Analytical moment–rotation curves for rigid foundations based on a Winkler model

Analytical equations for the moment– rotation response of a rigid foundation on a Winkler soil model are presented. An equation is derived for the uplift-yield condition and is combined with equations for uplift- and yield-only conditions to enable the definition of the entire static moment– rotation response. The results obtained from the developed model show that the inverse of the factor of safety, x; has a significant effect on the moment– rotation curve. The value of x ¼ 0:5 not only determines whether uplift or yield occurs first but also defines the condition of the maximum moment– rotation response of the footing. A Winkler model is developed based on the derived equations and is used to analyze the TRISEE experiments. The computed moment– rotation response agrees well with the experimental results when the subgrade modulus is estimated using the unload – reload stiffness from static plate load– deformation tests. A comparison with the recommended NEHRP guidelines based on the FEMA 273/274 documents shows that the choice of value of the effective shear modulus significantly affected the comparison. q 2003 Elsevier Science Ltd. All rights reserved.

[1]  Gary Norris,et al.  Simple Rigid Plastic Model for Seismic Tilting of Rigid Walls , 1992 .

[2]  Dimitris L. Karabalis,et al.  Dynamic response of 3‐D rigid surface foundations by time domain boundary element method , 1984 .

[3]  edited by Hans F. Winterkorn Hsai-Yang Fang.  Foundation Engineering Handbook , 2017 .

[4]  J. H. Atkinson,et al.  Non-linear soil stiffness in routine design , 2000 .

[5]  Renato Lancellotta,et al.  Monotonic and Cyclic Loading Behavior of Two Sands at Small Strains , 1993 .

[6]  Discussion: An experimental and theoretical comparison between static and dynamic torsional soil tests , 1990 .

[7]  Fumio Tatsuoka,et al.  ELASTIC DEFORMATION PROPERTIES OF GEOMATERIALS , 1992 .

[8]  Alexander M. Puzrin,et al.  Effects of the constitutive relationship on seismic response of soils. Part I. Constitutive modeling of cyclic behavior of soils , 2000 .

[9]  J. D. Frost,et al.  SHEAR MODULUS AND CYCLIC UNDRAINED BEHAVIOR OF SANDS , 1989 .

[10]  Nabil F. Ismael,et al.  Allowable pressure from loading tests on Kuwaiti soils , 1985 .

[11]  Raj V. Siddharthan,et al.  Stiffnesses of abutments on spread footings with cohesionless backfill , 1997 .

[12]  Malcolm D. Bolton,et al.  Discussion: An experimental and theoretical comparison between static and dynamic torsional soil tests , 1990 .

[13]  G. Mylonakis,et al.  Seismic Soil-Structure Interaction: New Evidence and Emerging Issues , 1998 .

[14]  A. Filiatrault,et al.  Effect of weak foundation on the seismic response of core wall type buildings , 1992 .

[15]  J. W. Meek.  Dynamic response of tipping core buildings , 1978 .

[16]  Jonathan P. Stewart,et al.  Empirical Verification of Soil-Structure Interaction Provisions in Building Codes , 1998 .

[17]  Jean-Louis Briaud,et al.  Behavior of Five Large Spread Footings in Sand , 1999 .

[18]  Ahmed Ghobarah,et al.  Performance-based design in earthquake engineering: state of development , 2001 .

[19]  Diego Carlo Lo Presti,et al.  Large-Scale Geotechnical Experiments on Soil-Foundation Interaction (TRISEE Task 3) , 1998 .

[20]  Omar Chaallal,et al.  Seismic Response of Flexibly Supported Coupled Shear Walls , 1996 .

[21]  Alain Pecker,et al.  Cyclic macro‐element for soil–structure interaction: material and geometrical non‐linearities , 2001 .

[22]  S. Rampello,et al.  Pre-failure deformation characteristics of geomaterials , 1999 .

[23]  Wai-Fah Chen,et al.  Bearing Capacity of Shallow Foundations , 1991 .