Estimation of Proper Strain Rate in the CRSC Test
Using a Artificial Neural Networks
Jum Sik Chae, Hyung Kyu Park, and Song Lee

University of Seoul
Seoul, Korea

ABSTRACTThe Constant rate of strain consolidation (CRSC) test, in which the
continuous loading is applied the sample has been developed to
overcome some of the problems associated with the incremental
loading consolidation (ILC) test. Therefore, it is able to reduce the test
time and provide a well defined the curve of effective stress versus
strain due to continuous Stress-strain points. Also, the CRSC test has
been accepted widely as a standard method in foreign countries because
of its many advantages. However, in Korea the CRSC test has not been
used in engineering practice and experimentally verified. Because there
is not a precise criterion of strain rate despite consolidation
characteristics are influenced on strain rate. Consequently, it is difficult
to apply in engineering practice.
In this study, artificial neural networks are applied to the estimation of
the proper strain rate of the CRSC test.
This study shows the possibility of utilizing the artificial neural

a rapid means of determining the preconsolidation pressure. In the
CRSC test, the imposed boundary conditions are similar to those in the
ILC test, but with one-way drainage. The specimen is loaded at a
constant rate of strain instead of incrementally. Therefore, new
interpretation methods were required for data obtained by the CRSC
test. The analysis method proposed by Wissa et al. (1971) has been
widely used in most countries. Their method is based on the
consolidation theory in which strain is assumed small and the
coefficient of consolidation is assumed constant in the vertical direction
at a time. They proposed some options for the analysis method by
assuming or not steadiness of the solution.
To perform the CRSC test, appropriate strain rate for the material tested
must be pre-selected. Because consolidation properties that calculated
using the CRSC test are influenced on strain rate. The methods that
generally recommended to select the strain rate in the CRSC test are
ASTM D 4186-82, Armour & Drnevich(1986) etc al.
However, the ASTM recommendation is not reasonable for soils with
high liquid limit. And Armour & Drnevich’s method is difficult to
apply because strain rate would depend on selection of the three
assumed values.
The purpose of this study is to examine the applicability of the ANN
model for the estimation of the proper strain rate.
This study was performed with strain rate that determined by various
estimate methods. Also, These results are compared to data calculated
using the CRSC test as well as the ILC test results on the same soil. METHOD OF ANALYSIS




−∆
−=
v
b
v
v
V
u
t
H
C
σ
σ
σ
1log2
log
1
2
2
(2)

where
H = current specimen height
21
,
vv

limit of the soil and assumed parameters. Also, Armour and
Drnevich(1986) proposed an empirical equation for calculating the
strain rate, as below

















−
−
=
max
1log
)38exp(
v
b
ow
oa

and connection weights, it is possible to realize complex

mapping

through its characteristics of distributed representations
.
ANN models
are efficient computing techniques that are widely used to solve
complex problems in many fields. In this study, a back-propagation
neural network model for estimating of proper strain rate form soil
parameter is proposed. The back-propagation neural network program
adopted in the present study essentially followed the formulations of
Eberhart(1990) as shown in Fig.1. The implementation of the back-
propagation neural network model for predicting proper strain rate
involved three phases
First, data collection phase involved gathering the data for use in
training and testing the neural network. A large training data reduces
the risk of under-sampling the nonlinear function, but increases the
training time. To improve training, preprocessing of the data to values
between 0 and 1 was carried out before presenting the patterns to the
neural network. The following normalization procedure (Master, 1993)
was used in this study.

minmax
min
VV
VV
A
−
−
Fig. 1 Flow chart for programming of the artificial neural network VERIFICATIONS OF MANN MODELIn order to verify the applicability of MANN model, a total of 46 data
of the consolidation test results are used. 43 learning data are used for
training the ANN model, and the others are used for the comparison
Data Collection
Data Normalization
Parametric Studies
Training and Testing ANN
Verify the reliance of the ANN
631
between the predicted value and the measured value.
The properties of the soil used for training of the MANN models are
shown in Table 1. Table 1. Properties of the soil used for learning of the MANN models


