**Department
of**

**Tong Qiu, Ph.D.,
P.E.**

**National Science Foundation**,
**U.S. Department of State***, ***Federal
Highway Administration, Federal Railroad Administration,***
***PennDOT, Alpine Equipment LLC***, ***Ben
Franklin Foundation***, *and Mid-Atlantic Universities
Transportation Center,

**Primary Research Interests**

Soil dynamics and geotechnical
earthquake engineering

Flow through porous media, fluid-solid
interaction

Numerical analysis in geotechnical
engineering

Soil-structure interaction

Granular mechanics

**Recent Research**

**Topic 1**: Pore Fluid Induced Damping in Saturated
Soil during Shear Wave Excitations

**Topic 2**: SPH Simulation of Geomaterial under
Large Deformations

**Topic
3: **Simulation
of Earthquake-Induced Slope Deformation using SPH Method

**Topic 1: Pore Fluid Induced Damping in
Saturated Soil during Shear Wave Excitations**

In this
research, we try to quantify pore fluid induced damping in
saturated soil during shear wave excitations through
analytical and experimental investigations. Damping is
an important soil property in soil dynamics and geotechnical
earthquake engineering. Figure 1 illustrates the
effect of soil damping on site response during an
earthquake. As the earthquake waves travel between the
bedrock and ground surface, their energy is dissipated due
to soil damping. Therefore, a higher soil damping
would result in a smaller site response (which is
beneficial), assuming that everything else stays the same
(e.g., soil stiffness, soil profile, and acceleration time
history).

**Figure 1**. Schematic illustration of the
effect of soil damping on site response during an earthquake

When soils deform under dynamic loading, energy loss
occurs due to rolling and sliding at particle contacts and
the creation and deletion of particle contacts (see Figure
2). Damping due to these mechanisms is referred to as
"skeleton damping" and is the only source of material
damping in dry soils. In saturated soils, additional
energy loss occurs due to the relative motion between
viscous pore fluid and solid particles. Therefore,
saturated soils exhibit higher damping than the same soils
in their dry state. Although its existence has long
been recognized, systematic investigations on pore fluid
induced damping have been limited in literature. The
objective of this research is to quantify pore fluid induced
damping and provide practical solutions on this phenomenon
through combined analytical work and experimental testing.

**
Figure 2**.
Schematic illustration of soil skeleton and individual solid
particles

Sponsor: National Science Foundation
(CMMI-0826097)

Status: Currently we are performing
resonant column tests on glass beads and sands to validate
the analytical solution presented in the following
reference.

Reference:

Qiu, T. (2010). "Analytical Solution
for Biot Flow-Induced Damping in Saturated Soils during
Shear Wave Excitations," *Journal of Geotechnical and
Geoenvironmental Engineering*, ASCE, 136(11), pp.
1501-1508.

**Topic 2:
SPH Simulation
of Geomaterial under Large Deformations**

In this work,
we try to model solids, particularly granular materials,
under large deformations using the Smoothed Particle
Hydrodynamics (SPH) method. Listed below are some
results of our simulations of the experiments conducted by
Lube et al. (2004) on the collapse of initially vertical 3-D
axisymmetric columns of various granular materials.
Simulations and experimental results are compared for
granular columns with the same initial radius of 0.1 m but
different aspect ratios a=hi/ri , where
hi
and ri are the initial height and radius of the
granular column, respectively. Typical values of bulk
modulus and Poisson's ratio of loose sands, namely 5 MPa and
0.3 are used, respectively.

