Due to the limitations of geography and geology, cast concrete tunnel anchors were used to provide counterforces for Xingkang Suspension Bridge foundation at the left bank of Daduhe River. In this study, the in situ creep tests were conducted on two model tunnel anchors at a scale of 1:10 near the real working anchor site. Thus, the long-term deformation of the real working tunnel anchors installed at the bridge foundation could be determined from the creep test of model tunnel anchors. The creep tests were conducted under three different loads and lasted for 102.2 h, 167.5 h, and 189.4 h, respectively. The model anchor, the surrounding rock, and their interface were all monitored and measured during the creep testing. In addition, the numerical calculation, in which the Burger creep constitution was used for describing the surrounding rock and the Mohr–Coulomb criterion for describing the concrete anchor, was performed to further evaluate the long-term stability of the real working tunnel anchors. The numerical calculations are in good agreement with the laboratory testing results, and the creep deformations of the anchor and the surrounding rock have the same order of magnitude. The results show that the tunnel anchor and surrounding rock of Xingkang Bridge are in a stable creep state under the three different loads.
The Xingkang Bridge, located in Luding County of China, is a key engineering project of the Yakang Expressway connecting Ya'an City and Kangding City. The primary part of this bridge is a large-scale single-span steel truss suspension bridge with a length of 1100 m. Due to the limitations of geography and geology, use of several concrete tunnel anchors was adopted to provide counterforces for the bridge foundation at the left bank of Daduhe River. Compared to the cast concrete gravity anchor often employed in practice of engineering, the concrete tunnel anchor is rarely applied to the foundation of suspension bridge. The tunnel anchor seems to be in the shape of a thermos bottle plug, and it has a short side at the front and a long one at the rear in lengthwise section. Using the geometry of a bottle plug could increase the pullout capacity of an anchor. Thus, the mechanical properties of the rock mass surrounding the anchor could be efficiently used to provide the counterforce needed to guarantee the safety of the bridge foundation.
It is well known that the safety of suspension bridges depends on the stability of bridge foundation to some extent [
The creep phenomenon and long-term deformation of soft rocks and weak rock mass have been of great concern in practice of engineering since the 1930s. Griggs [
In this study, the in situ creep tests were performed on the tunnel anchor model at a scale of 1:10 considering the geological conditions at the installation site of the actual tunnel anchor, i.e., Xingkang Bridge foundation near the bank slope at the left bank of Daduhe River. The creep deformations of the tunnel anchor model and the surrounding rocks were collected during testing. Furthermore, we employed the commercially available software FLAC3D to calculate the creep deformations based on the Burger creep model. The creep deformation pattern of actual tunnel anchor and its influence on the long-term stability of Xingkang Bridge were analysed in terms of experimental measurements and numerical calculations. These results are helpful to the reinforcement design of the foundation section of Xingkang Bridge in the Yakang Expressway. This bridge, opened in October of 2018, is in good operation up to date.
The design and reinforcement of bridge foundation depend primarily on the engineering geology conditions. The geological investigations show that there exist strong tectonic activity, frequent seismic activities, and high-intensity earthquakes since the late Pleistocene epoch in the region of the engineering project. The natural slope with a height of 400 m was formed due to the U-shaped bending at the left bank of the Daduhe River near the bridge foundation. The steep slope was covered with significant deposits of 3 to 5 m depth at the middle and lower positions. The underlaid rocks are primary composed of strongly altered adamellite. The plan view and profile of engineering geology are plotted in Figures
Geography and geology near the tunnel anchor site of the Xingkang Bridge.
Engineering geology profile at the I-I position of Figure
The in situ model tunnel anchors are located at approximately 100 m below the real working anchors of Xingkang Bridge foundation (Figure
Locations of model anchor and real working anchor tunnels.
Surrounding rocks around (a) real working anchor tunnel and (b) model anchor tunnel.
Physical and mechanical parameters of rock samples.
Parameter | tan | |||||||
---|---|---|---|---|---|---|---|---|
Range | 2.54∼2.68 | 1.06∼5.39 | 22.4∼46.7 | 2.5∼3.9 | 0.26∼0.31 | 0.6∼1.2 | 0.71∼0.92 | 1.07∼1.82 |
Average | 2.57 | 2.13 | 32.25 | 3.20 | 0.28 | 0.82 | 0.78 | 1.38 |
Standard deviation | 0.06 | 1.84 | 8.96 | 0.58 | 0.02 | 0.23 | 0.09 | 0.31 |
In order to determine the creep characteristics of the tunnel anchor and the surrounding rocks, the in site creep tests of two model anchors were conducted. The creep tests comply with the similarity theory in physics. The gas–liquid hydraulic loading system was used for the creep testing method, and grating displacement sensors and dislocation meters were employed to monitor the creep deformation.
