Loess has a unique structure and water sensitivity, and the immersion of loess leads to many tunnel lining problems in shallowly buried tunnels. Based on a tunnel in Gansu Province in China, two failure glide planes of a shallowly buried loess tunnel and their immersion modes are summarized. Finite element calculation of the structural Duncan-Chang constitutive model is realized via the secondary development of finite element software, by which the loads on the secondary lining are calculated and verified in comparison with measured results. The load characteristics of the secondary lining are studied. The load evolution is closely related to the immersion position and scope of the load. After the loess near the failure glide plane of the arch foot is flooded, the load on the arch foot sharply increases. As the immersion expands, the maximum load moves from the arch end up to the hance. After the loess near the failure glide plane of the hance is flooded, the load on the hance decreases slightly. The stability of the overlying loess decreases gradually, which causes the loads on the vault and arch shoulder to rapidly increase. Additionally, the load distribution characteristics on the secondary lining are summarized.
With the rapid development and construction of traffic infrastructure in Northwest China, tunnels through the loess area are continually increasing in number and expanding in scale. The special physical and mechanical properties of loess, such as its porosity, macroporosity, soluble salt content, and collapsibility, lead to significant changes in the strength and deformation of loess after water immersion, which greatly impact the stability and safety of existing loess tunnel linings, and a series of problems with the lining structure gradually occur. In loess areas, tunnel defects are closely related to the loess structure and its water sensitivity, and both of these factors should be considered when simulating the deterioration of flooded loess in loess tunnels.
Loess has significant structural characteristics, which is an important reason for the loss of strength and stability of loess under the influence of water. The Duncan-Zhang constitutive relationship is close to the stress-strain relationship of loess [
Studies on loess structural constitutive models have been widely conducted, which has laid a solid foundation for the application of loess structural constitutive models in loess tunnel engineering. The structural Duncan-Chang constitutive model was shown to accurately reflect the stress-strain relationship of loess based on a comparison with experimental data.
Scholars have performed many studies on the influence of the deterioration of loess on tunnel structure through theoretical analyses and model tests. Reznik [
In previous studies, the specific immersion water location and immersion scope were not reported, and the constitutive relation used in numerical simulation does not reflect the characteristics of loess. Additionally, the loads on the secondary lining under different immersion cases have not been reported.
Based on a project involving a loess tunnel in Gansu Province in China, this article summarizes four types of failure glide planes and their water immersion modes. Then, the formula for loess structure parameters is obtained using neural network fitting, and the finite element calculation of the structural Duncan-Chang constitutive model is realized through the secondary development of finite element software. The reliability of secondary development is verified by numerical simulation of triaxial tests. The loading characteristics of the secondary lining of shallowly buried loess tunnels under four immersion models are discussed.
This article studies a loess highway tunnel in Gansu Province, which is located on the Loess Plateau and is covered by thick loess. The strata lithology around the tunnel can be divided into three types from top to bottom: Quaternary Upper Pleistocene loess
The natural bulk density of
The natural bulk density of
The monitoring section of the secondary lining is located in the Quaternary Upper Pleistocene loess
Aerial panorama and monitoring section of the tunnel area (Google Earth).
Tunnel lining section.
Two surface cracks are found at the surface of the shallow burial area of the tunnel site, as shown in Figure
Surface cracks caused by tunnel construction.
During the excavation of shallowly buried loess tunnels, the overlying loess moves downward. It was observed that the loess at the arch foot cracked first, the columnar joints propagated due to the settlement of the loess, and the loess cracks gradually propagated upward toward the surface. Finally, the failure glide plane in the surrounding rock of the shallowly buried tunnel appeared, as shown in Figure
Failure glide plane of the surrounding rock in the tunnel project.
During rainfall and agricultural irrigation, the failure glide planes in the surrounding rock provide the best channels for water infiltration. The loess near the failure glide plane was softened by the water immersion, and its deformation increased. The downward displacement of the loess overlying the tunnel increased obviously, and the secondary lining load increased significantly, which negatively impacts the safe operation of the tunnel.
