The weak structure plane is an important factor affecting the stability of rock slope, and detecting the spatial structure of the weak structural plane is beneficial to analyze the stability of the slope and estimate the quantity of the landslide. Based on 3D electrical resistivity tomography, a model of rock slope with weak structure plane is established, and the characteristics of three-dimensional resistivity imaging of weak structure plane under different ground water conditions are simulated. The results show that the weak structural plane has a better reflection in 3D electrical resistivity tomography; the distribution of weak structural plane of 3D resistivity imaging can be roughly determined under different ground water conditions; the three-dimensional electrical resistivity tomography is feasible in the detection of weak structural plane of rock slope.
China is a mountainous country; the mountainous area of our country accounts for over 50% of the total land area; the problems of geological disasters occur frequently; the problem of slope instability is particularly prominent, which poses a threat to people’s lives. So it is very important to study the stability of the slope in the design and construction of the slope engineering. Weak structural plane is formed in the rock mass with a certain extending direction and length; thickness is relatively small geological interface; it includes material interfaces and discontinuities, such as level and unconformity face, joints and faults and so on. The weak structure plane in a large scale, such as low intensity, easy deformation, often influences the integrity, permeability, physical mechanical properties and stress transfer of engineering rock mass, which is one of the essential causes of non-homogeneous, non-continuous, anisotropic and non-linear elasticity of rock mass [
Drilling as a traditional geological prospecting method cost is high, and blind. In order to find out the geological condition quickly and accurately, the high density resistivity is a new geophysical prospecting method. Two-dimensional high density resistivity method development has been relatively mature, proposed by Japanese scholars in the eighties of the twentieth century; the high density resistivity method can collect data automatically, measure quickly, get a lot of information, draw 2D profile image and reflect the geoelectric structure fully; the method is superior to the traditional electrical method [
The three-dimensional electrical resistivity tomography is based on the difference of the underground medium resistivity, through the electrode to the underground power, to measure the different points of apparent resistivity in underground, apparent resistivity value is not a specific point resistivity values, but a comprehensive reflection of a regional resistivity and apparent resistivity calculation formula is:
where:
The core of 3-D resistivity tomography is forward modeling and inversion. The forward modeling is known geoelectric model and field source distribution, distributed of electric field problem is solved. Inversion is to find a geoelectrical model and enable the corresponding values of theoretical calculation and measured apparent resistivity values coincide with the best under certain rules. Forward modeling is the base of the inversion, and the theoretical value of the forward calculation is obtained. Inversion calculation is often the underground space is divided into several small cuboids, in comparing the theoretical value and the measured value during the process, the Jacobian matrix calculation is the core and the calculation method is generally divided into Gauss Seidel method and quasi Newton method, Gauss Seidel method in every iteration needs to compute the Jacobian matrix and long computing time, high precision and quasi Newton method do not need every time to calculate the Jacobian matrix, only need a calculation, back calculated by iterative formula, fast calculation and low precision. Modification of model parameters is for computational purposes. After reaching the accuracy, will give the theoretical value of each cuboid, get the final geoelectric structure [
When there is ground water in the weak structure plane, it is generally low resistance. The joints have strong joint development or discontinuous surface in the weak structure plane, and the resistance is generally higher when there is no water [
When there is groundwater, assuming the resistivity of surface covering layer is 50 W∙m, the weak structural plane is 5 W∙m, the bedrock is 100 W∙m. Numerical simulation results are shown in
The action is without groundwater, assuming the resistivity of surface covering layer is 10 W∙m, the weak struc- tural plane is 100 W×m, the bedrock is 50 W×m. Numerical simulation results are shown in
XY resistivity distribution diagram, the weak structural plane of high resistance influence range is significantly larger can be found, but from the resistivity distribution shape were observed, in layer 4 to 5 resistivity distribution shape change from square to approximate circular, the high resistivity anomaly area and weak structural plane location are basically consistent can be judged in layer 4. The high resistivity anomaly district about 12m length, about 10 m wide, the result is consistent with the model, indicating that high resistance patterns of the weak structure plane reflected well. From the XZ resistivity distribution diagram shows that the high resistance anomaly area is about 10 m wide, and the thickness has some error, the shape of the high resistivity anomaly area is basically the same as the position and the size of the weak structure plane. From YZ resistivity distribution figure seen, high resistivity anomaly mayor 12 m length, thickness of some error, but the high resistivity anomaly zone and weak structural plane where position corresponding. By comparing with the resistivity characteristics of the weak structure plane underground water, the resistivity imaging resolution of the weak structure surface underground water is found to be higher, the reflection of weak structural plane is better.
The inversion after the data collated into image processing software, after partition model adjust chromatography, the action of groundwater and without groundwater of weak structural plane are extracted from the 3D resistivity images, as shown in
the spatial form of the weak structure plane and estimate the size of the weak structure plane, weak structural plane has a higher accuracy under the action of groundwater, in the actual measurement can provide more accurate data, and the weak structural plane without ground water has a certain error, which needs to be reduced on the basis of the actual measurement. By measuring the angle between the weak structure plane and the horizontal direction, and use the formula:
where:
It can be used as a condition to judge the stability of rock slope, so as to make a reasonable safety evaluation for rock slope and provide scientific data for design and construction.
1) By means of three-dimensional electrical resistivity tomography numerical simulation of rock slope with weak structure plane, the electrical resistivity tomography resolution of the weak structure surface under different ground water is analyzed, illustrating the effectiveness of the three-dimensional electrical resistivity tomography in the detection of weak structural plane.
2) Three-dimensional electrical resistivity tomography overcomes the lack of 2D electrical resistivity tomography; the distribution of weak structural plane in rock slope can be found, judging the stability of rock slope, a rough estimate of unstable rock excavation amount; the result is intuitive and easy to explain.
3) In the numerical simulation of 3D electrical resistivity tomography of rock slope, the model is established without considering the influence of topography fluctuation on resistivity imaging, which should be worth attention in the future research. When the high resistance anomaly occurs, the weak structure plane is separated from the bedrock, and it should be properly reduced when estimating the amount of the landslide surface and the landslide. In the study of the mechanism of the instability of the soft surface, the relationship between the resistivity and the stress and strain of rock should be established.
This paper is funded by National Natural Science Foundation of China (51279219).
Xin Zhang, (2016) Numerical Simulation Study on the Detection of Weak Structural Plane of Rock Slope by Using 3D Electrical Resistivity Tomography. Engineering,08,438-444. doi: 10.4236/eng.2016.87041