Accurate predictions of the failure behaviors of quasi-brittle materials are of practical significance to underground engineering. In this work, a novel anisotropic damage model is proposed based on continuous damage mechanics. The anisotropic damage model includes a two-parameter parabolic-type failure criterion, a stiffness degradation model that considers anisotropic damage, and damage evolution equations for tension and shear, respectively. The advantage of this model is that the degradation of elastic stiffness only occurs in the direction parallel to the failure surface for shear damage, avoiding the interpenetration of crack surfaces. In addition, the shear damage evolution equation is established based on the equivalent shear strain on the failure face. A cyclic iterative method based on the proposed anisotropic damage model was developed to numerically simulate the fracture process of quasi-brittle materials. The developed model and method are important because the ready-made finite element software is difficult to simulate the anisotropic damage of quasi-brittle materials. The proposed anisotropic damage model was tested against a conventional damage model and validated against two benchmark experiments: uniaxial and biaxial compression tests and Brazilian splitting tests. The results demonstrate that the proposed anisotropic damage model simulates the mesoscale damage mode, macroscale fracture modes, and strength characteristics more effectively and accurately than conventional damage models.

The productivity ratio is a vital metric for assessing the efficiency of perforated completions. Accurate and rapid prediction of this ratio is essential for optimizing the perforation design. In this study, we propose a novel approach that combines three-dimensional finite element numerical simulation and machine learning techniques to predict the productivity ratio of perforated wells. Initially, we obtain the productivity ratio of perforated wells under various perforation parameters using three-dimensional finite element numerical simulation. This generates a sample set for machine learning. Subsequently, we employ the least squares support vector machine (LSSVM) algorithm to establish a prediction model for the productivity ratio of perforated wells. To optimize the parameters of the LSSVM algorithm, we utilize the particle swarm optimization (PSO) algorithm. We compare our proposed PSO-LSSVM model with that established based on other parameter optimization methods and machine learning algorithms, such as Grid search-LSSVM, PSO-ANN, and PSO-RF. Our results demonstrate that the PSO-LSSVM model exhibits rapid convergence, high prediction accuracy, and strong generalization ability in predicting the productivity ratio of perforated wells. This research provides a valuable reference and guidance for optimizing perforation design. Additionally, it offers new insights into predicting the productivity of complex completions.

The depletion of aquifers by excessive pumping is one of the prominent global sustainability issues in the field of water resources. It is mainly caused by the water needs of irrigated agriculture. The North China Plain is a global hotspot of groundwater overexploitation.