At the collapse zone, the effects of the thickness of the consolidation grouting layer and the water pressure on the steel lining are vital to the stability of steellined pressure diversion tunnels. In this paper, a joint element and the loadsharing ratio of the consolidation layer are introduced to investigate the joint loadbearing characteristics of the steel lining and the consolidation layer and to determine a suitable consolidation layer thickness; a coupling method for simulating the hydromechanical interaction of the reinforced concrete lining is adopted to investigate the effect of internal water exosmosis on the seepage field at the collapse zone and to determine the external water pressure on the steel lining. In the case of a steellined pressure diversion tunnel, a numerical simulation is implemented to analyse the effect of the thickness of the consolidation layer and the distribution of the seepage field under the influence of internal water exosmosis. The results show that a 10 m thick consolidation layer and the adopted antiseepage measures ensure the stability of the steel lining at the collapse zone under internal and external water pressure. These research results provide a reference for the design of treatment measures for largescale collapses in steellined pressure tunnels.
During the excavation of largesection hydraulic tunnels under complex geological conditions, collapses are relatively common geological disasters that have relatively significant detrimental impacts on tunnel construction and operation. For nonpressure hydraulic tunnels, the goal of a collapse treatment, similar to that for mountain tunnels and coalmine tunnels, is to ensure the stability of the surrounding rocks at the collapse zone by strengthening the support [
The aforementioned two problems are relatively less frequently quantificationally analysed when designing the treatment of the largescale collapses that occur in the steellined pressure diversion tunnel. With respect to the design of the thickness of the consolidation layer and the analysis of the effectiveness of the collapse treatment during the operating period, most designs are based on engineering experience. Therefore, to address the aforementioned two problems, a joint element and a coupling method for simulating the hydromechanical interaction of the reinforced concrete lining are adopted, which consider the effects of the joint loadbearing characteristics of the steel lining and the consolidation layer and the internal water exosmosis on the stability of the steel lining at the collapse zone. In this paper, a case study of the largescale collapse in pressure diversion tunnel of Hua’an hydropower station is conducted. Based on the actual conditions of the largescale collapse, a support system was employed consisting of the pipe umbrella arch and steel grid arch, combined with a consolidation grouting treatment of the loose collapse body in the collapse cavity. In addition, a numerical simulation is implemented to study the joint loadbearing characteristics of the steel lining and the consolidation layer and the distribution characteristics of the seepage field at the collapse zone and then to determine the thickness of the consolidation layer and the external water pressure on the steel lining.
Hua’an hydropower station is located in Fujian Province, China. The pressure diversion tunnel lies between the surge shaft and the powerhouse. The center axial elevation of the tunnel is 32.0 m. The length of the pressure tunnel is 148.1 m. The preceding 25.0 m of the pressure tunnel is a transition section from sections 0+00.0 m to 0+25.0 m, where the diameter of the excavation cross section changes from 10.5 m to 9.2 m gradually, and the thickness of the reinforced concrete lining is 1.0 m. After section 0+25.0 m, the steel lining is adopted. The inner diameter of the steel lining is 7.2 m, and the thickness is 28.0 mm. The longitudinal section and cross sections of the tunnel are shown in Figure
Longitudinal section and cross sections of the tunnel (unit: m).
When the excavation face was advanced at section 0+37.0 m, the weathered sandy soil was exposed at the left side of the crown. Subsequently, the schistose collapsing block fell out. During the urgent supporting, the collapse became serious and the scope of the collapse spread to the right side of the excavation face. The volume of the collapse body in the tunnel was approximately 2700 m^{3}; according to the area of the excavation section and the length of the collapse body in the tunnel, the height of the cavity above the tunnel might reach 30.0 m. At collapse zone, the strength of rock is weaker than that at noncollapse zone; the surrounding rock is broken and cut by a lot of structural planes, resulting in a number of blocks that are not conducive to the stability; the blasting excavation reduces the strength of the structural planes; under the effects of the gravity and the unloading, the blocks moves toward the tunnel; the structural plane’s strength is further reduced, eventually leading to collapse.
Based on the actual conditions of the tunnel collapse in the Hua’an project, the treatment measures were designed as follows (in Figures
Schema of the collapse treatment measures.
