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This study uses a semi-analytical technique (the scaled boundary finite-element method) to evaluate the load–displacement response of rigid circular footings embedded in a non-homogeneous elastic half-space. Results are presented in terms of dimensionless elastic stiffness coefficients. The footings are subjected to vertical, horizontal, moment and torsional loads. The cross-coupling between the horizontal and moment load case is also evaluated. The variation of soil shear modulus with depth may correspond to normally consolidated sand or clay, and the footing geometries considered cover a range of footings commonly encountered in engineering practice.

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