# Theoretical and Experimental Investigation of Effective Density and Pore Fluid Induced Damping in Saturated Granular Materials

Open Access

- Graduate Program:
- Civil Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- March 05, 2014
- Committee Members:
- Tong Qiu, Dissertation Advisor
- Tong Qiu, Committee Chair
- Chun Liu, Committee Member
- Farshad Rajabipour, Committee Member
- Mansour Solaimanian, Committee Member

- Keywords:
- Effective Density
- Pore Fluid Induced Damping
- Resonant Column Test
- Bender Elements Test
- Energy Dissipation

- Abstract:
- In current geotechnical engineering research and practice, two assumptions are generally made regarding the dynamics of saturated soil. The first is that pore fluid induced damping during shear wave excitations is negligible. The second is that saturated density can be used to calculate shear modulus based on measured shear wave velocity. The validity of these assumptions depends on the magnitude of fluid motion relative to solids during shear wave excitations. For soils with low permeability (e.g., silts and clays) and under low-frequency excitations (e.g., seismic waves), these assumptions are generally valid. However, relative fluid motion may be important for soils with high permeability (e.g., sands and gravels) and under high-frequency excitations, rendering the above mentioned assumptions questionable. This study presents an experimental investigation of the concept of effective density for propagation of small strain shear waves through saturated granular materials. Bender element tests and resonant column tests were conducted on various granular materials in dry and saturated conditions. Values of small-strain shear modulus measured for the dry condition are compared to corresponding values measured for the saturated condition using saturated density and effective density. Analysis of test results indicates that effective density instead of saturated density should be used to calculate small-strain shear modulus. For bender element tests, the use of saturated density produced errors in shear modulus as high as 28%; whereas the use of effective density resulted in errors generally less than 5%. For resonant column tests, errors in shear modulus obtained using saturated density were smaller than those for bender element tests due to the lower range of excitation frequency. This study presents two analytical solutions for Biot flow induced damping in saturated soil specimens in resonant column tests based on the half-power bandwidth and free vibration decay methods. These solutions are compared with a closed-form analytical solution readily available in literature. The solutions indicate that Biot flow induced damping may provide an important contribution to total soil damping in coarse sand and gravel, but can be practically neglected for less permeable soils (e.g., fine sand, silt, and clay). The solutions also indicate that Biot flow induced damping increases as porosity increases and decreases considerably as the ratio of the mass polar moment of inertia of the loading system to the specimen increases. It is concluded that Biot flow induced damping is suppressed by the boundary condition of typical resonant column apparatuses and is hence difficult to be measured. The solution from the free vibration decay method is compared to RC test results of various granular materials at dry and saturated conditions. The comparison suggests that the validity of this analytical solution is inconclusive, which is largely due to the very small magnitude of Biot flow induced damping in RC tests. In addition, a theoretical investigation of energy dissipation in a nearly saturated poroviscoelastic soil column under quasi-static compressional excitations, which is applicable to slow phenomena (e.g., consolidation), is also presented in this study. Different components of the energy dissipation are evaluated and compared. This investigation indicates that the magnitude of pore fluid induced energy dissipation is primarily a function of a normalized excitation frequency . For small values of , a drained soil column is fully relaxed and behaves essentially as a dry column with negligible pore pressure. In this case, fluid induced energy dissipation is negligible and the total damping ratio of the column is essentially the same as that of the solid skeleton. For very high values of , a drained soil column is fully loaded and the excitation-generated pore pressure decreases as the fluid becomes more compressible. In this case, the fluid pressure gradient only exists in a thin boundary layer near the drainage boundary, where drainage occurs and fluid induces energy dissipation; whereas the rest of the column is essentially undrained. Significant fluid induced energy dissipation occurs for moderate values of due to a combination of moderate fluid pressure, pressure gradient and fluid relative motion throughout the soil column. The effects of boundary drainage condition, saturation, porosity, and skeleton damping ratio on fluid induced energy dissipation are discussed.