First, steel pipes with the diameter of 108.0 mm, the spacing in the circumferential direction of 1.0 m, the external angle of 30 degrees, and the length of 7.0 m were inserted at the crown in range of 120 degrees, and then grout was injected through the pipes as the first consolidation grouting. Second, steel pipes with the diameter of 42.0 mm, the external angle of 15 degrees, and the length of 7.0 m were inserted between each of the two larger diameter pipes, followed by injection of grout as the second consolidation grouting.
As the stability of the surrounding rocks at the collapse zone was poor and they were easy to collapse during the excavation, the reserved core soil excavation method was adopted. First, the excavation footage was controlled in 50 cm, and a certain length of the core soil was reserved. Then, after two excavation cycles, the reserved core soil was excavated. After each excavation cycle completed, the concrete was sprayed onto the excavation face immediately to prevent it from contacting with damp air and improve the selfstability of the excavation face.
Φ32 screw thread steel was adopted as the main rebar and the spacing was 0.5 m. Φ25 screw thread steel was adopted as the connection rebar and the spacing was 0.6 m. The rebar grid arch was installed after each excavation cycle. The concrete was sprayed onto the rebar grid arch, and the thickness of shotcrete layer was 20.0 cm. After ten excavation cycles, the installation of steel grid arch support was completed.
The collapse body and the surrounding rocks were divided into three grouting layers. The collapse body (from sections 0+32.0 m to 0+42.0 m): ten grouting holes were arranged at the crown with an equal interval at each row; the spacing of rows was 2.0 m; the depths of the grouting deepened gradually with 2.5 m, 5.0 m, and 10.0 m. The surrounding rocks (from sections 0+00.0 m to 0+60.0 m): ten grouting holes are arranged with an equal interval at each row; the spacing of rows was 2.0 m; the depths of the grouting also deepened gradually with 2.5 m, 5.0 m, and 10.0 m. In addition, the grouting pressure increased gradually, followed by the depth of the grouting layers: the pressure of 0.3 MPa was adopted in the depth of 0.0 to 2.5 m, 0.7 MPa corresponding to 2.5 to 5.0 m, and 1.5 MPa corresponding to 5.0 to 10.0 m.
Two rows of curtain grouting holes were set at the junction between the reinforced concrete lining and the steel lining. The spacing between the two rows was 1.0 m. Two lines of drain holes were set at the bottom of the steel lining from section 0+25.0 m, and the diameter of the drain holes is 5.0 cm.
There were many uncertainties during the construction at the collapse zone. The rock mass at the collapse zone had a low strength and a low inherent bearing capacity; therefore, there was still the risk of instability. To address this issue, the deformation of the surrounding rocks at the collapse zone was monitored to ensure the safety and stability of the tunnel during the construction period. Two convergence measuring lines and one settlement measuring line were set at the collapse zone.
In Figure
Measured convergence and settlement curves of the tunnel at section 0+28.0 m.
After the loose collapse body in the collapse cavity is subjected to consolidation grouting, a consolidation layer with a certain thickness is formed, and the cavity is not fully backfilled, affecting the joint loadbearing characteristics. In addition, the gap between the steel lining and the consolidation layer is also a key that affects the joint loadbearing characteristics. To address these problems, based on the finite element theory, the present study introduces a joint element and the loadsharing ratio of the consolidation layer to investigate the joint loadbearing characteristics of the steel lining and the consolidation layer and determine the thickness of consolidation layer.
The concrete layer and the consolidation layer have a certain constraining effect on the steel lining. Factors such as construction and concrete shrinkage result in gap between the steel lining and the concrete layer. Under the internal water pressure, the steel lining has radial displacement. When the gap between the steel lining and the concrete layer is closed, the steel lining, the concrete layer, and the consolidation layer joint bear the load and simultaneously undergo deformation. In general, there is a stage at which the steel lining bears the load alone because of the gap. This stage continues until the steel lining fills the gap through deformation, at which time the steel lining and the concrete layer interact and jointly bear the load with the consolidation layer. Therefore, a joint element is introduced into the numerical simulation [
There are three main steps for simulating the process of the steel lining touching the concrete layer with using hierarchical loading and the iteration method by changing plastic stiffness [
The total load,
After calculating the elastic load of each level,
Whether the steel lining element is in contact with the concrete layer element can be judged by the relative difference between the radial nodal displacement of the steel lining element and the radial nodal displacement of the concrete element at the joint after
For the plastic load of each level,
The incremental displacement is calculated using
After the calculation of the elastic load
