A bedrock sagging sinkhole occurred in Jiangxi Province of China when constructing the Changli freeway above shallow karst caves. It was chosen as a case to investigate the failure mechanism and potential evolution. The in situ stress of the study area was measured and numerically reproduced. The Hoek–Brown strength parameters were obtained by laboratory tests. A strain-softening constitutive model was established according to the strain-softening behaviour exhibited by the specimens in the triaxial test. The stress-strain curves of the specimens were reproduced by numerical methods. Then, bedrock sagging sinkholes in strain-softening rock induced by embankment construction were simulated. The occurrence of the strain-softening zone and its transition to the residual zone were observed and classified into four stages. The stress paths of the four stages were analysed. Interestingly, in this case, the supports at both ends of the bedrock began to yield from the top and extended downward, while the midspan position began to yield from the bottom and extended upward, and the reasons for yielding were related to tension. Further analysis found that the failure mode was basically consistent with the size and direction of the bending moment. In fact, this failure mode was quite similar to a fixed supported beam. Then, the feasibility of calculating the stability of karst caves based on beam assumptions was discussed. Finally, potential evolution of the bedrock sagging sinkhole was discussed.
In karst areas, sagging of bedrock is generally induced by dissolution of soluble rock or engineering construction disturbance. These subsidence mechanisms produce bedrock sagging sinkholes [
To investigate the subsidence mechanism of the Snowy Mountains Highway in Australia, drilling investigations, electromagnetic method, and ground penetrating radar (GPR) were used by Rumbens to determine the extent of the underground karst cavities [
To enrich the study of sinkholes induced by engineering construction, the bedrock sagging sinkholes induced by the construction of Changli highway was selected as a case study. Changli highway is a main road connecting Nanchang city and Shangli city. The karst caves beneath the highway were surveyed before embankment construction. To prevent a highway collapse caused by potential sinkholes, a 0.5 m thick continuous reinforced concrete slab was constructed above the embankment. As a passive engineering measure, this procedure can prevent the sudden collapse of highways.
To analyse the bedrock sagging sinkhole occurring beneath the Changli highway, geological conditions and the in situ stresses of the study area were surveyed. Based on unconfined compressive strength tests, Brazilian splitting tests, and triaxial tests, Hoek–Brown strength parameters were obtained, and a strain-softening model was established. The strain-softening behaviour observed by triaxial tests was reproduced numerically. Then, the bedrock sagging sinkhole in strain-softening rock induced by embankment construction was simulated. According to the softening index, the bedrock was divided into an elastic zone, a strain-softening zone, and a residual zone. The occurrence of the strain-softening zone and its transition to the residual zone were analysed. The stress paths of the midspan position and the supports at both ends of the bedrock were analysed. The similarities and differences of the stress path of the strain-softening model and that of the elastoplastic model were summarized. The bending moments of the strain-softening numerical model, the simply supported beam model, and the fixed supported beam model were calculated. Finally, further evolution of the bedrock sagging sinkhole was discussed.
Changli highway is located in the Pingxiang-Leping EW-trending depression zone, where the Yangtze plate meets the South China Folds Belt. The Pingxiang-Leping depression zone mainly consists of sedimentary rock (limestone, conglomerate, argillaceous siltstone, and sandstone) and metamorphic rock (phyllite, tuffaceous sandstone, and slate) in late Palaeozoic Era and Permian period. The main topographies are low mountains and hills formed by erosion and denudation.
The study area is approximately 150 km west of Nanchang, China. The outcrop of the study area is mainly Quaternary silty clay sediment (Q4el) and Permian Lower Mouth Group limestone (Plm), as shown in Figure Quaternary silty clay sediment: it is composed by silty clay with a small amount of gravel. The predominant colour is yellow or brownish red. The sedimentation thickness varies from 0 to 12 m. Permian Lower Mouth Group limestone: karst caves are formed in medium to fine-grained limestone with a uniform composition. The rock mass is characterized by a blocky structure and moderately weathered surface. The predominant colour is grey.
Geological map.
