To investigate the dynamic response and dynamic evolution of a rock slope containing discontinuities under earthquake motion, model tests are conducted in this study. The slope model in the shaking table tests is scaled from the bank slope of the Jinsha River Bridge.
2.1 Case study
The Jinsha River Bridge crosses the Jinsha River. As shown in Fig.
1, it is an important bridge on the Huali highway connecting the cities of Lijiang and Huaping. The route crosses the Jinsha River at a vertical angle from east to west (as shown in Fig.
2). As the key project of the HuaLi highway, the main pile cap of the bridge is located in the middle of the slopes near the Jinsha River. The bank slope, on which the main pile cap was built, has a stepped topography due to the dip structure and flow along the river. The Huaping coast is along the bank slope, with a gradient of 20°–30°. The exposed strata of the project area are mainly a Permian basalt formation (P2 β3), basalt almond-shaped lithological volcano, breccia lava, and tuff. The site of the slope has a tuff structural surface and a step structural surface on the trailing edge (as shown in Fig.
3). This area can resist an earthquake with an intensity of VIII. Combined with the actual situation of the bridge, the main factors affecting the stability of the slope are the topography, stratigraphic lithology, combination of the structural surfaces, and seismic loads.
2.2 Material properties
According to the geologic conditions of the Huaping bank slope along the Jinsha River Bridge, the rock slope is assumed to be in a state of plane strain. The material characteristics of the models and test conditions should be confirmed using the law of similitude. The similarity ratio for the geometric dimensions is 375, the similarity ratio for the acceleration is 1, and the similarity ratio for the density is 1. The other physical quantities are calculated according to these similarity criteria, and are summarized in Table
1. 1
Table 1
Similarity criteria calculation
Quantity
|
Similarity criteria
|
Similarity coefficient
|
Geometric L
|
CL=375
|
375
|
Acceleration a
|
Ca=1
|
1
|
Density ρ
|
Cρ=1
|
1
|
Young’s modulus E
|
CE=CρCL
|
375
|
Poisson’s ratio µ
|
1
|
1
|
Cohesion c
|
Cc=CρCaCL
|
375
|
Internal friction angle φ
|
1
|
1
|
The results calculated with the similarity ratios indicate that a thickness of the tuff structure surface of 5 mm can be used in the test model. In order to meet this requirement, model materials are prepared by as a mixture of other materials, i.e., cement, sand, clay, and iron powder. Based on the ratio test, density test, materials test, and three static tri-axial tests, the selected mass ratio of cement, sand, clay, iron powder, mixture (admixture and water reducing agent) and water is 0.325:17:9:0.4:0.03:5. The physical parameters of this mixture are listed in Table 2. The tuff material on the structural surface is modeled with a PVC expansion sheet to obtain a similar cohesion of 21.1 kPa and internal friction angle of 23.2°.
Table 2
Physical-mechanical parameters of material parameters of the slope
|
Rock material
|
Density
γ/kN·m− 3
|
Young’s modulus
E/MPa
|
Cohesion
c/kPa
|
Internal friction angle
φ/°
|
Physical parameters (rock material)
|
Basalt
|
30
|
69000–82500
|
11250–14440
|
46.3–46.9
|
Tuff
|
\
|
\
|
\
|
29
|
Results of similarity criteria calculation
|
Basalt
|
30
|
184–220
|
30-38.5
|
46.3–46.9
|
Tuff
|
\
|
\
|
\
|
29
|
Physical parameters (similarity material)
|
Basalt
|
20.4
|
100
|
48.43
|
40.69
|
Tuff
|
\
|
\
|
\
|
23.2
|
2.3 Scale model
The model is 1.3 m in height and weighs more than 7 tons (as shown in Fig. 4). There are many challenges in construction of a model of this size. If the model is poured as a whole, the curing time will be excessively long. Because different areas in the model have different curing times, it is difficult to control the strength of the simulation material. In addition, it is difficult to place the sensor in the center of the model. Therefore, a special construction method is used to address these problems. The model is split into 224 blocks, and each block is poured with a corresponding mold. The curing times of all blocks are then precisely controlled. Typical blocks are shown in Fig. 5. To simulate the tuff structural surface, a PVC expansion sheet was inserted in the block during the corresponding stage. A typical block containing the tuff structural surface is shown in Fig. 5b. To simulate the step structural surface in the trailing edge, sand was inserted in the block during the corresponding stage. A typical block containing a step structural surface in the trailing edge is shown in Fig. 5c. After completion of the model, the PVC expansion sheet is connected to form the same shape as the tuff structural surface. Some cracks are used to simulate the step structural surface on the trailing edge, as shown in Fig. 5c. These cracks are cut with a 5-mm-thick iron sheet and filled with sand. After the block is poured, it is cured for 5d in a dry, cool environment.
To clarify the dynamic response of the rock slope, a simplified model was established and simulated. The model slope had a size of 280×140 cm and a height of 130 cm (shown in Fig. 3). The slope model was constructed with prefabricated blocks, which were assembled in seven layers. The angles of the structural plane and trailing edge of the steep structural surface slope in the model material were 30° and 75°, respectively. The slope model is shown in Fig. 6.
2.4 Measurements
The acceleration measurement setup is shown in Fig. 7. First, 20 accelerometers were arranged in the slope; accelerometers A8, A12, A15, A18, A22, A23, A24, and A25 were placed on the slope surface, while the other accelerometers were embedded at various depths in the slope. The accelerometers used are able to collect acceleration data in three directions simultaneously (as shown in Fig. 8). The frequency range of the acceleration sensors is 0–1500 Hz in the horizontal direction and 0–800 Hz in the vertical direction; the sensitivity is approximately 66 mV/m·s− 2 with a range of ± 20 m/s2. An additional buffer layer with a thickness of 10cm was designed to minimize the effects of the bottom boundary.
2.5 Input motions
The waveform was synthesized by a local earthquake prediction department based on local historical earthquake data and geological characteristics. The time history and response spectrum are shown in Fig.
9. The dominant frequency of the artificial synthetic wave was 4.5–5.5 Hz. The seismic waves were loaded horizontally in the tests. The working conditions of the tests are summarized in Table
3.
Table 3
No
|
Exciting direction
|
Earthquake intensity degree
|
amax(m·s− 2)
|
1
|
horizontal(x)
|
6
|
0.37
|
2
|
horizontal(x)
|
7
|
0.74
|
3
|
horizontal(x)
|
8
|
2.97
|
4
|
horizontal(x)
|
9
|
4.46
|