The surrounding rock failure glide plane of the loess tunnel widely existed in the shallow-buried loess tunnel. The failure glide plane is one of the main causes of the collapse of the shallow tunnel, the load increasing on lining, and structure damage during the construction period [
Under different tunnel excavation methods, two typical types of failure glide planes occur in the surrounding rock of shallowly buried loess tunnels: one type extends from the arch foot to the surface at a certain inclination angle along both sides of the tunnel (full section excavation), whereas the other type extends from the hance to the surface at a certain inclination angle along both sides of the tunnel (bench excavation) [
Failure glide planes and water immersion modes.
Because the parameters of the nonlinear model can be determined by conventional geotechnical tests, the nonlinear constitutive models (the modified Cambridge constitutive model and the Duncan-Chang constitutive model) are the most widely used in engineering applications [
The modified Cambridge model is based on the normal consolidation of saturated remolded soil, and it has few parameters and a clear physical definition. However, this model cannot accurately describe over consolidated clay. The Duncan-Chang model is a nonlinear elastic model based on incremental generalized Hooke’s law. It has clear physical definition and is easy to program, and its parameters could be easy to determine. However, this model does not consider the stress history of soil and does not reflect the dilatancy and compression hardness of geotechnical materials. In addition, both modified Cambridge model and Duncan-Chang model cannot accurately describe the stress-strain relationship of structural soil [
Loess is a typical structural soil. Establishing a nonlinear constitutive model considering structural properties is an effective way to study the mechanical properties of loess. Considering the structural changes in the loess stress process, the structural parameters are introduced into the Duncan-Chang constitutive model, which is more in line with the stress-strain changes of structural loess.
The difference between the structural Duncan-Chang constitutive model and the Duncan-Chang constitutive model is that the former considers the structure of the loess. Loess is a special type of soil with skeleton and void characteristics and particle cementation between soil particles. The skeleton and void characteristics can be eliminated by remolding and loading, and the cementation between the particles can be eliminated by water immersion. Considering the strength of soil, the loess structural parameter can be expressed by the principal stress difference of undisturbed soil, saturated undisturbed soil, and remolded soil corresponding to the same strain under the triaxial shear condition, which can be used to determine the structural strength of loess.
Under triaxial shear stress conditions, the ratio of the principal stress difference between remolded loess and undisturbed loess
This expression implies that the stronger the connection of undisturbed loess, the greater the strength loss of remolded loess and the greater the loess structural parameter. Moreover, the greater the structural damage of the flooded loess, the greater the strength loss of undisturbed saturated loess and the greater the loess structural parameter.
The formula fitting of the loess structural parameter was conducted using the BP neural network model of MATLAB, and the input layer, hidden layer, and output layer were applied. In the input layer, the loess structural parameter and its corresponding factors need to be input, and there are 1114 groups of data; thus, the input vector is a 4 × 1114 matrix. All data are quoted from the study by Xie et al. [
The expression of the BP network in this model is shown below:
Finally, the similarity coefficient
Loess has different structural stress-strain curves under different confining pressures, as shown in Figure
Structural stress-strain curves under different confining pressures.
USERMAT, which is a subroutine of the constitutive model in ANSYS, is programmed by user programmable features (UPFs) in FORTRAN to achieve the structural Duncan-Chang constitutive model in ANSYS. Based on the given strain increment, the stress increment is calculated to achieve the stress updating (
The elastic parameter in USERMAT is updated by the subroutine getLam. The mathematical expressions for the elastic modulus and bulk modulus in the loess structural Duncan-Chang constitutive model are as follows:
The different levels of structural stress
During the loading process, the structural tangent elastic modulus
During the unloading process, the structural unloading modulus
The formula of structural bulk modulus
Poisson’s ratio for loess is derived from the tangent bulk modulus
Poisson’s ratios of ideal elastic materials vary from 0 to 0.49; thus, the tangent bulk modulus
The structural Duncan-Chang constitutive model has a few parameters and clear physical meaning, and all parameters can be determined by triaxial shear tests. This constitutive model can describe the stress-strain relationship of loess under complex stress paths.
