求解地面沉降预测模型参数的逆问题

Inverse Problem For Finding Constant Aquifer System Parameters That Control Transient Land Subsidence

地下流体的抽取所引起的地面沉降的预测依赖于所选理论模型中参数的量化。本文所建立的逆问题模型中涉及到压缩承压含水系统中5个控制地面沉降的参数:压缩弱透水层的垂向水力传导系数K'、塑性贮水率S'skv和弹性贮水率S'ske、含水层的贮水率S'S和弱透水层的前期最大固结压力p'max0。逆问题模型由Newton-Raphson调整算法和Helm有限差分一维固结模型构成(COMPAC),其中固结模型可用其他模型替代。文中用一个理想压缩承压含水系统对该逆问题模型进行检验,检验结果显示该模型能求解出理想压缩承压含水系统的K'、S'skv、S'ske、S'S和p'max0的近似值,其中p'max0和S'skv是控制计算沉降量的两个最主要的参数。每个监测点计算压缩量的平均相对误差为7.8%,该误差仅由调整算法产生。该逆问题模型应用于上海F9地面沉降监测点上部承压含水系统参数的求解和变形量的预测,所求解出的K'、S'skv、S'ske、S'S和p'max0的近似值分别为8.58×10-4 m/a、3.50×10-4 1/m、6.39×10-6 1/m、1.19×10-5 1/m和-2.50m、每个观测点计算压缩量的平均相对误差为13.7%。误差的来源除了调整算法外,还包括地下水位、压缩变形的观测误差以及模型概化所产生的误差。

Prediction of land subsidence due to fluid withdrawal depends on the quantitative identification of parameters for a selected theoretical model.An inverse model is developed for finding the values of five constant parameters that control land subsidence： vertical hydraulic conductivity of compressible aquitards,K＇,nonrecoverable S＇skv,and recoverable S＇ske specific storage of the aquitards,specific storage of the aquifers,Ss,and the initial distribution p＇max0 of transient preconsolidation pressure within a confined auifer system.The procedure consists of combining the Newton-Raphson adjustment algorithm and Helm＇s one-dimensional finite-difference subsidence model（COMPACT）.The subsidence model can be replaced by any other appropriate model.The inverse model has been investigated by applying it to an idealized compressible confined aquifer system.The investigation shows that approximate values for K＇,S＇skv,S＇ske,Ss and p＇max0 can be found with p＇max0 and S＇skv controlling the calculated subsidence most significantly.The average relative error of predicted subsidence by application of the identified parameters is 7.8% per ＇observation＇ point.This error is produced only by the numeric adjustment algorithm.This inverse model was then applied to actural field data that were gathered over a period of about twenty years from the upper confined aquifer system at Multiple-Extensometer Site F9 in Shanghai.The approximate values for K＇,S＇skv,S＇ske,Ss and p＇max0 identified by this inverse model are 8.58×10-4 m/year,3.50×10-4 1/m,6.39×10-6 1/m,1.19×10-5 1/m,and-2.50m of H2O,respectively.The average relative error of simulated vertical compression and expansion（subsidence） by the application of the identified parameters is 13.7% per observation point.Field observation of transient changes in hydraulic head and transient compression and expansion,and the use of a subsidence model are possible sources of error in addition to the numeric adjustment algorithm.