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Arseny Antonov
Arseny Antonov

Rock Slope Engineering: Civil Applications, Fif... PATCHED


Slope stability analysis is a static or dynamic, analytical or empirical method to evaluate the stability of slopes of soil- and rock-fill dams, embankments, excavated slopes, and natural slopes in soil and rock. It is performed to assess the safe design of a human-made or natural slopes (e.g. embankments, road cuts, open-pit mining, excavations, landfills etc.) and the equilibrium conditions.[1][2] Slope stability is the resistance of inclined surface to failure by sliding or collapsing.[3] The main objectives of slope stability analysis are finding endangered areas, investigation of potential failure mechanisms, determination of the slope sensitivity to different triggering mechanisms, designing of optimal slopes with regard to safety, reliability and economics, designing possible remedial measures, e.g. barriers and stabilization.[1][2]




Rock Slope Engineering: Civil Applications, Fif...



Successful design of the slope requires geological information and site characteristics, e.g. properties of soil/rock mass, slope geometry, groundwater conditions, alternation of materials by faulting, joint or discontinuity systems, movements and tension in joints, earthquake activity etc.[4][5] The presence of water has a detrimental effect on slope stability. Water pressure acting in the pore spaces, fractures or other discontinuities in the materials that make up the pit slope will reduce the strength of those materials.[6]Choice of correct analysis technique depends on both site conditions and the potential mode of failure, with careful consideration being given to the varying strengths, weaknesses and limitations inherent in each methodology.[7]


Conventional methods of slope stability analysis can be divided into three groups: kinematic analysis, limit equilibrium analysis, and rock fall simulators.[8]Most slope stability analysis computer programs are based on the limit equilibrium concept for a two- or three-dimensional model.[10][11] Two-dimensional sections are analyzed assuming plane strain conditions. Stability analyses of two-dimensional slope geometries using simple analytical approaches can provide important insights into the initial design and risk assessment of slopes.


Limit equilibrium methods investigate the equilibrium of a soil mass tending to slide down under the influence of gravity. Translational or rotational movement is considered on an assumed or known potential slip surface below the soil or rock mass.[12] In rock slope engineering, methods may be highly significant to simple block failure along distinct discontinuities.[8] All these methods are based on the comparison of forces, moments, or stresses resisting movement of the mass with those that can cause unstable motion (disturbing forces). The output of the analysis is a factor of safety, defined as the ratio of the shear strength (or, alternatively, an equivalent measure of shear resistance or capacity) to the shear stress (or other equivalent measure) required for equilibrium. If the value of factor of safety is less than 1.0, the slope is unstable.


Rock slope stability analysis may design protective measures near or around structures endangered by the falling blocks. Rockfall simulators determine travel paths and trajectories of unstable blocks separated from a rock slope face.[35] Analytical solution method described by Hungr & Evans[36] assumes rock block as a point with mass and velocity moving on a ballistic trajectory with regard to potential contact with slope surface. Calculation requires two restitution coefficients that depend on fragment shape, slope surface roughness, momentum and deformational properties and on the chance of certain conditions in a given impact.[37]


Modelling of the continuum is suitable for the analysis of soil slopes, massive intact rock or heavily jointed rock masses. This approach includes the finite-difference and finite element methods that discretize the whole mass to finite number of elements with the help of generated mesh (Fig. 3). In finite-difference method (FDM) differential equilibrium equations (i.e. strain-displacement and stress-strain relations) are solved. finite element method (FEM) uses the approximations to the connectivity of elements, continuity of displacements and stresses between elements.[39] Most of numerical codes allows modelling of discrete fractures, e.g. bedding planes, faults. Several constitutive models are usually available, e.g. elasticity, elasto-plasticity, strain-softening, elasto-viscoplasticity etc.[38]


Discontinuum approach is useful for rock slopes controlled by discontinuity behaviour. Rock mass is considered as an aggregation of distinct, interacting blocks subjected to external loads and assumed to undergo motion with time. This methodology is collectively called the discrete-element method (DEM). Discontinuum modelling allows for sliding between the blocks or particles. The DEM is based on solution of dynamic equation of equilibrium for each block repeatedly until the boundary conditions and laws of contact and motion are satisfied. Discontinuum modelling belongs to the most commonly applied numerical approach to rock slope analysis and following variations of the DEM exist:[38]


Discontinuum program UDEC[40] (Universal distinct element code) is suitable for high jointed rock slopes subjected to static or dynamic loading. Two-dimensional analysis of translational failure mechanism allows for simulating large displacements, modelling deformation or material yielding.[40] Three-dimensional discontinuum code 3DEC[41] contains modelling of multiple intersecting discontinuities and therefore it is suitable for analysis of wedge instabilities or influence of rock support (e.g. rockbolts, cables).[38]


Discontinuous rock mass can be modelled with the help of distinct-element methodology in the form of particle flow code, e.g.program PFC2D/3D.[42][43] Spherical particles interact through frictional sliding contacts. Simulation of joint bounded blocks may be realized through specified bond strengths. Law of motion is repeatedly applied to each particle and force-displacement law to each contact. Particle flow methodology enables modelling of granular flow, fracture of intact rock, transitional block movements, dynamic response to blasting or seismicity, deformation between particles caused by shear or tensile forces. These codes also allow to model subsequent failure processes of rock slope, e.g. simulation of rock[38]


Hybrid codes involve the coupling of various methodologies to maximize their key advantages, e.g. limit equilibrium analysis combined with finite element groundwater flow and stress analysis ; coupled particle flow and finite-difference analyses. Hybrid techniques allows investigation of piping slope failures and the influence of high groundwater pressures on the failure of weak rock slope. Coupled finite-/distinct-element codes provide for the modelling of both intact rock behavior and the development and behavior of fractures.[38]


(a) Scope and application. This appendix contains specifications for sloping and benching when used as methods of protecting employees working in excavations from cave-ins. The requirements of this appendix apply when the design of sloping and benching protective systems is to be performed in accordance with the requirements set forth in 1926.652(b)(2).(b) Definitions.Actual slope means the slope to which an excavation face is excavated.Distress means that the soil is in a condition where a cave-in is imminent or is likely to occur. Distress is evidenced by such phenomena as the development of fissures in the face of or adjacent to an open excavation; the subsidence of the edge of an excavation; the slumping of material from the face or the bulging or heaving of material from the bottom of an excavation; the spalling of material from the face of an excavation; and ravelling, i.e., small amounts of material such as pebbles or little clumps of material suddenly separating from the face of an excavation and trickling or rolling down into the excavation.Maximum allowable slope means the steepest incline of an excavation face that is acceptable for the most favorable site conditions as protection against cave-ins, and is expressed as the ratio of horizontal distance to vertical rise (H:V).Short term exposure means a period of time less than or equal to 24 hours that an excavation is open.(c) Requirements -- (1) Soil classification. Soil and rock deposits shall be classified in accordance with appendix A to subpart P of part 1926.(2) Maximum allowable slope. The maximum allowable slope for a soil or rock deposit shall be determined from Table B-1 of this appendix.(3) Actual slope. (i) The actual slope shall not be steeper than the maximum allowable slope.(ii) The actual slope shall be less steep than the maximum allowable slope, when there are signs of distress. If that situation occurs, the slope shall be cut back to an actual slope which is at least horizontal to one vertical (H:1V) less steep than the maximum allowable slope.(iii) When surcharge loads from stored material or equipment, operating equipment, or traffic are present, a competent person shall determine the degree to which the actual slope must be reduced below the maximum allowable slope, and shall assure that such reduction is achieved. Surcharge loads from adjacent structures shall be evaluated in accordance with 1926.651(i).(4) Configurations. Configurations of sloping and benching systems shall be in accordance with Figure B-1.


UTEXASED4 is a computer software application for computing the stability of earth andearth-rock slopes and embankments. It is a Windows-based program that uses limitequilibrium procedures to calculate a factor of safety against failure. The factorof safety is defined with respect to shear strength, i. e. the factor of safety is theratio of the soil shear strength to the equilibrium shear stress. Values of thefactor of safety at or less than unity are considered to represent instability and failureof the slope. 041b061a72


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