The developed structural Duncan-Chang constitutive model is verified by comparing the numerical simulation results from triaxial tests with the calculation results of test constants. The triaxial tests are simulated in Solid185, which is the latest technology unit in ANSYS. The size of the model is
Model parameters of the structural Duncan-Chang constitutive model.
Parameter |
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---|---|---|---|---|---|---|---|---|
Value | 0.6286 | 0.0777 | 0.818 | 7.82 | 13.0 | 70 | 0.0861 | 1.5715 |
Triaxial test constants.
Confining pressure (kPa) |
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|
|
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200 | 0.0157 | 0.0055 | 63.69 | 181.82 | 0.818 |
300 | 0.0150 | 0.0037 | 66.67 | 270.27 | 0.778 |
400 | 0.0137 | 0.0028 | 72.99 | 357.14 | 0.737 |
Figure
Contrasting curves for principal stress difference-axial strain.
Loess is simulated by the structural Duncan-Chang constitutive model in the numerical model. Because the subroutine USERMAT in ANSYS does not support traditional units, plane182 is selected, which is the latest technology unit and has properties such as plasticity, superelasticity, stress stiffening, large deformation, and large strain. Geotextiles and waterproof boards are inserted between the secondary lining and primary support, and the interaction between these elements is represented by the contact unit conta172 and target unit targe169 [
The accuracy of the solution is closely related to the model boundary. Under the same conditions, the bigger the model boundary, the closer the solution will be to the real value. When the boundary range reaches a certain value, expanding the boundary range provides no obvious improvement on the accuracy of the solution. To minimize the adverse effects of the boundary constraint on the calculation results, the boundaries of the calculation model are set as follows: the horizontal width of the surrounding rock on both sides of the tunnel is 35 m; the bottom boundary is 35 m from the tunnel bottom; the depth of the tunnel is 30 m, which is the actual buried depth in monitoring section; and the whole model is 82 m wide and 75 m high. There are horizontal and vertical displacement constraints on the bottom and horizontal displacement constraints on both sides of the model. The top of the model is a free surface. The calculation model is shown in Figure
Calculation model.
In this model, the secondary lining is constructed of concrete C25 with a thickness of 40 cm, and the primary support is shotcrete with a thickness of 25 cm. The parameters of the lining concrete are shown in Table
Parameters of the lining concrete.
Elastic modulus (GPa) | Poisson’s ratio | Bulk density (kN/m³) | |
---|---|---|---|
Secondary lining | 30 | 0.167 | 25 |
Primary support | 23 | 0.167 | 22 |
According to the geological conditions, the loess in the model can be divided into two layers. The upper layer is Quaternary Upper Pleistocene loess
Model parameters of loess structure Duncan-Chang constitutive model.
Parameters |
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Loess |
Natural water content | 0.9343 | 0.2045 | 0.799 | 56.1 | 18.8 | 86 | 0.0889 | 1.7624 |
Water immersion | 0.6540 | 0.1431 | 0.879 | 39.3 | 13.2 | 65 | 0.0622 | 1.2382 | |
|
|||||||||
Loess |
0.6286 | 0.0777 | 0.817 | 7.82 | 13.0 | 70 | 0.0861 | 1.5715 |
Large-scale in situ water immersion tests suggest that if loess with a failure glide plane is flooded, the failure glide plane first fills with water, after which water infiltrates vertically and horizontally at its boundary [
Relations between infiltration depth and width.
Horizontal and vertical immersion ranges.
Item | Infiltration length | |||||
---|---|---|---|---|---|---|
Infiltration width (2 × |
0 | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 |
Infiltration depth |
0 | 0.83 | 1.66 | 2.49 | 3.32 | 4.16 |
Here,
Considering the immersion modes and the immersion range, the calculation cases are divided into four cases: loess immersion near the failure glide planes of both arch feet (Case 1), loess immersion near the failure glide plane of one arch foot (Case 2), loess immersion near the failure glide planes of both hances (Case 3), and loess immersion near the failure glide plane of one hance (Case 4). Case 1 corresponds to the immersion conditions of the project case. All calculation cases are shown in Table
Calculation cases.
