Study of base friction simulation tests based on a complicated engineered bridge slope

Abstract

In this paper, a physical base friction test model of a slope is established. The model is based on similarity principles and the geological conditions of a complicated bridge slope during construction, deformation and failure. The behavior of the slope in both its natural state and during excavation loading is qualitatively analyzed through base friction tests. The base friction test results are then subjected to comparison and analysis using finite element numerical simulation. The findings show that the whole engineered slope tends to stabilize in its natural state, whereas instabilities will arise at faulted rock masses located near bridge piers during excavation loading. Therefore, to ensure normal construction operation of bridge works, it is suggested that pre-reinforcement of faulted rock masses be performed.

Keywords

base friction test / slope stability evaluation / bridge slope

Introduction

The principle of base friction testing was first proposed and applied to the analysis of the stability of rock masses by Goodman and Hoek in 1969 [1]. In 1972, Erguvanli and Goodman used flour and oil as modeling materials for a base friction test simulation [2]. In 1979, Egger designed a base friction unit capable of applying constant loads to test models. With Egger’s work, the use of base friction testing became a standard practice [3]. In recent years, base friction testing has been used to simulate deformation and failure of landslide and engineered slopes [4-6]. The principle of base friction testing is to use friction forces to simulate natural gravity to study deformation and stability of model geotechnical materials under gravity. Base friction testing is one of the several available physical simulation methods.

In this paper, a scale slope model is established using similar materials based on the geological parameters of an actual bridge slope that is under construction. A stress analysis is carried out on the engineering slope using base friction tests. The work provides a reliable basis for evaluating the stability of the bridge slope.

Principle of base friction

In a base friction simulation, a gravity field is simulated by the force of friction in the model acting in the direction of friction. The force for the model tests is provided by changing the friction coefficient between the friction base plate and the model. The principle is to convert the profile of the research subject (i.e., the slope) into a planar model, level the plane, and move the base plate that underlies the model. The base plate is continuously moved such that the vertical direction of the original profile corresponds with the direction of motion of the base plate. The model moves with the continuous movement of the base plate. A fixed frame is arranged in the direction of motion of the base plate. A frictional force F is formed at all points of surface contact between the model and the base plate when the model is blocked by the fixed frame:

(1)F={\gamma }_m,t\mu ,

where, γ_m is the unit weight of the model material; t is the thickness of the model; and μ is the friction coefficient between the model and the sliding base plate.

According to Saint-Venant’s Principle [7], the force F can be used to simply simulate gravitational stress with the model. However, as the force F acts on all points of the model, whereas gravity would act at the center of the model, the model cannot be too thick. If the model were too thick, the simulation would be distorted.

Basis of test simulation

Geological conditions of study slope

A bridge is to be built on an engineered slope. The slope is located in a deeply cut valley and has a number of faults. It has been determined from slope survey data and field investigation that the height of the bridge bank slope is 430 m, the main rocks are slate and fault breccia, the average rock bed thickness is 10 m, and the average joint spacing is 20 m. The bedrock of the slope is broken, with faults F1 and F2 as well as potentially faulted rock masses (Fig. 1).

Test equipment and geometric parameters

The equipment used in the base friction test is self-developed based on the basic principles of the test method. A motor is used to provide continuous movement between the model and the base plate, and the friction coefficient μ of the base plate is 0.72, which provides a sufficient frictional force. The motor drives the friction plate to move at a uniform speed. The friction is read from a dynamometer installed on the pulling rope. The movement is controlled by increasing or decreasing the motor speed to meet requirements. Bridge loads are applied to the bridge surface with a hydraulic jack (Fig. 2).

To enable the base friction model to reflect actual conditions, the model must follow similarity principles with regard to geometric conditions, stress conditions, friction coefficients and other relevant parameters. In this paper, geometric dimensions and volumetric weight are taken as fundamental dimensions. With regard to similarity constants, the stress similarity ratio is C_σ = C_γ·C_L·C_L = 25000. This result is based on the dimensional analysis method with a geometric similarity ratio C_L = 500 and a volume weight similarity ratio C_γ = 1. The unit module size is L × W × H = 40 mm × 20 mm × 40 mm, which is based on a geometric similarity ratio of prototype to model of 500∶1, a calculated model height of 86 cm and a model length of 118 cm. The cross sectional size of a bridge pier is 60 mm × 40 mm, the apparent dip of the rock bed on a longitudinal section is 34°, the height of the rock bed model is 20 mm, the apparent dip of the model joint is 43°, and the joint model spacing is 40 mm.

Test model materials

The study slope mainly includes exposed slate and fault breccias. Barite powder and gypsum are selected as module materials in the base friction test. To improve the strength of the materials, small amounts of white cement and gypsum are added as setting-retarding materials to slow the setting rate during module fabrication. See Table 1 for the proportions of test materials used to simulate slate and fault breccia.

Test procedure

The proportionally sized module materials are arranged in the test model following the longitudinal profile of the slope, with attention given to the position of the apparent dip in the rock bed and the joint plane. A model bridge constructed from wood is then placed above the slope, with a hydraulic jack used to apply a load to the bridge surface through a pier. The bridge design uses a load of 2.75e4 kN at the bridge pier; using the similarity ratio of C_σ = 25000, the applied load F in the model is 1.1 kN. At the beginning of the base friction test, the motor is turned on to start the base plate motion. The plate movement is initially controlled, with the movement accelerated after the cohesion between the model and the base plate is broken. Deformation and failure of the model is observed as the base plate moves. The test is stopped when the model completely fails.

