Partially-drained loading of shallow foundations on sand
Authors: Mangal J.K. , Houlsby G.T. 
Published: October 2008

Abstract
Wave loading on offshore structures that are founded on sand can result in a partially-drained response of the foundation soil. The characteristics of the rate of loading, the permeability of the soil, and the size of the foundation affect the degree of partial drainage. Partial drainage refers to situations where pore pressures develop in the soil, and the response of the soil is neither fully drained nor undrained. This paper is concerned with the effects of loading rate, and consequent drainage, on the behaviour of a flat circular footing that is founded on the surface of a saturated sand base. The results of physical tests performed in the laboratory on a model-size footing are reported. The footing was founded on oil-saturated fine sand and was subjected to partially-drained vertical as well as combined loading. The effect of the vertical displacement rate re reported. The response of the footing is analysed in the context of existing drained foundation models that are based on work hardening plasticity theory. The rate dependency of the vertical load:deformation behaviour is examined in detail and the effects of rate on combined load yield surfaces are briefly described.

Introduction
In the offshore industry, bearing capacity methods are commonly used to calculate the ultimate drained and undrained capacity of foundations under vertical, inclined, and eccentric loads (Hansen1 and Vesic2). Butterfield and Ticof3 suggested that the combined load problem be analysed in terms of load interaction diagrams and also postulated the cigar shaped V:M:H failure surface shown in Fig. 1. Recent research has successfully interpreted the drained and undrained behaviour of shallow foundations in terms of plasticity theory4,5,6,7. Foundation models based on plasticity theory are simple and powerful methods for analysing the behaviour of shallow foundations.
These models can incorporate vertical as well as horizontal and moment loads, and also link loads and displacements. Some of the components of a plasticity based foundation model are shown in Fig. 2. A hardening rule is used to represent the vertical load:deformation behaviour and the size of the yield surface. A description of the yield surface, which defines the boundary (in load space) between elastic and plastic behaviour, is required. The combined load:deformation behaviour within the yield surface can usually be modelled as elastic behaviour. The ratios of the various components of displacement are modelled by a plastic potential.
The partially-drained response of sand, and hence of foundations on sand, is not well understood. Design procedures for estimating the vertical load:deformation behaviour, or even the bearing capacity, have not been established. The limited amount of experimental evidence in the literature indicates that the vertical capacity increases with load rate (for tests on dense sand). This is the case with both compressive and tensile loading.
The partially-drained bearing capacity (at the maximum load rate tested) was approximately twice the drained capacity in the model footing tests reported by Vesic et al.8. The dimensionless bearing capacity factor for these tests is plotted against the penetration rate in Fig. 3[a]. The increase in the penetration rate had no effect in the tests on the dry sand samples. This indicates that the change in capacity was drainage related. The reduction in the drainage that occurred with the increase in the penetration rate also resulted in more ductile load:deformation behaviour, as shown in Fig. 3[b].
The data reported by Houlsby9 indi