Study On Response Surface Method For Slope Reliability Based On Return Mapping In Principal Stress Space

The slope instability（landslide）has always been one of the geological disasters with the highest frequency and the greatest loss in personnel and property.Generally,the factors causing slope instability are uncertain,thereupon the slope reliability analysis to be increasingly achieved attention.The efficiency and accuracy of the reliability method used to determine the slope reliability are dominated by both itself and the method calculating the factor of safety.Under the support of the National Natural Science Foundation（41772321）and the Chengdu Center of China Geological Survey（DD20160272）,this paper improves and innovates the response surface method is widely used in slope reliability analysis on the basis of the finite element method and the strength reduction method.The main works of this paper are as follows:（1）A return mapping algorithm is proposed in this paper for the Mohr-Coulomb strength criterion and a series of non-linear yield criteria which ignore the influence of intermediate principal stress.When the proposed algorithm is applied to these non-linear yield criteria,the equivalent Mohr–Coulomb strength parameters,the derivatives of their functions,and the tensile strength of these non-linear yield criteria are merely demanded because the equivalent Mohr–Coulomb strength parameters are considered in the derivation of the algorithm,and these yield criteria can be realized in finite element software.The effectiveness of the proposed algorithm is verified by taking Mohr–Coulomb strength criterion and Hoek–Brown strength criterion as examples.By comparison,the proposed algorithm in this paper is more suitable for the associated flow criterion.（2）The active learning method is introduced into the slope reliability analysis.An improved U active learning function was proposed in this paper and can obtain good fitting accuracy under the overall region through searching a relatively small number of optimal sample points.The response surface method with the improved U active learning function demonstrates its efficiency and accuracy.Compared with the traditional response surface method,the calculation efficiency has been improved obviously due to the reduction of the number of training samples.（3）A supplementary sampling method for Mohr–Coulomb strength criterion is proposed,which can generate any number of supplementary samples and guarantee the distribution of supplementary sample points on the limit state surface and on both sides of the limit state surface.Because supplementary samples do not need to perform deterministic analysis（strength reduction method）to obtain the factor of safety,it can significantly improve the efficiency of the response surface method.A method system combining the active learning method,the supplementary sampling method,and response surface method is proposed for slope reliability.The supplementary sampling method can make up for the deficiency of the improved U learning function,so that the training samples needed by the response surface method can be further reduced,while the computational efficiency can be further improved.The reliability of Yangjiagou landslide in Wen County,Gansu Province,is evaluated.The results show that the failure probability of Yangjiagou landslide is 0.0%.It is currently in a stable state and does not need reinforcement.（4）This paper further extends supplementary sampling method for Hoek–Brown strength criterion on the basis of the direct strength reduction method.The reliability of Laohuzui slope is evaluated based on the proposed method system combining the active learning method,the supplementary sampling method,and response surface method.The calculation results show that the supplementary sampling method for Hoek–Brown strength criterion can significantly improve the accuracy of response surface model,a small number of samples are needed to establish response surface model.The average factor of safety for Laohuzui slope is between 1.113 and 1.229.The direct reduction method based on m_i andζ_ci is relatively conservative,and the reliability index of Laohuzui slope is 0.7381.However,the direct reduction method based on s,m_b,andζ_ci can overestimate the factor of safety for Laohuzui slope,and the reliability index of Laohuzui slope is0.8414.The reliability index of Laohuzui slope calculated by the direct reduction method based onζ_ci and GSI is 0.7782.Therefore,Laohuzui slope does need reinforcement.