In this study, based on the concept of the sharing ratio of surrounding rocks (the percentage difference between the stress on the buried pipe and the stress on the exposed pipe under the effect of the same internal pressure), the loadsharing ratio of the consolidation layer is defined as
Under the internal water pressure, the seepage field and stress field in the concrete lining interact. After the concrete lining enters the plastic damage stage from the elastic stage, with the extent of damage of the concrete increasing, cracks occur in the lining, which increases the permeability of the concrete and generates larger seepage pressure, thereby aggravating damage in the concrete lining [
In this paper, the concrete is treated as an elastoplastic material. And a damage coefficient,
The differential expression for the stress increment of the concrete in the damage state is as follows:
DruckerPrager yield criterion is used for the concrete. And the iteration method by changing plastic stiffness is used to solve the stress field. The load increment at each stage is applied to the structure as follows:
After the concrete lining cracking, the constitutive relationship of the cracked element becomes anisotropic and the stress matrix of cracked element under local coordinate system can be obtained by [
Then the modified stress matrix can be transferred into the global coordinate with using the coordinate transfer matrix.
According to Darcy’s law, the basic equation of threedimension stable seepage is as follows:
Based on the principle of FEM, the basic equation of threedimension stable seepage of FEM is as follows:
The seepage volume load generated by the hydraulic gradient of the seepage field is applied on the element nodes, resulting in a change in the stress field of the lining structure. The seepage load is calculated as follows:
In this paper, there are three kinds of boundary conditions for the threedimension stable seepage.
Under the internal water pressure, cracks in the concrete lining are generally caused by the actual strain of the concrete element exceeding the ultimate tensile strain. When cracks occur in the lining, seepage flow in the concrete will be governed by these cracks. To represent the interaction between crack and permeability, the modified cubic law [
The following formula is used to estimate the crack width [
After the concrete cracking, there is a sliding displacement between the rebar and the concrete as a result of the decrease in the bearing capacity of the concrete, the concrete only bears the corresponding load with its residual bearing capacity, and the remaining load is borne by the steel rebar. The portion of the load allocated to the steel rebar and the concrete is based on the damage coefficient of the concrete,
Substituting (
In addition, the uncracked concrete could be regarded as an isotropic material, and, based on the KozenyCarman formula, the permeability of the uncracked concrete,
Calculate the seepage field and get the seepage nodal loads
Apply
Calculate a new damage coefficient,
Repeat the calculation steps (A) to (C) until the stress field satisfies the convergence condition.
In this section, in a case study of the steellined pressure diversion tunnel in the Hua’an hydropower station, the adopted analysis and simulation methods are used to investigate the joint loadbearing characteristics of the steel lining and the consolidation layer and the distribution of the seepage field at the collapse zone, and, then, the thickness of the consolidation layer and the external water pressure on the steel lining at the collapse zone are determined. The reasonableness and effectiveness of the determined consolidation layer thickness and the adopted antiseepage measures are also investigated to ensure that the steel lining still meets the original design requirements.
As shown in Figure
3D finite element mesh for the numerical model: (a) the numerical model mesh and (b) the mesh at the collapse zone.
The boundary conditions are that all the surfaces except the top surface are fixed in the normal direction and that the top surface is free. The seepage boundaries are as follows: the upriver and downriver surfaces of the model are treated as the first seepage boundaries, and the water levels of the upstream and downstream surfaces are 91.0 m and 78.0 m, respectively. Under the load rejection condition, the inner surface of the reinforced concrete lining is treated as the first seepage boundary, and the total head on the inner surface is 123.0 m. The surfaces of the steel lining are impervious boundaries. The surfaces of the collapse cavity and the drain holes are treated as potential seepage boundaries.
The original ground stress is defined based on a selfweight stress field. The initial conditions for the operating period are determined after the tunnel has been excavated and the lining has been installed. Because of the limitation of the finite element method for simulating the process of tunnel collapse, the method of excavationbackfilling is adopted to approximately simulate the effect of collapse. The process of collapse is regarded as the excavation, and the remaining collapse body in the collapse cavity is result of backfilling. The support effects of the pipe umbrella arch and steel grid arch are simulated by the equivalent parameters method; that is,
Mechanical parameters of the materials.
Materials  Deformation modulus/GPa  Poisson’s ratio  Cohesion/MPa  Friction angle/(°)  Tensile strength/MPa  Permeability coefficient/ m·s^{−1} 