Cases | Immersion location (shown in Figure |
Infiltration horizontal width (2 × |
---|---|---|
Case 1 | ① ④ ⑤ | From 1 m to 5 m |
Case 2 | ① ⑤ | |
Case 3 | ① ② ③ | |
Case 4 | ① ③ |
The load on the secondary lining is the contact pressure between the secondary lining and the primary support, which is monitored during the immersion process. There are 15 monitoring points distributed symmetrically on the outside of the lining at the vault, arch shoulder, hance, arch end, sidewall, arch foot, and inverted arch, as shown in Figure
Load monitoring points.
Figures
Load curves of the secondary lining in Case 1.
Load curves of the secondary lining in Case 2.
Loess immersion on one arch foot may cause the load to increase on both sides of the arch foot. The reason for the increased load on the arch foot of the nonimmersed side may be that the increasing loads on the immersed side form a biased pressure and the lining deforms toward the nonimmersed side, leading to an increased stratum resistance on the arch foot of the immersed side. As the immersion range expands, the maximum load on the arch on the immersed side moves upward from the arch end to the hance.
Figures
Load curves of the secondary lining in Case 3.
Load curves of the secondary lining in Case 4.
The loads on the immersed side increase much more than those on the nonimmersed side, except the load on the arch foot on the nonimmersed side, which is larger than that on the immersed side, opposite to Case 2. There are two explanations for this phenomenon: One is the “bias pressure,” which was discussed for Case 2. The other is that the increasing loads on the arch shoulder have a significant effect on the increased resistance of the arch foot. The increasing stratum resistance causes the load on the arch foot to increase. During the immersion process, the maximum load on the arch first moves upward from the arch end to the arch shoulder and then moves back to the arch end.
Figure
Load variation during immersion expansion (Case 1 and Case 2).
Figure
Load variation during immersion expansion (Case 3 and Case 4).
A comparison between the calculated results and the measured results for the secondary lining loads is shown in Figure
Comparison between the calculated results and the measured results.
The maximum loads are located at the arch foot on both sides, and the maximum difference load on the left arch foot is 474 kPa. The reason for this difference may be that the pressure on the primary support is relieved before the construction of the secondary lining, and normally, the pressure relief cannot be simulated well in numerical calculations. Thus, the measured loads on the secondary lining are smaller than the calculated loads.
Finite element calculation of the structural Duncan-Zhang constitutive model is realized in ANSYS and proved to be reliable by comparing the numerical results of triaxial tests and the calculation results of testing constants. The variation and distribution of the load on the secondary lining are closely related to the immersion position and range: When the loess near the failure glide planes of the arch foot is immersed (Case 1 and Case 2), the strength of the flooded loess decreases, leading to a sharply increased load on the arch foot. As the immersion expands, the loads on the sidewall and arch end first dissipate partially and then increase gradually. The maximum load on the arch moves upward from the arch end to the hance. The load increase on the immersed side results in bias pressure, and the load on the arch foot on the nonimmersed side increases significantly. When the loess near the failure glide planes of the hance is immersed (Case 3 and Case 4), the load on the hance dissipates slightly. The stability of the overlying loess decreases gradually, causing a general load increase on the upper lining. The loads on the vault and arch shoulder increase rapidly and work downward on the lining. Therefore, the load on the arch foot increases against the stratum resistance. The maximum load on the arch moves upward from the arch end to the arch shoulder and then down to the arch end. The load on the arch foot lining is always large after the surrounding rock is flooded, and the load on the arch foot when the loess is immersion near the arch foot is always larger than that in cases of loess immersion near the hance. When the immersed area is close to the load monitoring point, the load on this point decreases at first and then increases slowly.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no potential conflicts of interest.
This study was supported by the National Natural Science Foundation of China (grant nos. 51908051 and 51978064), the Fundamental Research Funds for the Central Universities, CHD (grant no. 300102289101), and the Traffic Construction Research Funds of Shaanxi Province (grant no. 2016-1-3).