Mechanism of Splitting Failure for High Sidewall Cavern of Hydropower Station Based on Complex Function and Strain Gradient

With the rapid development of society, the number of hydropower projects has increased. During the construction of these projects, due to excavation-induced unloading, the high sidewalls of the hydropower station are often subject to splitting failure, which produces many adverse effects on the construction of the cavern. In order to reveal the formation mechanism of splitting failure of hydropower stations, based on the strain gradient theory and elasto-plastic damage theory, we proposed an elasto-plastic damage softening model. Using the ODE45 program in MATLAB, we solved the numerical solution of displacement and stress of circular cavern based on our proposed elastoplastic damage model. Then, we apply the complex function method and use the Schwarz–Christoffel integral formula to obtain the mapping function from the outer domain of the high sidewall cavern to the outer domain of the unit circle. Finally, the elastic-plastic region and displacement distribution of the high sidewall cavern are obtained by mapping the obtained elastic-plastic solution of the circular cavern under the axisymmetric condition. In future research, it is necessary to further study the corresponding relationship between the internal length parameter of the material and its internal microstructure in order to accurately determine the internal length parameter.