The limit equilibrium method’s analysis index cannot be measured by on‐site monitoring equipment and cannot be used for monitoring and early warning of rock instability. The existing rock stability evaluation methods based on vibration information cannot evaluate the stability of rocks quantitatively. In this paper, the slope’s constraints on the rock were simplified to springs and a three‐dimensional analysis model of rock vibration was established. The equation for calculating the natural frequency of rock that includes the spring stiffness as an indicator was derived. The rock stability calculation function containing the index of natural frequency was brought into the traditional rock stability coefficient calculation equation, and a new rock stability analysis method based on natural frequency was established. The experiment proved the measurability of the index of the natural frequency of rock and the method’s effectiveness for the stability analysis of the rock based on natural frequency.

A rapid shrinkage of Daihai Lake was found in recent decades. The present study analyzed the characteristics of Daihai Lake shrinkage and quantified the contribution of climate and human activities. The results of Mann-Kendall- Sneyers test and moving t-test showed that there was an obvious mutation point of lake level in 2006 and the descending speed of Daihai Lake level post-2006 (-0.46m/a) was 3.22 times that of pre-2006 (-0.14m/a). The centroid of Daihai Lake moved 1365.18 m from southwest to northeast during 1989 ~ 2018 with an average speed of 47.08 m/a. The results of Mann-Kendall trend test revealed that the annual evaporation showed a significant downward trend with a rate of approximately -5.33 mm/a, while no significant trend was found in precipitation. Daihai lake water level showed a very weak relationship with evaporation (r = 0.078, p < 0.01) and precipitation (p>0.05) respectively. Daihai Lake was influenced by human activities mainly from land use/ land cover, building reservoirs, pumping groundwater and directly consuming Daihai Lake water by Daihai power plant (DHPP). It was thought-provoking that DHPP began to consume Daihai lake water in 2006, which was consistent with abrupt change of Daihai lake level. The proportion of human impact was fluctuating upward. Human factors were the main factor of lake water reduction in last 10 years and the 5-year average contribution of human activities to Daihai Lake shrinkage was more than 61.99%. More attention and economic support should be given to prevent the continuous shrinkage of Daihai Lake.

Lithology variations, which are recognized as rock type differences, significantly affect the physical properties of rock masses in red beds. In this paper, we introduce a statistical method for quantitatively evaluating the degree of lithology variations in layered red beds with depth. The core of this method is to use borehole logs as random variables for statistical analysis to calculate the percentage of a specified lithology at a given elevation, which involves seven steps of attitude calculation, reference point selection, distance calculation, elevation modification, data discretization, data statistics, and curve plotting. The Yellow River Guxian Dam is chosen as a field case study. We classify rock types of feldspar sandstone, fine sandstone, and conglomerate into hard rocks and that rock types of calcareous siltstone, argillaceous siltstone, and mudstone into soft rocks. Borehole logs recorded during the geological investigation are used to plot the percentage curve of hard rocks. We find that the degree of lithology variations for each lithology group differs greatly, the general behaviors of lithology variations on two sides of the Guxian Dam riverbed are quite similar but still with some differences, and that some thick lithology groups can be finely divided into several subgroups. On the basis of the hard rock percentage curve, we introduce a lithology variation index to quantitatively characterize the degree of lithology variations, which can be used as an important index to supplement the traditional methods when performing rock mass classifications in red beds. We also plot the trilithology percentage curve of sandstone, calcareous siltstone, and argillaceous siltstone, which serves for the determination of physical parameters of the dam foundation rock mass, the identification of the potential shear sliding surface, and the search for an impervious grouting bottom. Moreover, we find that the crest and trough, which are local high and low points in the hard rock percentage curve, can be used to show some characteristics of shear zones. The locations of shear zones are well represented in the form of troughs and that the development of shear zones has a good linear relationship with the hard rock percentage of the corresponding crest. The method proposed in this paper can be promoted and applied in similar projects or studies.

Straightforward solutions have long been expected for the analysis of multiwell aquifer tests. In this paper, we derive series analytical solutions of steady-state groundwater flow in a rectangular-shaped aquifer with pumping/injection wells for both confined and unconfined conditions. Double Fourier Transform (DFT) technique is applied to deal with different combinations of impermeable and specified head boundaries on sides. The obtained solutions are compact and concise in mathematics and flexible in terms of well number, well locations, and pumping/injection rates. Hatoucaidang, a groundwater resource field in the Ordos Plateau, Northwestern China, is introduced as a field case study, where a multiwell aquifer test was conducted. One of the analytical solutions derived herein is used to estimate hydraulic conductivities by applying a direct calculation method and a least square estimation method regarding observed versus calculated drawdowns. By comparing with nearby single-well pumping tests, the reliability of the derived analytical solutions is proven. This study facilitates utilizing the multiwell aquifer test to analyze the general behavior of groundwater movement in aquifer systems.

The modeling of shear cracks in materials is critical in various engineering applications, such as the safety analysis of concrete structures and stability analysis of rock slopes. Based on the idea of Goodman element, the elastic‐plastic constitutive model of the shear cracks is derived, and the elastic‐plastic analysis of shear crack propagation is realized in the local radial basis point interpolation method (LRPIM). This method avoids the loss of accuracy caused by the mesh in the analysis of fracture propagation, and the crack propagation of rock brittle material is simulated. The investigation indicates that (1) the LRPIM results are close to the FDM results, which demonstrates that it is feasible to analyze shear cracks in rock masses. (2) Compared with the results of the built‐in oblique crack model, when the LRPIM is used to analyze crack propagation, the results are close to the experimental results, showing that the LRPIM can model shear crack propagation in a rock mass. (3) The propagation path using the LRPIM is not sufficiently smooth, which can be explained as the crack tip stress and strain not being sufficiently accurate and still requiring further improvement.