S. H. KRISHNAPILLAI ET AL.

470

ts that there are three major

di

itional fitting parameter Cr. Incorporating the

m

lthough there are nu merous SWCC models available in

e the popu-

lar models. The B-C and v-G models

e modified primarily to make sure that these models no

he improved Brooks and Corey (I-B-C) model is given

C

moditional fitting parameter is introduced.

ven though the maximum suction ψmax is incorporated

maximum suction is low, usage of such larger maximum

suction value might over predict shear strength in nu-

merical simulations. Similar to the B-C and v-G models,

the second form of the F-X model (Equation (5)) also

calculates an unrealistic suction when the normalized

water content is zero or less. Therefore, to avoid an un-

realistic suction value at zero normalized water content,

the maximum suction value should be specified even

with a residual water content specified. In addition, the

fourth model parameter Cr in the F-X model is chosen

from a wide range (1 to 1,000,000 kPa) and it creates

difficulties in achieving a unique set of calibrated model

parameters. Also, the Cr affects the initial portion of the

curve when the value of Cr is relatively low and it is

considered as another disadvantage [6]. The primary

objective of this study is to increase the flexibility o f the

B-C and v-G models so that these models can predict

realistic high suctions in low degree of saturations with-

out causing numerical instabilities in finite element simu-

lations. That is, in the modeling the dynamic behavior of

unsaturated soils, there are numerous constitutive rela-

tions that can cause “numerical problems” during the

simulation. The best example is the nonlinear constitu-

tive model (elastoplastic stress-strain model). The other

one is the soil water characteristic cu rve which is used to

calculate the suction value at a given time increment for

the calculated degree of saturation or vise versa. If the

calculated suction is really large or really small, it can

introduce really large or really small number in one of

the element matrices (mass, damping or fluid stiffness).

This might result in crashing the program even with

really small time increment.

It is very challenging to model the soil behavior from

a fully dry condition to a fully saturated condition using

a single fully coupled finite element computer code. The

current state of the art sugges

fficulties in developing numerically stable simulation

capability. They are: difficulties in dealing with multiple

nodal/element variables in finite element formulation of

porous media at these extreme conditions, difficulties in

developing stress-strain behavior with appropriate stress

state variables at these extreme conditions, and difficul-

ties in accurately calculating the suction over the entire

range of degree of saturation. The modified models can

be incorporated in finite element simulation without in-

troducing numerical instabilities from SWCC. The idea

here is to modify the original curve in such a way it cal-

culates a finite number at very low degree of saturation.

In the original model, the curve is very steep at low de-

gree of saturation. A small change in degree of saturation

can result in unrealistic suction value at very low degree

of saturation. Since the modified curve calculates finite

values, numerical instability can be reduced or elimi-

nated.

In this study, the B-C and v-G models are modified by

incorporating correction factors. Also, the correction

factor in the F-X model is modified to avoid the effects

of add

aximum suction as part of the model increased its

flexibility in fitting measured data of various soils over

the full range of S. All three models are improved with

the feature to specify both residual water content and

maximum suction values. The capability of the improved

models is verified by matching with the experimental

data and prediction of original models. Based on the im-

proved F-X model, the permeability function proposed

by Fredlund et al. [6] is modified and presented.

2. Improved SWCC Models and

Comparisons

A

the literature, this study is intended to improv

B-C, v-G, and F-X

ar

longer calculate high suction when the normalized water

content is zero or less. And also the modified models

have the feature to specify both residual water content

an d maximum suction values.

2.1. The Improved Brooks and Corey (I-B-C)

Model

T

in Equation (8). To preserve the advantage of the B-

el, no add

E

in the equation, it cannot be considered to be a fitting

parameter, as the shape of the SWCC cannot be changed

by adjusting the ψmax. The I-B-C model does not provide

a continuous mathematical function for the entire range

of degree of saturation but gives a finite number of suc-

tion value at very low degree of saturation value.

1if

if

r

n

sr

ψa

Cψa

a

(8)

The correction function for the I-B-C model is shown

below in Equation (9). A trial and error

followed to fit the data and there was no theoretical basis

for the equation for the correction function. An obvious

procedure was

condition needed to be satisfied was to obtain the correc-

tion function but to obtain

C

is equal to zero at the

residual water content.

1r

C

(9)

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