## ASDAbsorbingBoundary and non-linear dynamic analysis

Zhou_Jx
Posts: 47
Joined: Wed Mar 16, 2022 12:15 pm

### ASDAbsorbingBoundary and non-linear dynamic analysis

Dear STKO,

I recently conducted simulations using ASDAbsorbingBoundary to implement an absorbing artificial boundary condition. I found that this method effectively absorbed the outward scattered wave during linear dynamic analysis when both the soil domain and the free field were defined as elastic. However, when I applied this boundary condition in the non-linear dynamic analysis of a loose sand with a relative density of 30%, I encountered two new questions. I will elaborate on these questions below:

1. How can I define the absorbing boundary when the small-strain shear modulus (Gmax) increases with depth in the soil?

In my numerical model, the soil domain is simulated using the PDMY02 soil material, whose parameters is defined based on the recommended values by OpenSees. According to OpenSees https://opensees.berkeley.edu/wiki/inde ... d_Material, the Gmax of the soil material is a function of effective confinement (pr) and can be expressed as:

Gmax = Gr*(p'/pr)^d

where the Gr = 60 Mpa is the reference shear stiffness, the pr = 80 kPa, the d =0.5, and the p' is the confining stress of soil and can be expressed as:

p'=(sigma_v+2sigma_h)/3

Since both vertical and horizontal stresses (sigma_v and sigma_h) are functions of soil depth, the Gmax increases exponentially with depth. This presents a challenge in accurately reflecting this increase using the ASDAbsorbingBoundary element. To address this, I have approximated the exponential increase process by incorporating multiple equivalent ASDAbsorbingBoundaries along the lateral boundary. I am unsure if this is a reasonable approach, and would appreciate any suggestions you may have. The euqivalent Vs-recommended Vs, as well as the equivalent Gmax and the recommended Gamx profiles are shown below:
Equivalent Vs.png (48.93 KiB) Viewed 1551 times
Gmax-profile.png (52.56 KiB) Viewed 1551 times
2. How to simulate the weakening of Gmax in the ASDAbsorbingBoundaries .

It is commonly observed that dynamic loading leads to a degradation of the Gmax of the soil domain, resulting in a reduction of the shear wave velocity (Vs) of the soil. However, as the ASDAbsorbingBoundaries are defined as elastic, they tend to have a higher Vs than the soil domain. How can this issue be addressed?

I would appreciate your assistance with the two issues I have described above. For your reference, I have attached my numerical model and material properties below:
Absorb & PDMY02 sand.zip