Test phenomena and result analysis

Test process and natural state results

The slope model for the natural state is shown in Fig. 3. The deformed and failed areas of the slope in the whole base friction test are the exposed slope surface (as shown in Fig. 4) of the F1 fault and the front edge (as shown in Fig. 5) of the faulted rock mass. Cracks among the exposed surface modules of the F1 fault are small, and only individual modules slightly slide outwards. Cracks are formed by the front edge modules of the faulted rock mass sliding in the valley direction. The maximum width of the cracks is 4 mm, whereas the relative dislocation distance between layers is 3 mm.

The following results are noted from the slope base friction test for the natural state: The slope grade is gentle; there are no obvious deformations and failures; instabilities are noted for individual rock masses on the exposed surface of the F1 fault; and a 40 m (long) × 30 m (high) rock mass in a triangular area on the front edge of the faulted rock mass is unstable and needs to be reinforced to prevent the instability of the entire faulted rock mass under the long-term action of gravity. In general, the slope is in a basically stable state under natural conditions.

Test process and loaded state

The slope model is shown in Fig. 6 under loaded conditions. The deformation area of the slope is located at the module below the loaded bridge pier. No deformation or failure occurs to the module above the bridge pier (Fig. 7). A small deformation occurs that is caused by the front edge of the faulted rock mass sliding in the valley direction under load. The faulted rock mass module below the bridge pier slides 10 mm in the valley direction without cracking, as shown in Fig. 7. A small-scale local rock mass slide occurs near the F1 fault (Fig. 8).

The following results are noted for the slope base friction test under loaded conditions: The entire faulted rock mass below the bridge pier at the right bank of the bridge slides in the valley direction under loading conditions with an actual slip distance of 5 m, and the entire faulted rock mass is unstable. If the entire faulted rock mass is pre-reinforced or the foundation of the bridge pier is properly moved backward, the stability of the rock mass will be significantly improved.

Numerical simulation and comparative analysis

To demonstrate the reliability of the base friction simulation test, a finite element method is used to conduct a numerical simulation analysis of the engineered slope. The simulation results are shown as stress and displacement nephograms in Figs. 9-12.

Several observations are made based on the figures. With regard to the natural state, the stress field characteristics of the bank slope show that the valley is controlled by gravity. Meanwhile, under the effect of the structural features of slope rock masses, the stress field of the bank slope changes near the F1 fault transition zone and the faulted rock mass contact zone. However, the whole bank slope tends to stabilize in a natural state based on the analysis of the displacement nephogram; this result conforms to field investigation conditions.

With regard to the loading by the bridge pier, the stress concentrates at the front part and the bottom of the bridge foundation at the slope, and shear failure occurs to sliding rock masses around the bottom of the bridge foundation. Meanwhile, the shear stresses in the gravel soil areas above the F1 and F2 faults tend to increase. It can be observed from the displacement nephogram that obvious displacement occurs to the faulted rock mass, indicating instability and deformation of rock masses at the lower part and front part of the bridge foundation, It is preliminarily determined that a large shear deformation will occur to rock masses at front bank slope and bottom of the bridge foundation after loading, thus causing instability failure.

Conclusions

The following conclusions can be drawn regarding the use of the base friction test for the bridge bank slope:

1) The entire engineered slope is in a stable state under natural conditions. Dangerous rocks and falling rocks at the exposed fault should be subject to stability treatment.

2) After the engineered bridge is loaded, the faulted rock mass below the bridge pier will slide in the valley direction and lose stability; this mass should be pre-reinforced to ensure normal bridge construction and operation.

3) The results of the base friction test are in accordance with numerical simulation results and field investigation results, which demonstrates that the results of the base friction test are usable.

References

[1] Goricki A, Goodman R E. Failure Modes of Rock Slopes Demonstrated with Base Friction and Simple Numerical Models. Rock Slope. 2003:25–30.

[2] Erguvanli K, Goodman R E. Applications of models to engineering geology for rock excavations. Bulletin of the Association of Engineering Geologists, 1972, 9: 89–104

[3] Egger P. A new development in the base friction technique. Proc. Symp. on Physical Geomechanical Models.1979:67–81.

[4] Xu Q, Zhang D X, Zheng G. Failure mode an stability analysis of left bank abutment high slope at JINGPING I hydropower station. Chinese Journal of Rock Mechanics and Engineering., 2009, 28(6): 1183–1192 (in Chinese)

[5] Feng W K, Shi Y C, Chai H J. Study of mechanism of deformation failure of a low-angle bedded high slope with physical simulation method. China Journal of Highway and Transport., 2001, 17(2): 32–36 (in Chinese)

[6] Chen X B, Li Y S, Zhao X P. The application of bottom friction gravity test to the study of the stability of the toppling rock mass. Earth Science Frontiers, 2008, 15(2): 300–304 (in Chinese)

[7] Toupin R A. Saint-Venant's Principle. Archive for Rational Mechanics and Analysis, 1965, 18(2): 83–96

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg