Page - 976 - in Book of Full Papers - Symposium Hydro Engineering

Where c: cohesion of the soil (kN/m2); z: depth to shear plane (m); h: height of ground water level above shear plane (m); γ: density of soil (kN/m3); γw: density of water (kN/m3); β: slope angle (º) and φ: angle of friction (º). The modified equation for translational failure on an infinite slope taking the effects of vegetation into account is defined by Eq. 2. 𝐹 𝑂 𝑆 = (𝑐 𝑅 )+{[(𝛾 𝑧 −𝛾 𝑤 ℎ)+𝑊 ]𝑐 𝑜 𝑠 2𝛽 +𝑇 𝑠 𝑖 𝑛 𝜃 }𝑡 𝑎 𝑛 𝜑 +𝑇 𝑐 𝑜 𝑠 𝜃 [(𝛾 𝑧 +𝑊 )𝑠 𝑖 𝑛 𝛽 +𝐷 ]𝑐 𝑜 𝑠 𝛽 [2] Eq. 2 incorporates four additional variables defined as: cR: the enhanced shear resistance due to roots (kN/m2); T: tensile root force acting at the base of the shear plane (kN/m), W: surcharge of the vegetation (kN/m2) and D: wind loading parallel to the slope (kN/m). to ascertain these variables, a set of experimental studies were carried out [7]. The values of parameters are selected based on that experiment and worst case scenario demonstrated in Table 1. Table 1. Values of variables Parameter 𝛾 𝛾 𝑤 Z* h W D 𝜑 c cR T Value 11 9.81 0.1-0.5 0.5 0 0 16 10 10 5 * Maximum depth of roots of grass and forbs is usually no greater than 0.5 [9]. Employing Eq.1 and 2 for reliability analysis, several assumptions are made. The weight of the surface vegetation and its subsequent normal force on the soil are quantified as W, the surcharge. This surcharge is included in the calculation primarily due to the plausibly high force exerted on soils by trees, in this paper W has been assumed to be zero as the surcharge exerted by grass is likely to be very small and of little consequence. The tensile root force for the grass is selected based on literature [10]. The wind loading force, D, is chiefly concerned with the effect of ‘wind throw’. In the case of grass, the surface area upon which wind can act is small in comparison to trees, additionally grasses tend to be flexible and unlikely to transfer a great deal of force to the roots. The angle between roots and slip plane, θ, has been taken to be equal to that of the slope angle, β, as it was assumed that roots had grown in a gravitonic manner. 4. RELIABILITY AND MONTE-CARLO SIMULATION Reliability analysis deals with the relation between the loads a system should carry and its ability to carry those loads. Both the loads and the resistance may be uncertain, so the result of their interaction is also uncertain. Reliability analysis of a system means evaluating the probability of satisfactory performance of that system under specified conditions and given time. The engineering design is to create a balanced relation between optimization of maximum safety and minimum 976