The paper presents a method to compute the effective dynamic stiffnesses $\left(\overline{K}\right)$ and dashpots (C) of arbitrarily shaped, rigid surface machine foundations placed on reasonably homogeneous and deep soil deposits. The method is based on a comprehensive compilation of a number of analytical results, augmented by additional numerical studies and interpreted by means of simple physical models. All results are offered in the form of easily understood dimensionless graphs and formulas, covering the six modes of vibration and a wide range of frequencies, for both saturated and unsaturated soils. Comparisons are made with the widely used equivalent circle approximation. The proposed method is applicable to a variety of area foundation shapes, ranging from circular to strip and including rectangles of any aspect ratio as well as odd shapes differing substantially from rectangle or circle. The results confirm that both frequency and foundation shape may significantly affect $\overline{K}$ and C. Insight is gained into the mechanics of radiation damping and a general conclusion is drawn regarding its magnitude at high frequencies for different foundation shapes and vibrational modes. The practical application of the method is illustrated with a specific example, while a companion paper (7) presents supporting experimental evidence from model tests.

Results of twenty‐one free vibration tests on surface model footings on moist sand having different base shapes and about equal base area have been reported by Stokoe and Erden (5,8). These tests are used here to verify the analytical method of the companion paper (3), for circular, square and rectangular base shapes with aspect ratios up to 6, and including vertical, torsional and coupled swaying‐rocking oscillations. Close agreement is found between predicted and measured frequencies in all cases, and also between damping ratios in vertical and torsional vibration. The experiments provide strong support for the vertical and torsional radiation damping graphs developed in Ref. 3, including verification of the increased damping ratios predicted for the longest footings. The accord is also reasonably good for damping in those swayingrocking tests in which rocking and material damping are dominant and the overall damping ratio is about 3%. However, the method of Ref. 3 overpredicts the measured swaying‐rocking damping ratios in those tests in which swaying and radiation damping are also important, and for which larger damping ratios are predicted (4% to 9%). This discrepancy between half‐space predicted swaying‐rocking damping and measured values is explained by the effect of boundary wave reflections on the test results.

Sand liquefaction is a very important problem during earthquake excitation. This paper details the development of equivalent linearization theory for sand, based on both the extended Kalman filter and the weighted global iteration method, and shows how this theory can be used to analyze liquefaction. The equivalent linearization model presented in this paper is very simple and numerically efficient. This numerical model for liquefaction allows direct determination of progressive pore‐water pressures. The model requires a relatively small number of parameters in comparison to an effective stress model by Finn et al. (13). The pattern of progressive pore‐water pressure based on the equivalent linearization law agrees reasonably well with Finn's model based on effective stress analysis for the dynamic response of saturated sand. However, the equivalent linearization law is computationally less efficient and a simple tool for evaluating progressive pore‐water pressure during earthquake motions.

An approach is presented for analytical modeling of the full range of material behavior of normally consolidated to heavily overconsolidated clays. The approach has the capability of describing both drained and undrained, path dependent inviscid response under static and cyclic loads. The modified Cam‐clay form of the yield surface is allowed to expand or contract depending on the loading history. Numerical experiments and comparisons with experimental results show that various load‐deformation responses including strain hardening, strain softening, dilation, and hysteresis effects can be modeled.

Laboratory tests have been conducted to investigate the potential of millisecond delays in blast‐densification of saturated cohesionless sand. A large liquefaction tank was used to prepare and contain the sand. Commercially available blasting caps were used as the explosive. Cone penetration tests and sand surface elevation changes were measured. In addition to lowering the peak body wave ground motions, densification with millisecond delays was shown to be comparable to densification by a single large blast with a total charge weight equal to the sum of the delays. Increases in cone penetration resistance were measured 10–40 cm (4–16 in.) from the charges. A gradual increase in point resistance was observed with time after each blast. The increase in penetration resistance may be attributed to gradual improvement of intergranular bonds and dissipation of explosion created gases.

If volume changes followed a definite pattern of development, the ability to predict the behavior of structures, schedule construction, select techniques and make decisions would be greatly improved. This note shows that all types of volume change follow a unique trend of trilinear development with time on a log-log plot. Laboratory and field data from literature on swelling, field settlement, heave and rebound are used to illustrate the trend of three-phase development of volume change. In addition, laboratory measurements of volumetric and one-dimensional linear shrinkage of compacted clay are presented to show that shrinkage also follows a three-phase development.

The strain field during cone penetration is studied. The strain field is obtained by integrating the strain rates induced by the cone in steady penetration of an inviscid, incompressible fluid along paths of particle movement. The results indicate that cone penetration induces a complicated field of axial, radial and shear strains. The octahedral strain variation from 30 % to 0.2 % along a distance 15 times the radius of a 60 degree cone exceeds the strains corresponding to the peak strength of soft cohesive soils. Strains sharply decrease for decreasing apex angles.