Analysis on Bearing Capacity of Tunnel-Type Anchorage of a Long-Span Suspension Bridge

INTRODUCTION

Tunnel-type anchorage has obvious advantages in bearing capacity versus investment (Liu and Hu, 1996). However, it is rarely used in a practical project because of its requirement of good rock conditions. Siduhe bridge (Fig. 1), which lies in the Badong mountains in the west plateau of Hubei Province, is the longest suspension bridge with tunnel-type anchorage in China. The bridge site is mainly composed of limestone, and it is suitable for tunnel-type anchorage. The bridge will be built in a ravine and there is only 40 m between its pylon on Yichang bank and the entrance of Baziling highway tunnel. The tunnel-type anchorage lies just above the tunnel. As such, the design and construction of the anchorage are very involved.

Figure  1.  Elevation view of Siduhe bridge.

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According to the function of the anchorage, two demands must be fulfilled. First, the strength and stiffness of the anchorage must be high enough to bear the bridge cable forces. Second, the rock around the anchorage must be strong enough to bear the forces transferred from the anchorage body. Of these, the latter is more important. A prototype test is infeasible due to the complicated rock structure and surrounding environment, making a numerical method be the preferred choice. A three-dimensional finite-element model was established to simulate the whole construction procedure, including the construction of the highway tunnel, the excavation of the tunnel-type anchorage, casting concrete, prestressing, installation of main cables, etc.. By using a numeric and overloading method, the bearing capacity and forecast possible destruction pattern was analyzed to provide a reliable basis for the design and construction of the bridge.

DESCRIPTION OF THE ANCHORAGE

The tunnel-type anchorage of Siduhe bridge is mainly constituted of three parts: the saddle room, anchorage body and back anchoring room. The anchorage body is 40 m long and the distance from its base to the top of the tunnel is 23 m.

The saddle room contains the saddle and must be long enough to deploy the wires of the main cables to fix them properly. A prism shape has been chosen for the room and the distance from the saddle to the front of the anchorage is 20 m. Allowing for the different topography at two sides of the anchorage body, and to ensure minimum damage to the mountain slope, the lengths of the saddle room at two sides are different according to the transformation of the topography (Fig. 2a).

Figure  2.  Layout of anchorage on Yichang bank (a) and distribution of prestress strands in rear anchoring plane (b) (unit: m).

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The anchorage body, which is a prestressed concrete structure, transfers the forces from the main cables to the rock mass. Its longitudinal surface, the front of which is small and the rear large, is in dovetail form. The anchorage produces positive pressure towards the rock mass due to axial tension force. The top of the transverse section is an arc and the side walls and base are lines (Fig. 2b). There is one 2-meter-long projecting strip per 4 m around the circumferential surface of the anchorage body in a longitudinal direction, like the whorl of the skew steel bar.

ANALYSIS OF BEARING CAPACITY

The general purpose code ABAQUS (Hibbit, Karlson & Sorensen Inc., 2003) was used for the numerical analysis and the numerical overloading method was used.

Generalized Geotechnical Model and Parameters of Rock Mass

The generalized geotechnical model and computation parameters of the rock mass form the basis of the mechanical analysis. This research is based on the geological exploration results and parameters offered in reference (Zhou and Chen, 2003). The mechanical parameters of the rock mass in the anchorage area are listed in Table 1.

Table  1.  Mechanical parameters of rock mass used in anchorage area of Siduhe bridge

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Range of Rock Mass for Computation

The excavation of a whole hole in the tunnel-type anchorage, and the action of the tensile force of the cable, can be considered as an infinite-field problem. When the finite-element method (FE) is used, it is difficult to determine where to set the boundary condition so it has the minimum influence on results. When a larger range is selected, there would be accurate computation results and a longer computation time, which is limited by computer memory. When a smaller range is selected, the results will be affected by the man-made boundary condition. There are different suggestions about the selection of the compu-tation range in Lu et al. (1999). In this research, synthesizing the research results of others and considering the interaction between tunnel-type anchorage and the highway tunnel under it, the computation range is selected as 7 times the dimension of the cavern; that is 324.2 m in length, 240 m in width, and 229 m vertically.

