条形基础加筋砂土地基极限承载力计算

基于传统的极限平衡条分法，利用临界滑动场法计算了条形基础的加筋地基极限承载力。假定土体处于极限平衡状态时，土体与筋材间存在均匀的摩擦力，通过建立土体条块极限平衡方程，推导了地基承载力的递推关系式。首先，设定计算土体范围，并划分条块和离散状态点；其次，根据递推公式计算各个状态点的参数，并搜索临界滑面；最后，根据搜索出的滑面计算地基承载力。通过实例比较进一步验证了计算结果的可靠性，并分析了首层筋带埋深、铺设层数和长度对地基承载力和滑面位置的影响。研究结果表明：地基承载力随着筋带埋深的增加先增大后减小；随着层数和长度的增加先逐渐增大，最后趋于稳定；滑面位置的变化规律主要是垂直影响深度和水平影响范围增大或减小。该方法原理简单、易于编程，为条形基础加筋地基承载力的计算提供了一种新思路，是临界滑动场法在地基承载力计算中的推广应用。

A method for calculating the ultimate bearing capacity of a strip footing on the reinforced sand

The ultimate bearing capacity of a strip footing on the reinforced sand is studied based on both the limit equilibrium slice method and the critical slip field method. It is assumed that friction of the interface between the soil and reinforcements is uniform when the reinforced foundation soil is in the limit equilibrium state. Based on the limit equilibrium equations of soil slice, a recursion expression of slice force is derived. Firstly, the borders of the soil mass with potential sliding are determined, then soil mass is divided into a series of slices, and the state points is distributed on interfaces between the slices. Secondly, the recursion expression is used to calculate the parameters of all state points and search the critical slip surface. Finally, the bearing capacity can be determined according to the critical slip surface which meets the balance of forces and moments. The reliability of calculation results is shown by comparing with the results in literature. Effects of distance from footing bottom to top reinforcement, layer numbers and length of reinforcement on bearing capacity and slip surface are also presented. The results show that the bearing capacity increases firstly and then decreases as the depth increases, or it increases firstly and becomes stable lastly as layer number and length increase. It is also shown that the slip surface changes mainly in the vertical and horizontal ranges. Because the proposed method is easy to understand and numerically implement, it provides a new idea to calculate the bearing capacity of strip footing on reinforced sand, and it extends the critical slip field method to the calculation of bearing capacity.