线状和面状群井抽水导致场外地面沉降呈s-lnr线性关系

在单井抽水造成地面沉降符合s-lnr线性关系的基础上，应用积分的方法，对线状和面状群井抽水产生的地面沉降进行推导，得出群井抽水导致地面沉降的积分公式。对于场外远处，即距抽水中心距离远大于抽水区域长度或宽度的情况，对沉降积分公式进行简化，仍可得到场外地面沉降呈s-lnr线性关系的结果。选取第三方文献中的理论解、数值解和工程实例对以上研究成果进行拟合验证，相关系数分别为99.91%、98.67%、96.60%、99.63%、99.43%，所以线状和面状群井抽水导致场外地面沉降呈s-lnr线性关系的理论分析结果得到极好验证。

Linear s-lnr relation of land subsidence induced by group wells pumping distributed as line and area

Based on linear s-lnr relation of land subsidence from a single well pumping, equations of land subsidence from group wells pumping distributed as line and area were derived by applying the method of integration. For the observation point far away from the center of group wells, after simplifying the equations above, the result of formula reveals that the linear s-lnr relation is satisfied too. The result is proved by the monitored data from the third party literatures including classical theoretical solutions, numerical solution and engineering example. The monitored data agrees well with the new formula. The correlation coefficients of fitting curves are 99.91%, 98.67%, 96.60%, 99.63% and 99.43%. So the linear s-lnr relation of land subsidence from group wells pumping distributed as line and area are verified well.