2. Verification and Validation

2.1. 2D Column 1D Shaking

A 2D free field effective stress analysis is performed by s3hark and demonstrated in this section. The simulation is described in a json file, which can be downloaded from this link. This file can be loaded by s3hark to build the analysis automatically. The ground motion used in this simulation can be downloaded from here. The results are verified against FLAC and Plaxis. The soil column being analyzed is 6 meters high sitting on a rock. The ground water table is at 2 meters below the soil surface. In the column, there are a total of three soil layers. Each layer is meshed by elements with a size of 0.25 meter in height. Basic properties of soil layers and the rock are shown in Fig. 2.1.1 and Fig. 2.1.2. The first two layers are modeled by PM4Sand and the third layer is modeled by elastic isotropic material. (The implementation work of PM4Sand [BZ15] is done in University of Washington by Long Chen and Pedro Arduino. Chaofeng Wang at UC, Berkeley contributed to the code optimization for speed improvement. ) The rock layer will be simplified to a [LK69] dashpot, which accounts for the finite rigidity of the underlying elastic medium. The parameters of the dashpot are calculated solely based on rock layer’s density and \(V_{s30}\).

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Fig. 2.1.1 Soil layers

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Fig. 2.1.2 Basic information of each layer

The detailed properties of the material in each soil layer are shown in Fig. 2.1.3, Fig. 2.1.4 and Fig. 2.1.5.

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Fig. 2.1.3 Layer 1

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Fig. 2.1.4 Layer 2

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Fig. 2.1.5 Layer 3

For the verification and validation purposes, s3hark’s results are compared with FLAC an PLAXIS, as shown in Fig. 2.1.6. All three programs generally produce very similar response with different levels of differences shown in PHA, maximum shear strain, CSR, maximum pore pressure ratio. The differences come from multiple sources, such as numerical discretization methods, solvers, etc. For example, FLAC tends to produce higher dilation pulses in liquefied layer. This is possibly due to a combination of different reasons, e.g., interpolation of data from integration points at different locations, numerical methods for integration, formulations for solid fluid coupling, etc. (Long Chen and Andrew Makdisi at University of Washington, Gregor Vilhar at PLAXIS BV, Chaofeng Wang at UC, Berkeley contributed to the verification of PM4Sand in s3hark.)

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Fig. 2.1.6 Compare with FLAC and PLAXIS

2.2. 3D Column Bidirectional Shaking

A 3D free field effective stress analysis is performed by s3hark and demonstrated in this section. The results are verified against OpenSees. The soil column being analyzed is 30 meters high sitting on a rock. The ground water table is at 2 meters below the soil surface. In the column, there are a total of three soil layers. Each layer is meshed by elements with a size of 0.5 meter in height. Basic properties of soil layers and the rock are shown in Fig. 2.2.1 and Fig. 2.2.2. The layers are modeled by PDMY02 material. The rock layer will be simplified to a [LK69] dashpot, which accounts for the finite rigidity of the underlying elastic medium. The parameters of the dashpot are calculated solely based on rock layer’s density and \(V_{s30}\). The slope parameters are set to be \(\alpha=1.145762838175103^{\circ}\) and \(\beta=-90^{\circ}\)

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Fig. 2.2.1 Soil layers of a 3D column

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Fig. 2.2.2 Soil layers of a 3D column

The ground motion used in this simulation can be downloaded from here. The simulation itself is described in a json file, which can be downloaded from this link. This file can be loaded by s3hark to build the analysis automatically. It includes all the configurations, the soil table and parameters for each layer - all the information needed to reproduce the simulation. In s3hark, go to the menu and choose to open and load this json file into the application, You’ll see the detailed properties of the material in each soil layer as those shown in Figures Fig. 2.2.3, Fig. 2.2.4, Fig. 2.2.5 and Fig. 2.2.6.

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Fig. 2.2.3 Detail soil properties and material model parameters of a 3D column: Layer 1

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Fig. 2.2.4 Detail soil properties and material model parameters of a 3D column: Layer 2

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Fig. 2.2.5 Detail soil properties and material model parameters of a 3D column: Layer 3

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Fig. 2.2.6 Detail soil properties and material model parameters of a 3D column: Rock

In the Configure tab, put the path of the downloaded motion file into Rock motion. Then, click the Analyze button to perform the simulation. For the verification and validation purposes, s3hark’s results are compared with OpenSees, as shown in Fig. 2.2.7.

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Fig. 2.2.7 Compare with OpenSees

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