Yield Criterion

The rock mass is considered an elasto-plastic body. For rock/soil material, the Mohr-Coulomb (M-C) and Drucker-Prager (D-P) criteria are widely used (jumikis, 1983). In this paper, we use the extended M-C criterion for numeric analysis. The yield function is

and the plastic potential function is (Menétrey and William, 1995)

where c₀ is the initial cohesion of the material; ε is the meridional eccentricity; ϕ is the friction angle; ψ is the dilation angle; p is the hydrostatic pressure; q is the equivalent Mises stress, and J₃ is the invariant of the third stress deviator. The normal flow rule is adopted and no strengthening of the material is considered.

Original Stress Field and Loads

The surrounding rock is in its original stress state before the whole hole of the tunnel-type anchorage is excavated. Temperature stress is not considered because the anchorage is located in a shallow field (the maximum depth is about 100 m). The original stress field could be computed according to the gravitational field of the rock mass.

There are three types of loads: (1) Weight of anchorage and lining structure, which will be changed into a nodal force by the software according to the physical force. (2) Prestressing force. There are 73 bundles of prestress strands in each anchorage body, and the prestressing force will be changed into area loads following the size of the anchoring surface. Considering the working area is 38.88 m², the effective prestress 1 116 MPa could be converted into an area load 9 659 MPa. (3) Designed force of cables. The designed force for each cable is 220 MN and the corresponding area load is 5 658 kPa.

Simulation of Construction Procedure

In the FE analysis, by means of pilot calculations, the construction progress is simulated by 29 construction steps in consideration of the configuration of the computer, the structure type and the possible construction states. The steps are as follows: establishment of original stress state (steps 1-2), excavation of Baziling tunnel and lining (steps 3-9), excavation of saddle room and lining (steps 10-15), excavation of anchorage body (steps 16-21), backfilling of anchorage body (step 22), prestressing on anchorage body (step 23), application of cable force (step 24), the numeric and overloading trial with 3 times cable force (step 25), 5 times cable force (step 26), 7 times cable force (step 27), 9 times cable force (step 28), and 10 times cable force (step 29).

Element Types and Boundary Conditions

For the purpose of this study, a complete 3D FE model was established, as shown in Fig. 3 (longitudinal direction along bridge axis is denoted by 1, vertical direction by 3, and transverse direction by 2). In this model, two types of finite elements are used. The rock mass and anchorage body are modeled as hexahedral elements, and ejecting concrete and the lining are modeled as tetrahedral shell elements. There are 16 844 hexahedral elements, 944 tetrahedral shell elements and 21 198 nodes. Assuming the remolding thickness due to excavation of surrounding rock is 1 m, the cementation strength of the rock mass and anchorage body concrete is considered. The shearing strength parameters of the concrete/rock in Table 1 were adopted. The normal displacement in side directions, three-dimensional displacements in the base are all restrained, and the top is free.

Figure  3.  FE model. (a) hexahedral elements of rock mass; (b) shell elements of lining.

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Distribution of Plastic Areas in Surrounding Rock

The computation results suggest that the plastic area only emerges in the surrounding rock of the back anchor rooms under designed cable force P. The plastic area extends slowly at the back, but develops quickly in front and to the sides of the body. At 7 times the designed cable force, the majority of the surrounding rock would be in a plastic state. Figure 4c shows that 70 % of the rock mass is in plasticity, and plastic areas between two anchorage bodies as shown in Fig. 5c. With 9 times the designed cable force, almost all surrounding rock is in plasticity (Fig. 4d) and plastic areas run through and extend around in a transverse direction (Fig. 5d).

Figure  4.  Plastic areas in rock mass (left side of anchorage, perspective view). (a) 3 times cable force; (b) 5 times cable force; (c) 7 times cable force; (d) 9 times cable force.

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Figure  5.  Plastic areas in rock mass (transverse section). (a) 3 times cable force; (b) 5 times cable force; (c) 7 times cable force; (d) 9 times cable force.

