Keywords: underground engineering; numerical simulation; excavation length effect, major principal stress; displacement; damage initiation; CPU time

Terzaghi proposed two-dimensional (2D) arching theory through trapdoor tests based on the assumption of a vertical slip surfaces. However, the original 2D assumption is different from a real three-dimensional (3D) excavation condition and an actual slip surfaces caused by downward movement of a trapdoor is an inclined surface. Therefore, a 3D theoretical model was proposed in this study considering inclined slip surfaces. Horizontal thin layer differential element method was used to obtain the loosening soil pressure. Using the 3D theoretical model, the effects of buried depth ratio of loose area, length of loose area, soil parameters, and lateral earth pressure coefficient were investigated. The loosening earth pressure was highly affected by inclination angle of slip surface, buried depth ratio and length of loose area. Neglecting the inclined slip surface will underestimate the value of the loosening earth pressure, which will lead to the insecurity of the design. Loosening earth pressure calculated by this study was also compared with trapdoor tests. Results from this study was in good agreement with the experimental results. Compared with the traditional 2D solution, results from this study can more accurately analyze the soil arching effect in 3D excavation cases.

In urban areas, deep excavation-induced ground deformation may damage adjacent existing structures and is conventionally evaluated by levelling at installed settlement points. However, a small number of measurements cannot represent the total change in ground deformation adjacent to excavation sites. Furthermore, significant local subsidence may occur in places where settlement points have not been installed and only noticed after an accident. For deep excavation sites located in urban areas, paved pedestrian sidewalks are often located adjacent to sites, and construction activity can cause these paving blocks to displace. This study introduces a method to detect paving block displacement adjacent to deep excavation sites using terrestrial photogrammetry. A digital camera creating point cloud data (PCD) and an acquisition method satisfying the frontal and side overlap requirements were demonstrated. To investigate the displacement detection and measurement capabilities by PCD analysis, an experimental program was conducted, including a PCD comparison containing the uplift, settlement, and horizontal paving block displacement and reference data. The cloud-to-cloud distance computation algorithm was adopted for PCD comparison. Paving block displacement was detected for displacements of 5, 7.5, and 10 mm in the uplift, settlement, and horizontal directions; however, the horizontal displacements were less clear. PCD analysis enabled satisfactory measurements between 0.024 and 0.881 mm for the vertical-displacement cases, but a significant error was observed for the horizontal-displacement cases owing to the cloud-comparison algorithm. The measurement blind spot of limited settlement points was overcome by the proposed method that detected and measured paving block displacement adjacent to excavation sites.

Translational rockslides caused by toe excavation are one of the commonly seen geohazards in mountainous regions due to line traffic construction. Quantifying their failure extension length (FEL) and travel distance are of significant interest as well as huge challenges in landslide hazard assessment. In this paper, a simple criterion is proposed for predicting these two factors based on the principles of rigid body limit equilibrium and kinetic energy theorem. Further, the proposed criterion is validated against the field observations and numerical results with a practical case of the Xinjianan landslide, a medium-sized translational rockslide that occurred in 2013 in Nanchuan District, Chongqing. The findings indicate that a tiny discrepancy can be found in FEL between the field observations and the proposed criteria, while this discrepancy could be considerable in travel distance between different methods. However, the relative discrepancies all fall within 20%, deemed acceptable.

The objective of this study is to investigate the use of excavation behavior prediction and analysis software in the field of civil en-gineering. PLAXIS and SoilWorks, widely used in the engineering and academic communities, were employed as research tools for analyzing gravel layers and deriving appropriate ranges of soil elastic modulus for different software programs. By collecting excavation cases in the Xindian area of New Taipei City, Taiwan, and conducting deep excavation analysis using the displacement of retaining walls, this study provides recommended ranges for localized selection of soil elastic modulus. The suggested range for PLAXIS is 7,840 N/m² to 9,800 N/m², while Soil-Works suggests a range of 2,450 N/m² to 3,430 N/m². These ranges allow for reasonable estimation of maximum deformations during the final excavation stage. Based on the research findings, it is recommended that engineers refer to the provided ranges when selecting soil elastic modulus for excavation analysis in gravel layers using different soft-ware programs in the Xindian area of Taiwan to improve the accuracy of deformation predictions during the final excavation stage. These results serve as important references for engineers and contribute to the effective prediction and management of excavation behavior in civil engineering projects.

The notion of potential-growth indicator came to being in the field of matrix population models long ago, almost simultaneously with the pioneering Leslie model for age-structured population dynamics, albeit the term has been given and the theory developed only recent years. The indicator represents an explicit function, R(L), of matrix L elements and indicates the position of the spectral radius of L relative to 1 on the real axis, thus signifying the population growth, or decline, or stabilization. Some indicators turned out useful in theoretical layouts and practical applications prior to calculating the spectral radius itself. The most senior (1994) and popular indicator, R0(L), is known as the net reproductive rate, and we consider two more ones, R1(L) and RRT(A), developed later on. All the three are different in what concerns their simplicity and the level of generality, and we illustrate them with a case study of Calamagrostis epigeios, a long-rhizome perennial weed actively colonizing open spaces in the temperate zone. While the R0(L) and R1(L) fail respectively because of complexity and insufficient generality, the RRT(L) does succeed, justifying the merit of indication.