Time integration with stress–strain updating is a key step for the application of elasto-viscoplastic models to engineering practice. Currently, the estimation robustness of algorithms is lacking, which poses difficulties in the selection and improvement of algorithms. To solve this, the study selected four typical implicit time integration algorithms (i.e., Newton-Raphson, Katona, Stolle, and cutting plane) for the same simple elasto-viscoplastic modified Cam-clay model (EVP-MCC). Some necessary enhancements are discussed that were made for the integration. A series of laboratory tests was simulated, based on which the variations of the relative errors of stresses and iteration numbers with step size were investigated and compared. For the Newton-Raphson algorithm and the Katona algorithm with $\theta =0.5,\hspace{0.17em}1.0$ , the maximum step sizes ensuring convergence were found to be at least one order of magnitude larger than those of the other algorithms, and their total iteration numbers and relative errors of stresses were at least one order of magnitude lower than those of the other algorithms. Furthermore, the model using different algorithms was implemented in a finite-element code, and the global convergence and calculation time were investigated for a boundary-value problem. The robustness of all algorithms was estimated based on the calculation performance in terms of convergence, accuracy, and efficiency. The results demonstrate that the global iteration number for the cutting-plane algorithm is at least 20 times higher than the others at any mesh density, which leads to the result that the central processing unit (CPU) time for the cutting-plane algorithm is almost 10 times higher than the others. All comparisons demonstrate the performance of different time integration algorithms with a prior order of Newton-Raphson, Katona, Stolle, and cutting-plane algorithms.

T-shaped fractured rocks in the engineering rock mass with different inclination angles, quantities, and cross patterns will cause slope landslides, cavern collapse, roof fall, and other disasters under the action of external forces. Deformation evolution of the T-shaped fractured rock is also significant for monitoring the stability of rock engineering structures. In this paper, the compression test of T-shaped fracture specimens was carried out under different loading rates. By modulating both the fracture inclination angle and the loading rate, the attributes pertaining to energy dissipation in the T-shaped fractured specimen were scrupulously scrutinized and subsequently expounded upon. The difference in the energy characteristics between fractured rock and intact rock was investigated to understand the deformation evolution of T-shaped fractured rock samples. The results show that when the fracture angle is 45° and 90°, the elastic strain energy and dissipated energy decrease as the secondary fracture angle increases. At the peak point, as the secondary fracture angle increases from 0°, the total absorbed energy, elastic strain energy, and dissipated energy of the T-shaped fractured rock increase, the ratio U^e/U of elastic strain energy to total energy increases, and the ratio U^d/U of dissipated energy to total energy decreases. The increase in loading rate leads to an increase in U^e/U and a decrease in U^d/U at the peak point of the T-shaped fractured rock specimen. The increase in loading rate leads to an increase in the total absorbed energy and elastic energy at the peak point of the T-shaped fractured rock, while the dissipated energy decreases. Investigative endeavors into the mechanics and energetic attributes of T-shaped fractured rocks bestow pragmatic and directive significance upon the safety assessment and stability prognostication of sundry geological undertakings.

After the rupture of pressurized water supply pipes in urban underground areas, seepage-induced ground subsidence becomes a severe geological hazard. Understanding the permeation and diffusion patterns of water in soil is crucial for deciphering the mechanisms underlying soil settlement and damage. Notably, the pressure within water supply pipes significantly influences the settlement and damage of the soil. Therefore, this study simulated experiments on soil settlement and damage caused by water seepage from a preexisting damaged pipeline under various internal pipe pressure conditions using an indoor model apparatus. The results indicate that the internal pressure of the pipe significantly influences the settlement of the soil. High-pressure seepage causes noticeable erosion in the soil, forming cavities within it. In contrast, low-pressure seepage results in water diffusing in an ellipsoidal pattern, leading to the formation of circular surface cracks. The degree of surface settlement increases with higher pipe pressure. The onset of subsidence at a specific point on the ground is not directly related to whether the moistening front within the soil has reached that point horizontally. Instead, it is associated with the moisture content below the subsidence point within the soil. The research results further illustrate the water diffusion and moisture content increase processes after water seepage from pipes with different pressures, revealing the influence of pipe pressure on the degree and form of soil settlement damage and clarifying the relationship between water diffusion and settlement in the soil.