Present effective vertical pressure (
2
/ cmkg
)
0.04 ~3.86
Strain rates (%/min) 0.01 ~ 0.5
The number of neuron for each hidden layer is determined as 7 from
the results of consolidation test and the learning ratio is determined as
0.1 to optimize network learning. In this analysis, system error was
limited to 2.0E-5 after about 30,000 cycles of training as shown in Fig.
2. With the learning results, the most important factors on the
preconsolidation pressure ratio are LI and strain rate as shown in Fig. 3.
0 10000 20000 30000
Iteration Number (N)
1E-005
0.0001
0.001
0.01
0.1
Learning Error (Er)Fig. 2 Variation of the learning error with Iteration Number Table 2.
Properties of the soil used for verification of the MANN models

Class

A B C
Wn (%)

110.2

74.0 42.9

LL (%)

79.0 80.9 44.4
PI

47.4 44.8 22.9
LI

1.66 0.85 0.93
Gs 2.58 2.66 2.70
o
e

2.861 1.938 1.161


( )
)()( ILCCCRSC
CC
. The
abscissa presents the measured values from the consolidation tests, the
ordinate shows the predict values using the ANN model. The results
show the high correlation between the measured value and predicted
value. This result implies that the ANN model can predict the
consolidation properties with high degree of confidence.

632
0 0.4 0.8 1.2 1.6 2
Measured Value
0
0.4
0.8
1.2
1.6
2
Predicted value
Preconsolidation Stress Ratio
Compression Index RatioFig. 4 Comparison between the predicted and measured values
TEST PROGRAM



1.774 1.522 ~ 2.029

d
γ
)/(
3
cmg

0.970 0.891 ~ 1.067
60
D
(mm)
0.011 0.011 ~ 0.023
Passing the # 200 (%) 99.1 97.8 ~ 99.8
Clay fraction < 2µ (%)
29.7 10.5 ~ 38.0
0
p
(
2
/ cmkg
)
1.24 0.64 ~ 1.42
ASTM 0.004 0.004 ~ 0.010
Armour & Drnevich 0.086 0.008 ~ 0.086
Strain rates
(%/min)
MANN model 0.008 0.008 ~ 0.046
All tests were performed on specimens, 2 cm high with a diameter 6 cm,

1.6
1.8
2
Preconsolidation Pressure Ratio
Predicted Value
Measured Value
PR = 34.36 * r
2
+ 1.87 * r + 1.00
R
2
= 0.98Fig. 5 Comparison between the predicted and measured values
for preconsolidation pressure ratio with strain rate Fig. 6 shows the preconsolidation pressure ratio obtained from the
consolidation test performed with various strain rates. These strain rates
are determined by various estimate methods. As can be recognized
form Fig. 6, the ranges of strain rates obtained from ANN model were
between those from ASTM recommendation and those from Armour &
Drnevich’s method. Also, the preconsolidation pressures measured
from the CRSC test with strain rate determined by ANN Model were
close to those from the ILC test. This implies that the predicted strain
rates of ANN model are reasonable.
According to these results, ANN model can predict the proper strain
rate of the CRSC test with high reliability.
633


The ranges of strain rates obtained from ANN model were between
those from ASTM recommendation and those from Armour &
Drnevich’s method.

In general, the preconsolidation pressures ratio measured from the
experiment was closed to that predicted from the ANN Model. This
implies that the predicted strain rates of ANN model are more
reasonable than those of other methods.

These limited results show the possibility of utilizing the Artificial
neural network model for prediction of the proper strain rate of the
CRSC test.. REFERENCESArmour, DW, and Drnevich, VP (1986). "Improved Techniques for the
Constant Rate of Strain Consolidation Test," Consolidation of soils :
Testing and Evaluation. ASTM STP 892, Philadelphia, pp 170-183.
Bailey, D, and Thompson, D (1990). "How to develop neural network
application," AI Expert, 5(6), pp 38-47.
Crawford, CB (1988). "Importance of Rate of Strain in the Consolidation
Test," Geotechnical Testing Journal, Vol 11, No 1, pp 60-62.
Ellis, GW (1992). "Neural network modeling of the mechanical behavior
of sand," Proc. 9
th
Conf. ASCE, New York, pp 421-424.
Garson, GD (1991). "Interpreting neural-network connection weights," AI