(a)
(b)

(c)

**Figure 3.**
Comparison of experiment and SPH simulation for
a sand column with a=0.55 :

(a)
experimental
final
profile;
(b)
simulated
final
profile; (c) animation of the collapse

(experiment image from Lube et al. 2004)

(a)
(b)

(c)

**Figure 4.** Comparison of experiment and
SPH simulation for a sand column with a=0.9:

(a) experimental final
profile; (b) simulated final profile; (c) animation of the
collapse

(experiment image from Lube
et al. 2004)

(a)
(b)

(c)

**
Figure 5.** Comparison of experiment and SPH
simulation for a sand column with a=2.75:

(a) experimental final profile; (b) simulated final profile; (c) animation of the collapse

(experiment image from Lube et al. 2004)

Lube et al. (2004) observed that depending on the aspect ratio, different flow patterns exist during the collapse. For 0<a<0.74 , it was observed that a circular undisturbed area at the top of the column remains at the initial height; for 0.74<a<1.7 , the inner circular region is eroded gradually by outer moving particles, leaving a sharp cone at the center with its tip remaining at the initial height; for a>1.7, the entire upper surface of the column starts to flow and the height of column decreases immediately. These observations are reproduced by the SPH simulations satisfactorily as demonstrated in Figures 3 to 5.

Status: Currently various constitutive
models are being implemented into the developed 3-D SPH
model to simulate different phenomena involving large
deformations of solids, particularly geomaterials.

References:

Chen, W. and Qiu, T. (2012).
"Numerical simulations for large deformation of granular
materials using smoothed particle hydrodynamics method," *International
Journal of Geomechanics*, ASCE, 12(2), 127-135.

Lube, G., Huppert, H.E., Sparks,
R.S.J. and Hallworth, M.A. (2004). "Axisymmetric collapses
of granular columns," *Journal of Fluid Mechanics*,
508, 175-199.

**Topic 3: Simulation of Earthquake-Induced
Slope Deformation using SPH Method**

In this
research, we aim to develop, calibrate, and validate a SPH
model for the simulation of seismically induced slope
deformation under undrained condition. A constitutive model
that combines the isotropic strain softening plasticity and
the modified Kondner and Zelasko rule is developed and
implemented into a 3-D SPH model developed by Chen and Qiu
(2014). The developed SPH model accounts for the effects of
wave propagation in the sliding mass, cyclic nonlinear
behavior of soil, and progressive reduction in shear strength
during sliding, which are not explicitly considered in the
Newmark-type analyses widely used in current research and
practice.

The developed SPH model is validated against a readily available and well documented model slope test on a shaking table (Wartman 1999, Wartman et al. 2001, Wartman et al. 2005). The model simulated slope failure mode (Figure 6), acceleration response spectra, and slope deformations are in excellent agreement with experimental data as reported in detail by Chen and Qiu (2014). It is thus suggested that the developed SPH model may be utilized to reliably predict earthquake-induced slope deformations.

**Figure 6.** Comparison of simulated
failure mode and deformed shape with model slope test:

(a) t=13.4 s; (b) t=20.2 s; (c) t=32.0 s; (d) final deformed profile and sliding surface

from model slope test (from Wartman et al. 2005).

Status: Currently parametric study is being conducted to investigate the effects of boundary condition, slope profile, soil properties, and characteristics of strong ground motion on seismically induced slope deformation. Particular emphasis is being placed on the effect of strain softening behavior on the progressive and total slope deformation.

References:

Chen, W. and Qiu, T.
(2014). "Simulation of earthquake-induced slope deformation
using SPH method." *International Journal for Numerical
and Analytical Methods in Geomechanics*, 38(3),
297-330.

Wartman, J. (1999). "Physical model studies of seismically induced deformation in slopes." Ph.D. Dissertation, The University of California, Berkeley.

Wartman J., Seed R.B.
and Bray J.D. (2001) "Physical model studies of seismically
induced deformations in slopes." *GeoEngineering Report
No. UCB/GT/01-01*, Department of Civil and
Environmental Engineering, University of California,
Berkeley.

Wartman, J., Bray, J.D.,
and Seed, R.B. (2005). "Shaking table modeling of
seismically induced deformations in slopes." *Journal of
Geotechnical and Geoenvironmental Engineering*, ASCE,
131(5), 610-622.