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A set of realizations of any statistical distribution can be generated and used to develop reliability based designs. The method is based on including numerous constraint sets, each representing one set of transmissivities, in a linear programming formulation of the design problem and allowing a certain percentage of the constraint sets to be violated. A small example is used to developed the method and a large more realistic example is used to test the method and compare it to other design methods.","abstract_html":"A new distribution free chance constrained programming technique is developed and applied to the design of hydraulic gradient control methods for containment and removal of contamination in an aquifer. The spatial distribution of parameters such as transmissivity in a heterogeneous domain make the value at any point uncertain. Because of this uncertainty a reliability based method is required. 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