Hyperbolic Gap Material

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This command is used to construct a hyperbolic gap material object.

uniaxialMaterial HyperbolicGapMaterial $matTag $Kmax $Kur $Rf $Fult $gap

$matTag integer tag identifying material
$Kmax initial stiffness
$Kur unloading/reloading stiffness
$Rf failure ratio
$Fult ultimate (maximum) passive resistance*
$gap initial gap*


  • This material is implemented as a compression-only gap material. $Fult and $gap should be input as negative values.
  • Recomended Values:
$Kmax = 20300 kN/m of abutment width
$Kcur = $Kmax
$Rf = 0.7
$Fult = -326 kN per meter of abutment width
$gap = -2.54 cm


This file contains the class implementation for HyperbolicGapMaterial. This material is based on abutment stiffness models for bridge simulation proposed by Patrick Wilson and Ahmed Elgamal at UCSD. The abutment stiffness models are based on large-scale abutment tests performed on the outdoor shaking table at UCSD. The model is described for a 1.68 meter (5.5 ft) tall backwall height (typical size) and a 1 meter wide section along the width of the abutment (to be scaled accordingly). The hyperbolic force-displacement model is based on work by Duncan and Mokwa (2001) and Shamsabadi et al. (2007) with calibrated parameters from UCSD abutment tests. This model matches very well with test data up to 7.64 cm of longitudinal displacement.

<math>F(x) = \frac{x}{\frac{1}{K_\text{max}} + R_f \frac{x}{F_\text{ult}}}</math>




Duncan, J. M., and Mokwa, R. L. (2001). "Passive earth pressures: theories and tests." Journal of Geotechnical and Geoenvironmental Engineering, 127(3), 248-257.

Shamsabadi, A., Rollins, K. M., and Kapuskar, M. (2007). "Nonlinear soil-abutment-bridge structure interaction for seismic performance-based design." Journal of Geotechnical and Geoenvironmental Engineering, 133(6), 707-720.

Wilson, P and Elgamal, A (2006). "Large scale measurement of lateral earth pressure on bridge abutment back-wall subjected to static and dynamic loading." Proceedings of the New Zealand Workshop on Geotechnical Earthquake Engineering, University of Canterbury, Christchurch, New Zealand: pp 307-315.

Code Developed by: Mathew Dryden, UC Berkeley and Patrick Wilson, UCSD