Strength criteria for intact rock are essential for the safe design of many engineering structures. These criteria have been derived mainly from tests in the compressive stress region. Very few results have been published for confined, direct tensile tests on intact rock. No appropriate criteria are available for addressing the issue on tensile strength of intact rock at current stage. We present the results of direct triaxial tensile tests on Longmaxi Shales under varying confining stresses. These and the results from previous tests in marble and sandstone prove that the phenomenon of “tension cut-off” at low confining stress and the positive correlations between confining stress and tensile strength above the confining stress threshold for brittle rocks occur also in more ductile rocks like shales. Such findings are consistent with the concept that tensile failure processes for intact rock are universal. Our results demonstrate that friction processes still have a significant role on intact rock strength in the tensile region which is leading to confined tensile failure and transitioning to a purely tensile mode. Further, strength criteria are presented which consider the frictional processes leading to failure under confined, direct tension tests and validated against published tensile strength data.

Digital elevation models (DEMs) are foundational for critical tasks such as flood inundation simulation, disaster risk assessment, and ecosystem monitoring in coastal zones, yet their vertical accuracy is significantly compromised by complex terrain and surface characteristics. This study quantitatively decomposes the vertical errors of three 30 m global DEMs (COP30, NASADEM, and AW3D30) across the subtropical coastal region of Southeast China using ICESat-2 ATL08 data as a reference. By integrating an eXtreme Gradient Boosting (XGBoost) model with SHapley Additive exPlanations (SHAP), we successfully decoupled systematic biases from random noise. The results show that NASADEM achieved the lowest RMSE (7.775 m), followed by COP30 and AW3D30. While the Terrain Ruggedness Index (TRI) and categorically encoded Land Cover were identified as the universally dominant error drivers across all datasets, explainable analysis revealed distinct secondary mechanisms: X-band COP30 is notably susceptible to canopy height, exhibiting significant positive bias in forests exceeding 15 m; C-band NASADEM shows a systematic bias related to topographic position, typically overestimating ridges and underestimating valleys; and optical AW3D30 is significantly affected by stereo-matching errors. Furthermore, the analysis quantified a systematic error component of ~40%. These findings provide a data-driven basis for DEM selection and highlight that accuracy improvements should prioritize vegetation removal for radar DEMs and enhanced stereo-matching for optical models.