Surface water is mainly surface runoff, which is derived from meteoric water and bedrock fissure water. The groundwater is mainly bedrock fissure water, which is hosted in weathered bedrock. It is mainly recharged by pore phreatic water. Surface water and groundwater are scarce. The groundwater level detected in the borehole is below the cave.
In evaporite karst areas, bedrock sagging sinkholes are generally induced by dissolution of evaporites [
The carbonate formation in Jiangxi Province, China, is mostly buried by Quaternary sediment formation. The buried karst had once been exposed in Permian period and then was buried in Quaternary period. Most karst caves remain stable under natural conditions until they are disturbed by surface engineering construction. There have been few reports on sinkholes in Jiangxi Province in the past. However, they have gradually increased in recent years, mainly focusing on sinkholes induced by engineering construction. For example, a bedrock sagging sinkhole was induced by highway construction in Fengcheng city, with a maximum of 12 cm of settlement [
Borehole drilling and electrical resistivity tomography (ERT) were used to determine the extent of the karst caves. The ERT surveys were carried out using the Wenner array. The survey line is arranged along the geological profile (Figure
ERT profile.
The geological profile is shown in Figure
Geological profile.
Many classical rock mass classification systems, such as the rock mass rating (RMR) system, Q-system, and geological strength index (GSI) system, have been developed for years. More recently, a novel rock mass classification system in karst has been put forward by Andriani and Parise in 2017 [
The Hoek–Brown strength criterion can be expressed as
The GSI value is related to weathering conditions and rock structure. The
Two types of core samples can be drilled from the site: intact rock samples and rock mass samples with randomly distributed joints and fractures, as shown in Figure
Intact rock sample (a) and rock mass sample (b).
To simplify writing, here, we define a parameter vector
To overcome this problem, an indirect method to determine
Determination procedure of Hoek–Brown strength parameters.
For intact rock, the GSI value is assumed to be 100. According to equation (
The
Unconfined compressive strength test, Brazilian split test, and triaxial test were conducted on rock samples. Unconsolidated undrained triaxial tests were conducted on embankment filling and silty clay samples. Embankment construction was completed within one month. However, it generally takes several years for the embankment filling and silty clay to be fully consolidated. The permeability of silty clay is very small, and its drainage during construction is neglected. Therefore, unconsolidated undrained triaxial tests were carried out.
To ensure the reliability of material parameters, three samples were tested at a time, and then the test results were averaged to eliminate errors. Three unconfined compressive strength tests, three Brazilian splitting tests, and 18 triaxial tests were conducted on intact rock and rock mass samples, respectively. Cylindrical samples with a diameter of 50 mm and a height of 25 mm were used in the Brazilian splitting tests. Cylindrical samples with a diameter of 50 mm and a height of 100 mm were used in the unconfined compressive strength and triaxial tests. The confining pressures of the triaxial tests were 5, 10, 15, 20, 30, and 40 MPa, as shown in Figure
Fitting curves of triaxial tests.
The test results are summarized in Table
Basic material properties.
Materials |
|
|
|
|
|
UCS (MPa) |
|
---|---|---|---|---|---|---|---|
Embankment filling | 50 | 0.35 | 2100 | 24 | 10 | – | – |
Silty clay | 30 | 0.35 | 1900 | 20 | 50 | – | – |
Intact rock | 60000 | 0.25 | 2700 | 44 | 23000 | 120 | 11 |
Rock mass | 44000 | 0.25 | 2700 | 40 | 13000 | 88 | 3.5 |
Intact rock samples with slight weathered surface were collected from BH2 and BH3, 3 m beneath the caves B and C. Rock mass samples with moderately weathered surface were collected from BH2 and BH3, 3 m above the caves A and C.
According to the uniaxial tests,
According to the assumptions, rock mass and intact rock have the same
Substitute
Hoek–Brown strength parameters.
Materials | GSI |
|
|
|
|
---|---|---|---|---|---|
Intact rock | 100 | 13 | 13 | 1 | 0.5 |
Rock mass | 88 | 13 | 8.5 | 0.3 | 0.5 |
In the absence of test data, the values of GSI and
Comparison between the fitting method and the published estimating method.