Rock mass  8.0  0.27  0.55  37.0  1.4 

Grouted rock mass  10.0  0.26  0.80  40.0  1.6 

Collapse body  3.0  0.32  0.27  33.0  0.6 

Consolidation layer  5.0  0.29  0.45  35.5  1.0 

Antiseepage curtain  10.0  0.26  0.80  40.0  1.6 

Concrete  28.0  0.18  2.15  50.0  1.2 

During the water filling operation, the maximum total head in the tunnel is 123.0 m under the load rejection condition. To study the joint loadbearing characteristics of the steel lining and the consolidation layer and determine the thickness of the consolidation layer of the collapse body above the tunnel, analyses with consolidation layer thicknesses ranging from 0 m (without consolidation grouting) to 30 m (i.e., complete backfilling) are performed under the load rejection condition. The consolidation layer, in comparison with the surrounding grouted rocks, has a relatively low strength and a low inherent bearing capacity; therefore, this study focuses on the crown and the consolidation layer above the tunnel at the collapse zone.
The displacement on the top of the steel lining and the range of displacement (the difference between the maximum displacement and minimum displacement) of the steel lining with the consolidation layer thicknesses from 0 m to 30 m are shown in Figure
Displacements and the range of displacements of the steel lining at section 0+37.0 m.
The calculated loadsharing ratio of the consolidation with the consolidation layer thicknesses from 0 m to 30 m is shown in Figure
Loadsharing ratio of the consolidation layer.
From Figures
The distributions of the tensile stress in the steel lining with 0 and 10 m thick consolidation layers are shown in Figure
Tensile stress distributions of the steel lining at the collapse zone from sections 0+29.8 m to 0+46.3 m: (a) with 0 m thick consolidation layer and (b) with 10 m thick consolidation layer (unit: MPa).
The distributions of the third and first principal stresses on a 10 m thick consolidation layer are shown in Figure
Stress distributions in the 10 m thick consolidation layer at section 0+37.0 m: (a) the third principal stress and (b) the first principal stress.
As demonstrated by the results, when the steel lining and consolidation layer jointly bear the internal water pressure, the effect of the 10 m thick consolidation layer’s loadsharing is obvious, which makes the distribution of the deformation and stress in the steel lining even. In addition, the consolidation layer is in a good stress state and does not damage, which ensures the structural stability of the consolidation layer itself. In general, when the steel lining and the 10 m thick consolidation layer jointly bear the internal water pressure, the steel lining is stable.
The critical external compressive resistance of the original design for steel lining is 0.68 MPa. If there is neither collapse nor internal water exosmosis, the external water pressure on the steel lining at the collapse zone is approximately 0.5 MPa. However, changes in the seepage field at the collapse zone caused by the collapse cavity and the aggravation of internal water flowing out to the rock mass through the cracks in the reinforced concrete lining have significant influences on the external water pressure on the steel lining. Therefore, determining the external water pressure on the steel lining at the collapse zone is a key. In view of these considerations, based on the theory of coupled hydromechanical interaction of the reinforced concrete lining and with the influence of the cavity above the tunnel and the internal water exosmosis taken into account, the distribution of the seepage field at the collapse zone is investigated. Based on the calculated seepage field, suitable antiseepage measures are adopted to ensure that the external water pressure on the steel lining satisfies the requirements of the design specification during the operating period.
When the tunnel is quickly evacuated for inspection or another problem, the external water pressure caused by internal water exosmosis does not dissipate immediately, which results in high external water pressure on the steel lining, especially under the load rejection condition. Therefore, the load rejection condition is treated as the most unfavourable condition in this study. An analysis of the following three scenarios is performed under the load rejection condition and with consolidation grouting (in Table
Scenarios considered.
Scenarios  Exosmosis condition  Antiseepage condition 

Scenario 1  With internal water exosmosis  Without antiseepage measures 
Scenario 2  Without internal water exosmosis  Without antiseepage measures 
Scenario 3  With internal water exosmosis  With antiseepage measures 
First, the results for the adopted coupling method are analysed. Figure
Distribution of the total head isolines in the concrete lining at section 0+10.8 m in scenario 1 (unit: m).
Based on the coupling method, in scenario 1, the stress distribution in the concrete lining is analysed. Figure
Tensile stress distribution of the concrete lining at section 0+10.8 m in scenario 1 (unit: MPa).
Crack width distribution of the concrete lining elements at section 0+10.8 m in scenario 1 (unit: mm).
A comparison of the different scenarios is then performed. Figure
Distributions of the pressure head isolines: (a) along the tunnel axis in scenario 1; (b) along the tunnel axis in scenario 2; (c) along the tunnel axis in scenario 3; and (d) at section 0+37.0 m in scenario 3 (unit: m).
Compared with scenario 2, in scenario 1, as the internal water exosmosis generates an internal source of seepage, the pressure head increases and the isolines are distributed densely in the grouting zone near the concrete lining and then affect the seepage field at the collapse zone. In Figure
Comparison of the external pressure head on the steel lining in the three scenarios: (a) at section 0+37.0 m and (b) at section 0+27.0 m.
Based on the distribution of the seepage field in scenario 1, an antiseepage curtain is placed between the reinforced concrete lining and the steel lining to diminish the influence of internal water exosmosis on the collapse zone, and two rows of drain holes are placed at bottom of the steel lining to decrease the external water pressure on the steel lining.
With the antiseepage curtain and the drain holes, in scenario 3, the maximum external pressure head on the steel lining at the collapse section decreases to 29.6 m from 54.3 m, its value in scenario 1 (in Figure
From the above analyses, the internal water flowing out to the rock mass through the cracks in the concrete lining and the collapse cavity above the tunnel have significant influences on the distribution of the seepage field at the collapse zone. The adopted antiseepage curtain and drain holes effectively improve the seepage environment at the collapse zone, limit the external water pressure on the steel lining to a critical external compressive resistance of 0.68 MPa, and ensure the safety and stability of the steel lining during the operating period.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This study is supported by the National Key Basic Research Program of China (2015CB057904) and the National Natural Science Foundation of China (51279136 and 51579191). This support is greatly acknowledged and appreciated.