The greatest variability in both shear strength and roughness exists for joint samples with smaller size, which underscores the necessity of performing representative sampling. This study aims to provide a representative sampling method for series size joint surfaces. The progressive coverage statistical method is introduced to provide the sufficient sample capacity for series sampling sizes by setting different propulsion spaces. The statistical law of the joint surface morphology at different sampling sizes is measured by the 3D roughness parameter with $${{\theta }}_{\max }^{\ast }/({C}+1)$$θmax⁎/(C+1) . Through an application in nine natural large-scale rock joints, nine consecutive sampling sizes from 100 mm × 100 mm to 900 mm × 900 mm are selected and 121 samples are successfully acquired from each sampling size. According to the frequency distribution of roughness statistics, a new sampling method combining the layering principle and K-medoids clustering algorithm is proposed to screen representative joint samples for each sampling size. The sampling results that meet the test accuracy requirements suggest the possibility of realizing an intelligent sampling method. In addition, the representative of the interlayer cluster center is validated. Finally, the comparison results with the traditional stratified sampling method prove that the proposed method has better stability.

The vertical expansion of existing landfills can hold significant amounts of domestic waste and solve practical difficulties such as local government site selection. This research topic has become increasingly popular in the field of environmental geotechnical engineering. This study examined vertical expansion stability of landfills considering high leachate water level. The results showed the following. (1) Four slope instability modes for landfill vertical expansion are categorized according to the following slip surface positions: shallow slippage of the existing landfill, shallow slippage of the expanding landfill, interface slip between the existing landfill and expanding landfill, and deep slippage passes through the foundation soil. (2) The factor of safety decreases as the height of leachate level increases. When the height of leachate level rises from 2 m to 20 m, the factor of safety of the landfill is reduced by 13.2–15.4%. (3) As the vertical expansion height increases, the factor of safety of the existing landfill decreases, and when the expansion height increases to 30 m, the stability factor of safety of the old waste landfill is reduced by 4.83%. A landfill in Xi’an is considered as an example for the analysis, which shows that a leachate drainage layer can discharge leachate from the landfill body efficiently, reduce the leachate level height of the landfill body, and improve the stability of vertical expansion of the landfill. This study and its findings can be used as a reference for similar expansion projects.

This study mainly establishes a novel intelligent assessment model for peak shear strength of rock joints based on the relevance vector machine (RVM). RVM is a state‐of‐the‐art soft computing technique that has been rarely utilized in joint shear strength assessment. To establish the hybrid intelligent model, three‐dimensional scanning tests and direct shear tests on 36 granite joint specimens were conducted. The peak shear strength ratio (τ_p/σ_n) is perceived as an explanation of four types of influencing factors, including joint surface roughness, strength of rock material, basic friction angle, and normal stress. In particular, the compressive strength and tensile strength of rock material are first considered together. A total of 36 experimental data were used in this study to train the RVM model to predict the peak shear strength of rock joints. The performance of the RVM model was assessed using the direct shear test data of rock joints collected from previous researches. Four different kinds of kernel functions were adopted to obtain the optimal model. Results show that the proposed model is significantly efficient in predicting the peak shear strength of rock joints. The proposed model is also a promising tool for peak shear strength of rock joints and provides a new research approach to research the mechanical properties of rock joints.