Method | Θ | Intact rock | Rock mass |
---|---|---|---|
Determined by fitting the failure curves | GSI | 100 | 88 |
|
13 | 13 | |
|
|||
Estimated by Hoek’s published tables | GSI | 100 | 50–60 |
|
9–15 | 9–15 |
The Mohr–Coulomb strength criterion was used to fit the model, and the results were compared with those of the Hoek–Brown strength criterion, as shown in Figure
According to the fitting curves, the UCS and
Comparison between Hoek–Brown criterion and Mohr–Coulomb criterion.
Samples | Intact rock | Rock mass | |
---|---|---|---|
UCS (MPa) | Laboratory measurements | 120 | 88 |
Estimated by Hoek–Brown | 120 | 62 | |
Estimated by Mohr–Coulomb | 111 | 72 | |
|
|||
|
Laboratory measurements | 11 | 3.5 |
Estimated by Hoek–Brown | 10 | 4.0 | |
Estimated by Mohr–Coulomb | 19 | 16 |
Figure
Strain-softening behaviour observed in laboratory tests.
Figure
Envelope of the yield limit and the residual strength. (a) Intact rock. (b) Rock mass.
In the test, Young’s modulus was denoted by
The trend of the drop modulus
The rock samples drilled at the site show significant strain-softening behaviour in laboratory tests. Obviously, this stress-strain relationship cannot simply be represented by an elastoplastic model. Therefore, a strain-softening model was chosen, as shown in Figure
Strain-softening constitutive model. (a) Stress-strain relationship. (b) Strength model.
The softening index
The softening index that marks the transition from the softening state to the residual state is denoted as
The strength parameters
It is often helpful to run a simple test of the selected material model before integrating it into a full-scale numerical model. For this aim, the selected strain-softening model was integrated into a numerical model to simulate the triaxial tests using FLAC3D software. Cylindrical models with a diameter of 50 mm and a height of 100 mm were used in the numerical simulation. The material parameters are shown in Tables
The simulated stress-strain curves were compared with the measured stress-strain curves, as shown in Figure
Strain-softening behaviour and numerical reproduction (rock mass).
The shear-strain increment contour map and the displacement vector map are plotted against the sample loaded to damage, as shown in Figure
Failure forms in triaxial tests and simulations (rock mass,
The borehole deformation gauge was used to measure the in situ stress in the study area. The layout of the survey points is shown in Figure
Projection of principal stresses.
Survey results of in situ stress.
No. | Depth (m) |
|
|
|
||||||
---|---|---|---|---|---|---|---|---|---|---|
Value (MPa) | Direction | Dip angle (°) | Value (MPa) | Direction | Dip angle (°) | Value (MPa) | Direction | Dip angle (°) | ||
S1 | 37 | 3.48 | N84°E | 8 | 1.43 | S7°E | –5 | 1.25 | S50°W | –100 |
S2 | 42 | 3.98 | N69°E | 13 | 1.67 | S21°E | –2 | 1.60 | S62°W | –103 |
S3 | 47 | 3.76 | N65°E | 4 | 1.79 | S26°E | –6 | 1.55 | S6°W | –97 |
S4 | 57 | 4.27 | N77°E | 1 | 1.91 | S13°E | –3 | 1.83 | S6°W | –93 |
S5 | 45 | 3.54 | N84°E | 5 | 2.01 | S7°E | –13 | 1.74 | S15°W | –104 |
S6 | 52 | 3.77 | N82°E | 12 | 2.3 | S10°E | –11 | 2.09 | S38°W | –106 |
S7 | 48 | 3.46 | N82°E | 7 | 1.8 | S9°E | –9 | 1.65 | S27°W | –102 |
S8 | 56 | 4.01 | N87°E | 9 | 2.12 | S3°E | –1 | 1.89 | S83°W | –99 |
The linear regression equation (
Trend of in situ stress along the depth.
Equation (
Simulation of the in situ stress.
The embankment construction was simulated using FLAC3D software, as shown in Figure
Numerical model.
Embankment construction term.
To compute the settlement of the karst cave C (Figure
Settlement computation.
