裂隙—基质双重介质地下水流解析模型的形状因子推导偏经验化。以标准抽水试验为 例，通过建构单一裂隙—带状基质介质的水流解析模型并求解其解析解，提出新的基质水流控制 方程及新的形状因子，避免经验化的水流方程和形状因子推导。对于裂隙网络—基质介质水流的 有限元数值解，新的水流方程和形状因子能够实现基质内无网格离散。结果表明：带状基质的形 状因子是基质宽度平方的倒数；圆形基质的形状因子是基质半径平方的倒数；其他形状基质的形 状因子是经验参数。基于新形状因子的解析解，预测的降深相对误差小于5%；然而采用既有形状 因子时，降深相对误差约为99%。当裂隙网络的面积与总面积的比值（裂隙密度）超过62% 时，裂 隙网络可简化为双重连续介质。数值解成功用于野外标准抽水试验。

Deriving shape factor in analytical models for flow in double-porosity media is partially empirical. This study proposes a new flow equation and new shape factor for matrixes without empirical derivations in considering the problem of the standard pumping test in double-porosity confined aquifers. For a single fracture-strip matrix medium, a new analytical model incorporating the new flow equation and new shape factor is developed; the analytical solution is derived. For a fracture network-matrix medium, a finite element solution depending on the new flow equation and new shape factor is built without discretizing the space in each matrix. Results show the shape factor for the strip matrix is the reciprocal of the square of the matrix width, for the circular matrix is the reciprocal of the square of the radius, but for other shapes of matrix is an empirical parameter. The relative error of the fracture drawdown predicted by the analytical solution with the new shape factor is less than 5%. The relative error considering existing shape factors is, however, about 99%. When the ratio of the fracture area to the total medium area (defined as fracture density) exceeds 62%, the fracture networkmatrix medium can be regarded as a double-porosity continuous medium. The finite element solution has applied to a field standard pumping test.