Bubbles (a.k.a. whales) that develop from gas entrapped beneath a geomembrane in pond liner applications lead to localized increases in geomembrane strain that warrant evaluation. Results from three-dimensional, geometrically-nonlinear, finite-element analysis are presented to show how geomembrane stiffness, fluid depth, volume of entrapped gas, and interface friction affect the deformed shape of, and maximum strain in the geomembrane. It is shown that the deformed geomembrane follows a bell-shaped curve and that geomembrane strain increases as the fluid depth increases until the bubble is submerged. The extent to which the maximum strain increases with decreasing geomembrane stiffness and increasing volume of entrapped gas are quantified. Design and operation charts are presented to provide a practical means of assessing strain in existing geomembrane bubbles or identify maximum fluid depths to limit geomembrane strain to a target value.

在池塘衬垫应用中，由截留在土工膜下方的气体产生的气泡（又名鲸鱼）会导致土工膜应变局部增加，需要进行评估。三维几何非线性有限元分析的结果显示了土工膜刚度、流体深度、截留气体体积和界面摩擦如何影响影响土工膜的变形形状和最大应变。结果表明，变形的土工膜遵循钟形曲线，并且土工膜应变随着流体深度的增加而增加，直到气泡被淹没。最大应变随着土工膜刚度的降低和截留气体体积的增加而增加的程度被量化。设计和操作图表提供了一种评估现有土工膜气泡应变或确定最大流体深度以将土工膜应变限制在目标值的实用方法。