An analytical model for stability analysis of a rock slope toppling mechanism driven by external loading

This study is devoted to the development of the methodology of applied geometry and its tools in the direction of creating a geometric apparatus for forming discrete frames of surfaces formed under the action of an external load normal to the surface. The basis for the formation of such surfaces is the static-geometric method [1]. This method is a kind of visual interpretation of the finite difference method based on the description of the static equilibrium of the nodes of a discrete mesh formed under the action of an external load on the mesh nodes. The internal forces in the mesh links that balance the external load are considered proportional to the lengths of the corresponding links, which allows describing the balanced mesh by a system of linear equations. Designing structures of long-span coverings of architectural structures remains an urgent task in our time. Among such coverings, a special place is occupied by those whose shape cannot be set arbitrarily, but is formed under the action of a certain external load, in particular, the shape of low-pressure pneumatic shells is formed under the action of negative internal pressure. Such surfaces can be represented only in a discrete form. In this study, the direction of the force of the normal external load acting on an arbitrary node of a discretely represented surface (DSP) is defined as perpendicular to the plane tangent to the discretely represented surface at this node. The work presents an algorithm for forming a discretely represented surface under the action of a normal load. The components of this algorithm look as follows: the initial parameters of the discretely represented surface are given; the distribution of normal forces between the nodes of the grid is given; the coordinates of all nodes of the initial approximation of the grid are given or determined; the coefficients A, B, C of two planes connecting the corresponding nodes of the grid star are determined for all internal nodes of the grid; the parameters of the normal load forces at each internal grid node are determined; the coordinate components of the force vector applied to the grid node are determined; a system of equilibrium equations of the grid nodes of the next approximation is constructed and solved, where the coordinates of the internal grid nodes and the forces are unknown; the determined coordinates are compared with the coordinates of the previous approximation. The iterative process ends if the difference between the coordinates of the current and previous approximations does not exceed the permissible error. Otherwise, the iterative process continues, starting from point 4.

Block-flexure toppling failure of rock slopes using an equivalent deformation compatibility method

Toppling mechanisms of rock slopes considering stabilization from the underlying rock mass

Centrifuge Model Test on Anti-dip Rock Slopes with Unequal Thicknesses Subjected to Flexural Toppling Failure

Influence of a Dominant Fault on the Deformation and Failure Mode of Anti-dip Layered Rock Slopes

The tension cracks and joints in rock or soil slopes affect their failure stability. Prediction of rock or soil slope failure is one of the most challenging tasks in the earth sciences. The actual slopes consist of inhomogeneous materials, complex morphology, and erratic joints. Most studies concerning the failure of rock slopes primarily focused on determining Factor of Safety (FoS) and Critical Slip Surface (CSS). In this article, the effect of inclined tension crack on a rock slope failure is studied numerically with Shear Strength Reduction Factor (SRF) method. An inclined Tension Crack (TC) influences the magnitude and location of the rock slope’s Critical Shear Strength Reduction Factor (CSRF). Certainly, inclined cracks are more prone to cause the failure of the slope than the vertical TC. Yet, all tension cracks do not lead to failure of the slope mass. The effect of the crest distance of the tension crack is also investigated. The numerical results do not show any significant change in the magnitude of CSRF unless the tip of the TC is very near to the crest of the slope. A TC is also replaced with a joint, and the results differ from the corresponding TC. These results are discussed regarding shear stress and Critical Slip Surface (CSS).

The excavation of hydrothermally altered rocks from construction sites in Japan has raised concerns over environmental pollution due to the arsenic (As) release beyond the regulatory limit. An accurate assessment of As leaching from these rocks is imperative to understanding potential environmental implications and formulating efficient containment measures. However, the conduction of column leaching experiments to evaluate As leaching from these rocks encounters a lack of well-established protocols primarily due to the ambiguity surrounding scaling effects resulting from alterations in particle sizes and the corresponding column dimensions. Our study aimed to address this critical issue by conducting column percolation experiments on hydrothermally altered rocks of two distinct particle size ranges and rock layer thicknesses. The pH value was found to be proportional to the specific surface area (SSA) of rocks and the rock layer thickness in terms of H+ concentrations. Furthermore, the concentration and leachability of As showed a similar proportionality with the SSA. In contrast, the concentration of As remained relatively unaffected by the increased rock layer thickness, while the leachability of As was noticeably diminished in the column with a thicker rock layer. The absence of elevated As concentration and the decrease in leachability can be attributed to the enhanced As onto Fe/Al oxyhydroxides/oxides within the half-bottom part of the column with a thicker rock layer. Our findings underscore the importance of considering the SSA of rocks and rock layer thickness in the column experiments and help in the design of effective strategies to mitigate environmental contamination.

