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Demonstration

Example 2a: Direct shear test using the GQ/H backbone curve formulation

This example demonstrates a single element direct simple shear test that utilizes I-soil with GQ/H backbone generation method (Groholski et al., 2016). For this particular example, the units defining the parameters are N, kg, and meter (m), and the material definition is created using following input:

[Materials<<<{"href": "../syntax/Materials/index.html"}>>>]
  [./I_Soil<<<{"href": "../syntax/Materials/I_Soil/index.html"}>>>]
    [./soil_1]
      soil_type<<<{"description": "This parameter determines the type of backbone curve used. Use 'user_defined' for a user defined backbone curve provided in a data file, 'darendeli' if the backbone curve is to be determined using Darandeli equations, 'gqh' if the backbone curve is determined using the GQ/H approach and 'thin_layer' if the soil is being used to simulate a thin-layer friction interface."}>>> = 'gqh'
      layer_variable<<<{"description": "The auxvariable providing the soil layer identification."}>>> = layer_id
      layer_ids<<<{"description": "Vector of layer ids that map one-to-one to the rest of the soil layer parameters provided as input."}>>> = '0'
      theta_1<<<{"description": "The curve fit coefficient for GQ/H modelfor each soil layer."}>>> = '-2.28'
      theta_2<<<{"description": "The curve fit coefficient for GQ/H modelfor each soil layer."}>>> = '-5.54'
      theta_3<<<{"description": "The curve fit coefficient for GQ/H modelfor each soil layer."}>>> = '1.0'
      theta_4<<<{"description": "The curve fit coefficient for GQ/H modelfor each soil layer."}>>> = '1.0'
      theta_5<<<{"description": "The curve fit coefficient for GQ/H modelfor each soil layer."}>>> = '0.99'
      taumax<<<{"description": "The ultimate shear strength of the soil layers. Required for GQ/H model"}>>> = '7500'
      initial_shear_modulus<<<{"description": "The initial shear modulus of the soil layers."}>>> = '20000000'
      number_of_points<<<{"description": "The total number of data points in which the backbone curve needs to be split for all soil layers (required for Darandeli or GQ/H type backbone curves)."}>>> = 10
      poissons_ratio<<<{"description": "Poissons's ratio for the soil layers. The size of the vector should be same as the size of layer_ids."}>>> = '0.3'
      block<<<{"description": "The blocks where this material model is applied."}>>> = 0
      initial_soil_stress<<<{"description": "The function values for the initial stress distribution. 9 function names have to be provided corresponding to stress_xx, stress_xy, stress_xz, stress_yx, stress_yy, stress_yz, stress_zx, stress_zy, stress_zz. Each function can be a function of space."}>>> = '-4204.286 0 0  0 -4204.286 0  0 0 -9810'
      density<<<{"description": "Vector of density values that map one-to-one with the number 'layer_ids' parameter."}>>> = '2000'
    [../]
  [../]
[]
(examples/ex02a/HYS_GQH.i)

where

theta_1 through theta_2 ; are curve fitting parameters obtained from DEEPSOIL (Hashash et al., 2016).

taumax = 7500 ; specifies maximum shear strength achieved at large shear strains.

Other parameters are the same as in Example 1. Once the same boundary conditions are applied as in Example 1, the following response is obtained

Figure 1: Hysteretic response under 0.02 cyclic strian amplitude.

commentnote

Observe that in Example 2a, the shear stress mobilized at shear strain of 0.02 is 6 kPa whereas in Example 1a, the mobilized shear stress is ~ 4 kPa. This is because in Example 1a, the backbone asymptotically approaches to 4 kPa which is implied by Darendeli (2001) at large strains whereas in Example 2a, the shear stress asymptotically approaches to 7.5 kPa at large strains (0.1)

References

  1. M. B. Darendeli. Development of a new family of normalized modulus reduction and material damping curves. PhD dissertation, University of Texas at Austin, 2001.[BibTeX]
  2. D. Groholski, Y. Hashash, B. Kim, M. Musgrove, J. Harmon, and J. Stewart. Simplified model for small-strain nonlinearity and strength in 1d seismic site response analysis. Journal of Geotechnical and Geoenvironmental Engineering, 2016.[BibTeX]
  3. Y. Hashash, M. Musgrove, J. Harmon, D. Groholski, C. Phillips, and D. Park. Deepsoil v6.1, user manual. Urbana, IL, Board of Trustees of University of Illinois at Urbana-Champaign, 2016.[BibTeX]