Data are presented concerning the shear modulus and damping ratios of sands and gravelly soils as determined by laboratory and field tests. A simple relationship is proposed to relate the shear modulus of a cohesionless soil to a modulus stiffness coefficient, which is a soil property and depends on the characteristics of the soil, and the effective mean principal stress at any point in the soil. Values for the modulus coefficient at low strains are suggested, and it is shown that these values for sands can be estimated from the standard penetration resistance of the sand. Values for gravels are generally greater than those for sands by factors ranging from 1.35–2.5. Suggestions are also made for determining the variation of shear modulus with shear strain and the damping ratios for both sandy and gravelly soils.

Moduli and Damping Factors for Dynamic Analyses of Cohesionless Soils

A complete set of algebraic formulas and dimensionless charts is presented for readily computing the dynamic stiffnesses (\IK\N) and damping coefficients (\IC\N) of foundations harmonically oscillating on/in a homogeneous half-space. All possible modes of vibration, a realistic range of Poisson’s ratios, and a practically sufficient range of oscillation frequencies are considered. The foundations have a rigid basemat of any realistic solid geometric shape. The embedded foundations are prismatic, having a sidewall-soil contact surface of height \Id\N, which may be only a fraction of the embedment depth \ID\N. Two numerical examples illustrate the use of the formulas and charts and elucidate the role of foundation shape and degree of embedment on radiation damping for various modes of vibration. A companion paper (Gazetas and Stokoe 1991) presents supporting experimental evidence from model tests. The two papers aim at encouraging the practicing engineer to make use of results obtained with state-of-the-art formulations, when studying the dynamic response of foundations.

Formulas and charts for impedances of surface and embedded foundations

An elastic analysis is presented for the horizontal displacement and rotation of a laterally loaded pile group and the distribution of horizontal forces within the group. The interaction between two identical equally loaded piles is analyzed first, and the increases in displacement and rotation of the piles, in relation to the single pile values, are expressed in terms of interaction factors. Using these interaction factors, a method for calculating the displacement and rotation of a general pile group, based on the principle of superposition, is described. An examination of the behavior of square groups of piles reveals that the displacement, rotation, and load distribution in the group is largely influenced by the length-to-diameter ratio of the piles and the relative pile flexibility. It is also found that the displacement depends on the breadth of the group rather than the number of piles in the group. A reasonable measure of agreement is found between a limited number of reported measurements and theoretical predictions of group displacements.

Closure to “Behavior of Laterally Loaded Piles: II-Pile Groups”

Ground vibrations from sheetpile driving in urban environment: measurements, analysis and effects on buildings and occupants

The finite element method is used for the determination of the collapse load of a rigid strip footing placed on a uniform layer of purely frictional soil subjected to inclined and eccentric loading...

Bearing capacity of strip footings on purely frictional soil under eccentric and inclined loads

The bearing capacity of an eccentrically loaded footing is determined by analytical formulation. In this analysis, the footing has been considered rigid with a rough base. It has been assumed that the rupture surface is a log spiral, and failure occurs on the same side as the eccentricity with respect to the center of the footing. The resistance mobilized on this side is fully passive and partial on the other. The footing has been assumed to lose contact with increase in eccentricity and the results are given in the form of bearing capacity factors N γ , N q , and N c . For the verification of analytical solutions, model tests were conducted on sand both in dense as well as loose states. Footings were tested both at surface and at a depth such that D f / B = 1 and eccentricity of load ranged from 0.1 B and 0.4 B , in which D f and B are, respectively, depth and width of footing. Test data of the previous investigators are also analyzed and compared with the proposed theory. A reasonable agreement was found between the theory and the test data.

Bearing Capacity of Eccentrically Loaded Footings

Discussion of "Lateral Load Behavior of Pile Group in Sand"

Discussed here is the state-of-the-art design of machine foundations and the principles of soil engineering, soil dynamics and theory of vibrations. Complete and comprehensive treatment of design methods for different types of machines are described including reciprocating machines, impact machines and rotary machines. Embedded foundations and foundations on piles are also covered, along with step-by-step design procedures and several solved examples. Two main methods of analysis, Elastic Half Space and Linear Spring are described in detail, and material is provided on wave propagation for determining dynamic soil properties - essential to the safe design of machine foundations. The chapter on vibrations should prove helpful to the reader in understanding the dynamic nature of the problem. This book presents a systematic, concise and thorough discussion of the subject, complete with solved examples, bibliography and concluding commentary.

Foundations for machines : analysis and design

Bearing capacity of footings under inclined loads

One of the significant effects of considering soil-structure interaction in the analysis of structures is the increase in the fundamental natural period compared to the fundamental natural period of a similar structure, fixed at the base. Applied Technology Council (ATC) originally set forth some provisions to calculate the fundamental natural period of flexible based structures using the period of a similar structure, fixed at the base, and lateral and rocking stiffness coefficients of the foundation. These provisions became the basis of current soil-structure interaction recommendations in several building codes. The fundamental natural periods of structures founded on different types of foundations computed using recommendations of the ATC are compared with those computed using a simplified model to perform soil-structure interaction of shear-type structures. Results show that the provisions given in ATC may be used for structures supported on shallow footings but may not be applicable for structures supported on pile foundations or foundations having the ratio of lateral to rotational stiffness coefficients different from those of shallow foundations. An equation, similar to the equation recommended by ATC, is presented to estimate the fundamental natural period of structures supported on pile foundations.

Shamsher Prakash

Papers

Bearing Capacity of Eccentrically Loaded Footings

Discussion of "Lateral Load Behavior of Pile Group in Sand"

Foundations for machines : analysis and design

Bearing capacity of footings under inclined loads

Estimation of fundamental period for structures supported on pile foundations