Finite difference analysis of slope anchor frame resting on Vlasov Foundation considering influence of friction resistance and axial loads

Abstract

Abstract With the development of anchorage technology, slope anchor frames have become a preferential earth-retaining structure in controlling landslides or reinforcing slopes. However, no accurate and highly efficient design calculation method has been proposed. To date, they are usually simplified as cross-foundation beams resting on flat ground without considering the influence of friction resistance and axial loads induced by the tensile forces of anchor bolts. That will lead to a calculation result significantly deviating from the reality. For that, the paper regarded them as the actual cross beams resting on a slope viewed as the accepted Vlasov Foundation. A new concept, the friction-mobilizing ratio, was presented to establish the flexural differential equation of the beams. The finite difference solution to this problem was then proposed. The friction-mobilizing ratio can also be employed to determine and avoid the upclimbing phenomena of a frame. In the meantime, a highly efficient approach for the load share and adjustment at the intersections of the vertical and horizontal beams was presented. The entire computation process can be implemented by the finite difference program developed using MATLAB. The proposed method was validated through the finite element method but is much more efficient than the latter.