The process of backward erosion piping poses a threat to dams and dikes on foundations of nonplastic sands and silts. The available models for design and predictions focus predominantly on the progression of the pipe. However, sand boils in the field will occur as a result of the initiation of sand transport. Although criteria are available for predicting sand boiling and heaving in columns, there is no model describing the initiation of piping in situations where the exit flow is not uniform, as is the case in most backward erosion experiments and situations in the field. This study compared laboratory experiments in which the process of initiation leads directly to failure with analytical and numerical groundwater flow calculations and heave criteria. The aim was to develop a model for the onset of pipe formation. It emerged that the sand bed needs to be fluidised over a distance of at least 20 times the grain diameter from the toe of the structure for a pipe to initiate. The proposed model explains the scale effects of grain size and configuration on a critical gradient. This approach clarifies the processes governing pipe initiation and progression and it can be used to establish a conservative estimate of the critical head in uniform sands, which is essential for laboratory work on this topic and for the appraisal of sand boils in practice.
SUMMARYThe aim of this study is to arrive at a better understanding of the phenomenon of locking of low-order compatible displacement type of "nite elements in particular for the hour-glass mode of the plane four-node element and dilative materials. To this end the properties of "nite elements are investigated in an analytical way, where a "nite element is considered as a plane boundary value problem with prescribed boundary displacement (Dirichlet problem). In this paper for the sake of simplicity the simplest possible linear comparison solid, namely isotropic linear elasticity, is applied, although recognizing fully that for a dilative material elasto-plasticity would be more realistic. From the study described in this paper it is concluded that locking of the four-node element is not due to any particular numerical formulation of this compatible "nite element since, even the analytical solution su!ers from this problem. The locking of this element is not related to incompressibility of the material either as the analytical solution shows locking to occur at a parameter set which di!ers signi"cantly from the one in case of incompressibility. It is shown that locking is a consequence of the combination of the dilative material behaviour and the compatible displacement type of boundary conditions, which leads to in"nite isotropic stresses in the element. These in"nite isotropic stresses occur at the limit of uniqueness of the solution, which for this element is shown to occur outside the parameter range of the su$ciency of uniqueness.
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