The computation results of schemes 3 and 4 are completely consistent before EC3, but divergence emerges after EC3. The divergence between them rapidly enlarges as the embankment construction proceeds. This is because the surrounding medium was in an elastic state before EC3. Therefore, the elastoplastic model and the strain-softening model exhibit the same mechanical behaviour. After EC3, the strength of the strain-softening rock in scheme 4 decreases significantly. Therefore, the deformation of strain-softening rock is more severe than that of elastoplastic rock after EC3.
Different constitutive models were adopted in schemes 1 and 2, but their computational results are completely consistent from beginning to end. This is because both schemes assume that the surrounding medium is composed of intact rock, which has a high strength. The assumed intact rock remains in an elastic state from beginning to end, and therefore, both schemes exhibit the same mechanical behaviour.
In Figure
As shown in Figure
The occurrence of the strain-softening zone and its transition to the residual zone.
The occurrence of the strain-softening zone and its transition to the residual zone were observed and classified into four stages. During EC1–EC3, the surrounding medium remained elastic, and this period was defined as stage 1 for convenience. During EC3–EC5, the supports at both ends of the bedrock began to yield from the top and extended downward. This period was defined as stage 2. During EC5–EC7, the residual zone emerged in the supports at both ends of the bedrock, and the midspan position began to yield from the bottom and extended upward. This period was defined as stage 3. During EC7–EC9, the strain-softening and residual zones expanded in the supports at both ends of the bedrock, and the residual zone emerged in the midspan position. This period was defined as stage 4.
In summary, in this case, the time when the supports at both ends of the bedrock began to yield was earlier than that at the midspan position, but the later development was slower than that at the midspan position. The time when the midspan position began to yield was later than that in the supports at both ends of the bedrock, but the yield zone enlarged quickly.
The strain-softening model was used to analyse the stress paths of the midspan and the supports at both ends, as shown with the black solid line in Figure
Stress path of the bedrock. (a) The support at the left end. (b) The support at the right end. (c) Midspan.
The stress paths of the supports at both ends were quite similar. As the bedrock tilted to the left, the left end experienced more load, so the stress on the left end was slightly higher than that on the right end. In stage 1,
The stress path of the midspan was obviously different from those of the supports at both ends. In phase 1,
In stage 1, the stress path of the elastoplastic model was exactly the same as that of the strain-softening model. The supports at both ends were gradually loaded to the tensile strength and eventually yielded at the end of stage 1. After yielding, the stress at both ends continued to develop along the yield curve. The stress of the midspan increased along the loading path, but the loading amplitude was significantly less than that of the strain-softening model. The midspan still remained in an elastic state until the end of stage 4. Therefore, the stability of caves in elastic-plastic strata is obviously higher than that in strain-softening strata. If strain-softening behaviour is neglected, the deformation of the cave will be significantly underestimated, and the stability will be significantly overestimated.
It is generally believed that the underground cavern may lose stability due to tensile yield in the midspan or shear yield in the support at the two ends [
The bending moments were calculated with the following three models: (1) the strain-softening numerical model; (2) the simply supported beam model; and (3) the fixed supported beam model. The results are shown in Figure
Bending moment of bedrock. (a) Stage 1. (b) Stage 2. (c) Stage 3. (d) Stage 4.
Calculating schemes of the bending moment.
Scheme | Bending moment solution |
---|---|
Numerical simulation |
|
Simply supported beam solution |
|
Fixed supported beam solution |
|
In stage 1, the supports at both ends were in tension on the top with a bending moment of approximately −18000 kN·m and eventually yielded due to tension; the midspan was in tension on the bottom with a bending moment of approximately 8000 kN·m. At the end of stage 1, the midspan was still elastic. In stage 2, the supports at both ends were in a strain-softening state with a bending moment of approximately −23000 kN·m and eventually entered the residual state; the midspan experienced an increased bending moment of up to 8000 kN·m and eventually yielded due to tension. In stages 3 and 4, the bending moment of the supports at both ends increased to approximately −27000 kN·m after they entered the residual state; the midspan entered the strain-softening state and the residual state successively with a rapidly increased bending moment of up to 24000 kN·m.