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The bearing capacity is about 5-7 times of the designed cable force based on the analysis of the distribution of plastic areas in the surrounding rock. It could be regarded that the anchorage has been destroyed at 7 times the normal cable force. There is no plastic area in the surrounding rock near the tunnel under the anchorage with cable force increasing from 3 to 10 times.

Distribution of Shearing Stress in Surrounding Rock

From the back plane of the anchorage body to the saddle room, four central paths are defined along the direction of the cable force, in order to study the distribution of shearing stress (Mises stress q) in the surrounding rock. The left and right paths are de-fined by facing the bridge and looking along the di-rection of the cable force: the left-hand path is Path-L, the right-hand path is Path-R, the top path is Path-T and the bottom is Path-B. Figure 6 shows the variation of Mises stress along the four paths. The distance from the back surface of the anchorage body is represented along the horizontal (m) and the Mises stress is represented vertically (MPa). The suffix in the symbol box represents the corresponding construction step number; for example, "24" represents the 24th construction step.

Figure  6.  Mises stress along four central paths in surrounding rock. (a) Path-B-central line at bottom; (b) Path-T-central line at top; (c) Path-L-central line at left side; (d) Path-R-central line at right side.

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It can be seen from Fig. 6 that the distribution of shearing stress along the different paths is almost the same. Owing to the prestressed anchoring system without bond, shearing stress near the back plane of the anchorage is larger, and gradually decreases moving forward, approaching zero at the front plane.

There are differences in the distribution of shearing stress. It is obvious that shearing stress along Path-L varies little under different cable forces. For example, it increases only 1 MPa when cable force is increased from 1 to 10 times. This is quite different from the other three because of the expansion of the palstic zone in the surrounding rock between anchorages. The stress near the back plane of the anchorage spreads to the right due to the development of a plastic area in the rock between the two anchorage bodies, and the maximum shearing stress along Path-R approaches 4 MPa in the surrounding rock at the right side of the anchorage. The stress along Path-T is similar to that along Path-L with a comparative maximum value of about 3 MPa; it shows a wider range of stress under different cable forces. The variety of stress along Path-R is the most obvious one where the shearing stress varies from 0.5 to 4.0 MPa. The maximum value of shearing stress along all the four paths appears at a point 10 m from the back plane of the anchorage, and then decays. An explanation is that some distance is required when cable forces are transferred from the back plane of the anchorage to the concrete anchorage bodies.

With 7 times the designed cable force, the value of the shearing stress of the surrounding rock is about 3 MPa at the bottom and right side of anchorage, and about 2 MPa at the top and left side. The gap between them is about 1 MPa. The possible destruction pattern of the surrounding rock is concluded to be the following: plastic areas between anchorages cut through and this leads to unloading in these areas, then the stress transfers to the surrounding rock at the bottom and right side, and the two anchorage bodies are pulled out in the end.

This conclusion can also be proved by differences between the displacements near the front and back faces of the anchorage body on Path-T (Fig. 7, node 3 228 is near the front face, node 1 465 is near the back face of anchorage body. U2 is the displacement in direction 2).

Figure  7.  Lateral displacement in surrounding rock near the front and back faces of the anchorage.

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CONCLUSIONS

A complete 3D FE model was established for the tunnel-type anchorage in Siduhe suspension bridge in order to analyze its bearing capacity. From this analysis, the main conclusions can be summarized as follows: (1) The plastic area in the surrounding rock extends slowly backwards, but develops fast in forward and transverse directions. With 7 times the designed cable force, about 70 % of the surrounding rock is in plasticity and plastic areas between two anchorage bodies cut through. Under such circumstances, the rock appears to lose bearing capacity. It can be concluded that the safety factor of the anchorage is about 6 from this analysis. (2) In the prestressed anchoring system without bond, the maximum shearing stress appears at a point 10 m away from the back plane of the anchorage. It shows that 10 m is the necessary distance when cable forces transfer from the back anchorage head to the anchorage body for the tunnel-type anchorage of Siduhe bridge. (3) The possible destruction pattern of the surrounding rock is that plastic areas between two anchorage bodies cut through, which leads to unloading in these regions and stress transfers to the bottom and right side of anchorage, and finally the two anchorage bodies are pulled out.