In order to avoid the influence of model tunnel anchor on the real working tunnel anchor in the process of the creep tests, the two model anchors were placed under the real anchors. Their height difference is approximately 100 m. The location relation between the model anchor and the real one is plotted in Figure
The creep test of tunnel anchor model complies with the similarity theory in physics. The main parameters (strength, load, geometry, and elastic modulus) of the model anchor are determined from (
The tunnels for model anchor and real working anchor share exactly the same shape and axis direction (115°∠36°). The top and bottom of model anchor tunnels in cross section are both designed as arc shapes while the side walls are vertical. The two tunnels of model anchors (see Figure
(a) Left tunnel and (b) right tunnel of model anchors.
(a) Front-side surface and (b) rear-side surface of a single model anchor.
The gas-liquid hydraulic loading system, used for the creep testing method, was made by Jinan Saisite Equipment Co., Ltd. This loading system could offer a high loading capacity, a high-pressure servo control accuracy, and a convenient control function. The detailed configuration of the loading system is shown in Figure
(a) Loading system: data acquisition system, (b) site datum beam of model anchor, (c) temperature monitoring system, and (d) jack oil system of field loading system.
According to the design requirement, a single main cable should bear a tension of
After completing the tests at the three loading stages of 1.0
Grating displacement sensors were used to monitor the creep deformation of the model anchor during the test. Nine sensors were installed on the front anchor face, rear anchor face, and front rock mass along the tensile direction. A long steel beam with length of 12 m was used as a reference beam. The layout of the grating displacement sensors is plotted in Figure
Positions of grating displacement sensors.
The creep deformations at the front and rear faces of the left and right anchors were measured by the grating displacement sensors under loads of 1.0
(a) Deformation and (b) rate of point
As can be observed from Figure
The two model anchor tunnels excavated for the model anchors are separated by 2.70 m in the in situ test, as indicated in Figure
Comparison of creep deformations between two model anchors.
As shown in the figure, both the left and the right anchors show similar values of creep deformations at all loading conditions. With the same loading level, there is only a subtle difference between the creep deformations measured at different points. Meanwhile, the creep deformations measured at the front and rear faces of the model anchor are almost consistent with each other. The average values of creep deformations measured at
The creep behaviour at the surface of the surrounding rock was tested using grating displacement sensors at five measuring points, namely,
Multipoint displacement transducers along the (a) vertical direction and (b) tensile direction.
The creep deformations on the surface and inside of the surrounding rock were tested under loads of 1.0
(a) Deformation and (b) rate of points D1-3 measured during creep testing.
Final creep deformation of points
Final creep deformation along the (a) tensile direction and (b) vertical direction in the surrounding rocks.
As shown in Figure
It could be seen from Figure
Figure
In summary, both the creep deformation and the creep rate of the surrounding rock tend to increase with increasing load level. Meanwhile, due to the sandwiching effect from the two anchors on the left and right sides, the creep deformation at the surface of the surrounding rock tends to become smaller with increasing distance from the anchor. In contrast, the creep deformation becomes larger as it gets closer to the anchor.
To analyse the creep characteristics of the interface between model tunnel anchor and surrounding rock, six dislocation meters were installed between each model anchor and its contact surfaces with the surrounding rock. Specifically, these meters were arranged on three separate cross sections located at the top arc, bottom plate, and side wall of anchor. Figure
Dislocation meters around the two model anchors.
The creep deformations of the interface between anchor and surrounding rock were tested under loads of 1.0
(a) Deformation and (b) rate of point WCJ6 measured during creep testing.
Final creep deformations of interfaces for (a) left anchor and (b) right anchor.
As shown in Figure
As indicated in Figure
In order to validate the results of the in situ creep test, a 3D numerical model comprising the left anchor and the surrounding rock was solved on FLAC3D platform. In addition, the long-term deformations of the actual full-size tunnel anchors of the Xingkang suspension bridge were evaluated by adopting an empirical method.
The in situ testing data show that the surrounding rock exhibits a viscoelastic characteristic when applying the loads of 1.0
Schematic diagram of four-element Burger’s model.
The Kelvin model is suitable for describing the relaxation process under a constant stress condition [
When the anchor of a suspension bridge is affected by an axial tensile stress
To examine the relationship between the axial tensile stress
3D calculation model comprised of model anchor and surrounding rock.