In short, the supports at both ends were in tension on the top. They yielded earlier than the midspan. The midspan was in tension at its bottom. Due to the rapidly increasing bending moment, the yield zone enlarged quickly at the midspan position. Therefore, the failure mode of the bedrock shown in Figure
In the four stages, the supports at both ends did not bear any bending moment; the midspan was in tension at its bottom, with the bending moment increasing from 18000 kN·m to 30000 kN·m. Therefore, if the cave stability is calculated using the simply supported beam model, the stability of the midspan position would be underestimated, but the stability of the supports at both ends would be overestimated. The local regulation, Chinese technical guidance for highway foundation design and construction in a karstified area, recommends using the simply supported beam model to calculate the cave stability; however, the simply supported beam model may result in unrealistic deviations.
In stage 1, the bending moment of the fixed supported beam model was very close to that of the strain-softening numerical model, with a difference less than 10%. In stage 2, the bedrock began to yield; thus, the difference gradually increased to 20%. In stages 3 and 4, the strain-softening state and residual state emerged in the midspan. The bending moment calculated by the fixed supported beam model was far less than the strain-softening numerical model. Therefore, in the elastic state, it would be acceptable to calculate the cave stability using the fixed supported beam model. However, after yield, the bending moment would be underestimated, and the cave stability would be overestimated.
During embankment construction, the studied sinkhole occurred along with a gradual downward movement of the bedrock, leading to the progressive settlement of the Quaternary sediment. As shown in Figure
Evolution of the bedrock sagging sinkhole during the embankment construction. (a) Stage 1. (b) Stage 2. (c) Stage 3. (d) Stage 4.
An interesting distinction is that shear band C2 propagated vertically along the damaged mass M2, but the tensile band C3 propagated horizontally along the damaged mass M3, although both damaged masses were formed due to the reduction of support. A possible explanation for this is that the damaged mass M2 continued to be compressed by the pressure of the damaged mass M3 during subsidence, in contrast to the tensile stress state of the damaged mass M3. The constructed embankment was finally destroyed by several layered horizontal tensile bands C3.
According to the main sinkhole classifications [
In fact, the bedrock sagging sinkhole might be a precursor of potential collapse due to the potential further downward movement of bedrock and the overlaid Quaternary sediment. As suggested by Parise and Lollino, failures of underground caves do not occur without warning [
A progressive downward movement of the bedrock sagging sinkhole with overlaid Quaternary sediment was simulated to show a potential evolution to bedrock collapse sinkhole, as illustrated in Figure
Potential evolution from bedrock sagging sinkhole to bedrock collapse sinkhole. (a) Stage 1. (b) Stage 2. (c) Stage 3. (d) Stage 4.
In the initial stage of embankment construction, the surrounding medium remains in an elastic state. The elastoplastic rock and the strain-softening rock exhibit the same mechanical behaviour and deformation. However, in later stages after yield, the strength of strain-softening rock decreases significantly, and the deformation would be greatly underestimated if strain-softening behaviour were to be neglected.
In this case, the supports at both ends of the bedrock begin to yield from the top and extended downward, while the midspan position begins to yield from the bottom and extended upward, and the reasons for yielding are related to tension. Further analysis found that the failure mode is basically consistent with the size and direction of the bending moment. In fact, this failure mode is quite similar to a fixed supported beam.
In the elastic state, it would be acceptable to calculate cave stability using the fixed supported beam model. However, after yield, the bending moment would be underestimated, and the cave stability would be overestimated. Otherwise, if the cave stability is calculated using the simply supported beam model, the stability of the midspan position would be underestimated, but the stability of the supports at both ends would be overestimated.
According to the main sinkhole classifications [
All data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
Yaoting Zhu, Wenhua Hu, Huquan Wu, and Chaoqun Liu are the funders of the Technology Program of Jiangxi Transportation Hall (Grant no. 2015C0022). The authors would like to acknowledge their supports. This research was funded by the Technology Program of Jiangxi Transportation Hall (Grant no. 2015C0022) and the Fundamental Research Foundation of the Central Universities (Grant no. 310821175026).