The action of an unsteady external load on a circular elastic plate floating on shallow water

Theoretical and numerical analysis of flexural toppling failure in soft-hard interbedded anti-dip rock slopes

Seismic performance and failure mechanism of interbedded slopes with steep rock layers

Investigating the role of kinematics and damage in the failure of rock slopes

Sustainability in slope protection is very important to reduce environmental impact and loss of property and life. Landslides and slope failure frequently occur due to a variety of factors. The factors that contribute to the slope failure are the external load such as heavy machinery and also rainfall. The study area for this study is slope are at FT006, Section 61.50, Pulau Pinang. The objective of this study is to identify the factor of safety (FOS) of original slope and also factor of safety after slope protection applied. The soil nailing and also sheet pile are choosing as a slope protection. The 2D modelling using Slope/W software was created and analysed. This slope consists of multi-layers soil properties with the steepest angle of 52°. This model is applying with external load to stimulate the real situation of existing slope. The result shows that the minimum FOS for slope without any external load is 0.58 and the FOS decrease to 0.28 when the external load was applied. When the soil nailing was applied to the slope, it is increase to 3.74 without external loading and 1.247 with external load. Meanwhile, when sheet pile was applied the FOS increase to 3.88 without external load but with external load it is drop to 0.39. Therefore, the soil nailing was proposed to this slope as effective slope protection.

In the present paper, a probabilistic analysis procedure and related algorithm for the stability of rock slopes against block toppling failure have been developed using Monte Carlo simulation. For this purpose, first the deterministic model has been developed considering the presence of external loads and moments on the slope having non-orthogonal discontinuities. The discontinuity parameters (such as discontinuities orientations, friction angles) and seismic coefficient have been taken as normally distributed variables whereas spacing of discontinuities and pore water pressure have been considered as log normally distributed variables. The realizations of all the variable parameters, generated by central limit theorem, have been fed to the deterministic model for slope stability analysis. As a result, realizations of dependent variables [geometry, inter-block forces and factor of safety (FOS)] have been generated. Subsequently, the probability distribution function of FOS has been generated. Associated risk of slope failure in toppling for a particular value of FOS can be obtained. In addition, a comparative study has been performed to show the influence of external loads and moments on the stability of slope. External loads and moments have been found to have significant influence on the FOS and therefore probability of failure of rock slope.

Concrete cracking and deflection analysis of RC beams strengthened with prestressed FRP reinforcements under external load action

This paper presents an assessment of a rock planar slide, which took place at km 108 along the Tien Yen-Mong Cai expressway, an extension of the Halong-Vandon expressway in Vietnam. Half of the expressway has been covered by a large volume of rock deposit after its movement. The height of the slope in this study is 16 m and its width is 200 m. The main head scarp is about 11 m high. The sliding angle of the failure surface is from 12÷150. The stratigraphy mostly consists of weathered jointed siltstone, which is located in the upper part of the Ha Coi formation (J1-2hc2). The sedimentary rocks are thick bedded, fine-grained sandstones interbedded with medium-bedded chocolate pink siltstones or thin-bedded shales. In general, they are medium to thick bedded with the thickness of rock layer from 0.3÷0.8 m. The upper rock layer is the 9b-1 layer with RQD = 0÷36% whereas the lower one is the 9b-2 layer with RQD = 0÷92%. The topsoil layer is 0.5÷2.5 m thick. Rockplane and Plaxis computer softwares were adopted to perform stability analysis of the slope. Results showed that the overall factor of safety of the slope before treatment is lower than 1.0, which is in good agreement with the instability of the slope. In order to apply the countermeasures, part of the slope will be first excavated with an angle of 450. Then, the prestressed ground anchor system will be installed. After treatment, the overall factor of safety of the slope was increased to larger than 1.30, which meets the requirement by the Vietnam code.