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Determination of Forces Acting on an Anti-Slide Pile

Forces, acting on an anti-slide pile, are provided by the slope stability analysis. Calculation of slope stability SF is based on the equilibrium analysis of forces acting on blocks of soil above the slip surface. Vertical surfaces of individual blocks are subjected to action inter-block forces F_i and their determination is one of the steps of the slope stability analysis. If the soil blocks are exactly in the state of limit equilibrium, the inter-block forces at the beginning and at the end of the slip surface are equal to zero. The limit factor of safety SF_lim, for which the state of limit equilibrium is reached, is considered as a real factor of safety on an input slip surface. The distribution of inter-block forces along the sliding length is called the pressure line. The forces acting on an anti-slide pile are determined from the distribution of pressure lines calculated for the required factor of safety SF_s.

The following figure shows different distributions of inter-block forces F_i (pressure lines). Graph a) displays the distribution of forces F_i in the state of limit equilibrium, where zero values of inter-block forces are found both at the beginning and at the end of the distribution. It means that this state has been found for the value of the factor of safety SF_lim, which exactly expresses the degree of safety on an input slip surface. Graph b) displays the pressure line determined for a higher factor of safety than the one corresponding to SF_lim. An assumption of zero force F_n is adopted at the top of the slip surface and a non-zero force F_0,b at the bottom of the slip surface is subsequently recorded. This means that in order to arrive at the factor of safety SF, the base of the slope would have to be loaded by the pressure force having the value of F_0,b. Graph c) displays the pressure line for a factor of safety SF greater than SF_lim. It results from the assumption of a zero force F₀ on the bottom end of the slip surface at the top and then an unbalanced force F_n,c is encountered. Arriving at the state of equilibrium for the factor of safety SF would thus theoretically call for the action of a tensile force of this magnitude at the top end of the slip surface. Graf d) shows a distribution of inter-block forces for the case when an anti-slide pile is placed at point x. Part of the distribution corresponds to graph c) and serves to determine the magnitude of passive force P at point x. Above the pile the distribution according to graph b) is considered and serves to determine the active force T at point x. The difference between P and T is the force transmitted by the anti-slide pile.

Distribution of inter-block forces F_i

Figure caption (explanation):

a) distribution for the factor of safety SF = SF_lim (F₀ = 0 a F_n = 0)

b) distribution for the factor of safety SF > SF_lim with zero value of force at the top end

c) distribution for the factor of safety SF > SF_lim with zero force value at the bottom end

d) distribution for the factor of safety SF with an anti-slide pile at point x