Taking any cross section of the anchor, the axial tensile stress could be calculated by
The axial and radial deformations are calculated by
The radial displacement is calculated by
According to the assumption of Winkler’s foundation model [
When substituting (
The 3D numerical model comprising the left anchor and the surrounding rock was solved on FLAC3D platform. The geometry size of this model is 56.8 m × 20.0 m × 47.2 m, as illustrated in Figure
According to the measured results in Figures
Input parameters of Burger’s model used for surrounding rocks.
Load | ||||
---|---|---|---|---|
1.0 | 0.44 | 63900 | 5.04 | 20.31 |
3.5 | 0.23 | 30100 | 3.15 | 10.11 |
7.0 | 0.15 | 20300 | 1.54 | 4.02 |
Input parameters of surrounding rocks and concrete tunnel anchor.
Position | tan | |||||
---|---|---|---|---|---|---|
Surrounding rock | 2.57 | 0.32 | 0.41 | 0.70 | 0.28 | 2.13 |
Concrete tunnel anchor | 2.45 | 1.57 | 1.43 | 1.28 | 0.21 | 31.5 |
In addition, only the gravitational stress field was considered in the calculation, and the normal displacements of the nodes at bottom and sides were constrained. The results obtained from the numerical simulation were compared with the experimental measurements to determine the creep deformation and reveal the creep deformation pattern of the anchor and surrounding rock.
Sensitivity analysis is conducted to evaluate the effect of parameters used in the Maxwell and Kelvin models on the deformation of tunnel anchor. The parameters for sensitivity analysis of tunnel anchor strain include elastic moduli
Summary of the parameters used for sensitivity of strain.
Elastic moduli | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 |
Elastic moduli | 1 | 2 | 3 | 4 | 5 | 6 |
Coefficient of viscosity | 5 × 102 | 1 × 103 | 5 × 103 | 1 × 104 | 5 × 104 | 1 × 105 |
Coefficient of viscosity | 1 | 5 | 10 | 20 | 50 | 100 |
Load | 1.0 | 3.5 | 7.0 | |||
Time (h) | 98 | 168 | 189 |
Figure
Effect of
Figure
Effect of
The effect of elastic moduli
Effect of
Figure
Effect of
After assigning the parameters to the computational model, the numerical simulation was then carried out for at least 120 h under each loading condition. Figure
Comparison between experiment measurements and simulation results of (a) tunnel anchor and (b) surrounding rocks.
Figure
The above comparisons show that the creep deformation at the measuring points obtained from the numerical calculation shared the same order of magnitude and a similar trend with the experimental measurements. The experimental measurements and simulation results demonstrated the same trend in the change of creep deformation for the anchor and surrounding rock.
Here we further evaluate the long-term creep deformation pattern of the anchor in the suspension bridge and the surrounding rock. We conducted a calculation for the model shown in Figure
Long-term creep patterns of (a) surrounding rock and (b) real working anchor.
It could be seen from Figure
The Honshu–Shikoku Bridge Authority in Japan reported the calculation of allowable horizontal displacement for anchors used in ultralong suspension bridges (1000 to 1500 m long) [
The main span length of Xingkang Bridge is 1100 m. According to (
Clearly, the creep deformation of the anchor along the tensile direction increases with increasing level of load from 1.0
The creep deformations measured at the front and rear faces of the anchor were consistent with each other. The average creep deformations of anchors were 0.54 mm, 0.90 mm, and 1.39 mm under loads of 1.0 The region between the left and right anchors experienced the largest creep deformations of 0.49 mm, 0.85 mm, and 1.10 mm under the three loading conditions, respectively. The creep deformation became larger as it got closer to the anchor. Under the loads of 1.0 The maximum creep deformation was measured at point WCJ6 located on the interface between the bottom plate of the left anchor and the surrounding rock. The maximum creep deformations of the interface between anchor and surrounding rock were 0.15 mm, 0.64 mm, and 1.43 mm, respectively, under the three loading conditions. The difference between the creep deformations measured at different points on the interface between anchor and surrounding rock became more significant with increasing load. Numerical analysis shows that the creep deformation of anchor and surrounding rock shared the same order of magnitude and a similar trend with the experimental measurements. The locations with maximum stress in the anchor, the surrounding rock, and the interface experienced a creep deceleration stage. Only one type of concrete model anchor with one size (i.e., front face is 1.48 m × 1.56 m, rear face is 1.77 m × 1.90 m, and length is 4.00 m) and one type of rock (i.e., altered adamellite) is taken into consideration in this work. Hence, the presented results are applicable to limited cases, but the presented results merit close attention as a valuable source of reference in engineering projects with similar conditions.
The data used to support the findings of this study are included within the article.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
The authors thank Elsevier’s Webshop for editing and polishing this paper. This work was supported by the Key Research Project of Sichuan Province (Grant no. 20ZDYF1468)