through discussion on the mechanism of karst collapseand the establishment and application of the instabilitycriterion, the following conclusions may be drawn.

1. Although the potential erosion theory and the vacuumabsorption theory can explain the origin of typical karstcollapse macroscopically, the predicting criterion ofkarst collapse cannot be established if it is only basedon the two theories.

Table 1Parameters and evaluation results of nine karst collapse pits in Niuchang headwater ground of Guizhou

Ser.no.

Radiusof cave

Thicknessof the

CohesionC (kPa)

Angleof internal

Unit weight cZ F F¢ K

R (m) stratum H (m) friction / (�) c (kN/m3) (kPa) (kPa) DP=100 kPa DP=50 kPa KDP¼P0KDP¼P0=2

1 14.2 0.80 11.00 18.77 16.40 77.50 114.45 165.68 121.59 0.69 0.943.40 15.50 19.25 18.94

2 10.4 0.95 11.0 11.67 17.10 63.45 102.75 149.69 106.57 0.68 0.962.40 16.10 13.80 19.6

3 7.5 1.20 20.00 18.72 18.20 114.90 125.42 163.45 139.18 0.77 0.894.70 14.50 14.72 19.81

4 8.4 1.30 16.00 10.57 16.70 114.30 121.79 166.38 140.34 0.72 0.864.90 16.70 15.80 18.98

5 5.7 1.10 7.00 9.60 18.40 139.90 143.77 163.21 151.56 0.87 0.946.20 20.13 17.55 19.30

6 6.8 0.90 8.40 15.65 17.20 141.57 138.17 171.22 156.40 0.81 0.886.70 20.10 16.10 18.82

7 7.1 1.10 8.40 15.65 17.80 121.59 124.37 161.30 141.45 0.77 0.875.45 18.20 17.20 18.62

8 4.8 1.20 19.77 20.30 17.90 126.90 150.83 147.86 137.38 1.01 1.095.30 18.70 20.30 19.89

9 6.6 1.25 20.13 8.80 18.60 126.20 139.82 163.18 144.49 0.85 0.965.20 19.80 14.50 19.40

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Environmental Geology (2003) 43:720–724 723

2. Based on the two theories above, this paper considersthat the collapse is the result of limited equilibrium ofthe soil cover, which is broken under the mutual actionof all kinds of pressures acting on the soil cover. Theequilibrium of the soil cover begins to be broken from apoint, and then non-equilibrium develops from a pointto other points. These points are finally connected toform a complete plane, thus the overall equilibrium ofsoil is lost and collapse occurs.

3. The assumption that the failure of a point in the soilcover abides by the Mohr–Coulomb criterion and theplastic equilibrium theory of soil is the basis for theestablishment of the karst collapse criterion.

4. In Eqs. (8) and (9), almost all the factors affecting karstcollapse are taken into account, so the criterion willhave a certain accuracy in the prediction of karst col-lapse if the differential pressure DP and the flow ve-locity Uw of groundwater can be measured by anaccurate method. If the distribution of soil caves in thesoil cover can be determined through investigation, thestability of the soil cover can be quantitatively predictedby means of the criterion.

5. The analysis and prediction of the above-mentionednine karst collapses in Niuchang headwater ground ofGuizhou show that the evaluating results coincided withthe practical results, which indicates that the criterionhas a certain reliability.

Acknowledgements The authors are grateful to Chief EngineerGao Zongjun, Monitoring Station of Environmental Geology ofTai’an City, for supplying us with the data of karst collapse inGuizhou, and to Zhang Wenjie and Wang Bin for the excellentwork in the monitoring and data analysis for this research.

References

Huang C (1985) The several problems of karst land form inShandong Province. The karst land form and cave (in Chinese).Science Publishing Company, Beijing pp 12–16

Jiang X (1998) Inducement of karst collapse from groundwaterpressure (in Chinese). J Geol Disaster Prevent Controll China9(3):20–23

Li Z, Wang Z (1990) The basis of engineering geology (in Chi-nese). Publishing Company of China Geoscience University,Beijing, pp 176–179

Lu Y (1986) The karst view, type and scale in China (in Chinese).Geology Publishing Company, Beijing, pp 211–214

Wang J (1998) Study of the cap soil at the covered karst area bythe typical collapse mathematical models (in Chinese). J GeolDisaster Prevent Controll China 9(3):19–20

Yang Y (1987) Soil dynamics (in Chinese). Geology PublishingCompany, Beijing, pp 37–86

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