The earth pressure of retaining wall with cohesive fill based on principal stress rotation
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摘要:
填土水平墙背竖直光滑的挡墙，墙后土体处于以自重应力和水平应力为主应力的应力状态。实际工程中，挡墙背面与土体存在一定的摩擦及黏结力作用致使挡墙附近土体中的主应力发生偏转，此时，经典朗肯土压力理论不再适用。本文对挡墙附近土中的主应力状态进行旋转处理，通过分析墙后填土中应力状态摩尔圆，得到了考虑墙土摩擦和黏结力作用的黏性填土挡墙主被动土压力计算公式，分析了填土内摩擦角与墙土摩擦角对土压力的影响，使用算例将本文方法所得结果与现有黏性土土压力计算方法所得结果进行了对比分析。结果表明，朗肯土压力公式是本文所得计算公式的特例；随着墙土摩擦角和内摩擦角的增加，被动土压力逐渐加快增大；主动土压力随着内摩擦角的增加而减小；当内摩擦角较小时，主动土压力随着墙土摩擦角的增大不断减小，当内摩擦角较大时，主动土压力随着墙土摩擦角的增大先减小后增大；土内摩擦角的影响大于墙土摩擦的影响；相对于现有方法计算结果，本文方法所得主动土压力较大，被动土压力较小，墙土摩擦越大，2种方法所得结果的差值越大，土黏聚力还会加大这一差值。本文方法考虑了墙背土体主应力方向偏转的客观事实，所得计算结果将更符合实际情况。
Abstract:The soil behind a wall is in a stress state with self-weight stress and horizontal stress as the main stress for the Rankine retaining wall with horizontal fill. However, there is a certain wall-soil friction and bonding force in practice. The friction and bonding force may cause the principal stress deflection in the fill near the retaining wall, and the classical Rankine earth pressure theory is not applicable for this case. In the current study, the principal stress deflection of the fill near the retaining wall is processed both by the rotation and by the analysis of the stress from the Mohr circle in the fill behind the wall. The active and passive earth pressures of the retaining wall filled with the cohesive soil is derived, considering the wall-soil friction and bonding force. The influences of the fill friction angle and the wall-soil friction angle on the earth pressures are analyzed. The examples are further used to compare the results from this study with those with the improved Coulomb method. The results show that the Rankine earth pressure is a special case of the formula presented in this study. With the increase of the wall-soil friction angle and internal friction angle, the passive earth pressures gradually increase. The active earth pressures decrease with the increase of the internal friction angle, and the decreasing rate gradually decreases. When the internal friction angle is small, the active earth pressures decrease continuously with the increase of the wall-soil friction angle, and the decreasing speed gradually decreases. When the internal friction angle is large, the active earth pressures first decrease and then increase with the increase of the wall-soil friction angle. The effect of the fill friction angle is more obvious than that of the wall-soil friction angle. Compared with the results from other methods, the active earth pressures obtained with this method are larger, but the passive earth pressure is smaller, and their differences increase with the increase in the wall-soil friction, especially when the cohesion is considered. Because the deflection of the principal stress in the soil on the back of the wall is more consistent with the actual situations, the results from this study will be more suitable to compute the earth pressure in practice.
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表 1 主动土压力算例
Table 1. Example for the active earth pressure
δ/（°） c/kPa Ea/（kN·m−1） θa/（°） ωa/（°） 柯才桐法 卢廷浩法 朗肯理论解 本文解 0 0 392.21 392.21 392.21 392.21 0 0 0 10 273.08 273.08 273.08 273.08 0 0 5 10 250.02 250.02 252.87 3.69 8.64 5 15 197.58 197.58 201.64 3.69 11.09 10 15 178.11 178.11 193.87 7.64 22.35 10 20 131.16 131.16 151.77 7.64 28.33 
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表 2 被动土压力算例
Table 2. Example for the passive earth pressure
δ/（°） c/kPa Ep/（kN·m−1） θp/（°） ωp/（°） 胡晓军法 朗肯理论解 本文方法 0 0 1213.97 1213.97 1213.97 0 0 0 10 1442.48 1442.48 1442.48 0 0 5 5 1520.39 1502.71 9.88 5.37 5 10 1664.24 1644.58 9.88 5.67 5 15 1808.09 1786.50 9.88 5.92 5 20 1951.94 1928.44 9.88 6.14 10 5 1746.65 1665.38 20.26 10.66 10 10 1924.69 1833.87 20.26 11.19 10 15 2102.73 2002.48 20.26 11.64 10 20 2280.76 2171.20 20.26 12.01
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