Estimation of Proper Strain Rate in the CRSC Test Using a Artificial Neural Networks

Estimation of Proper Strain Rate in the CRSC Test Using a Artificial Neural Networks

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

ABSTRACT

The 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

networks model for estimation of the strain rate in the CRSC test

KEY WORDS: Constant rate of strain consolidation (CRSC);

incremental loading consolidation (ILC); preconsolidation

pressure; strain rate; artificial neural networks (ANN)

INTRODUCTION

Recently, a number of construction projects for obtaining industrial

areas have been increased in many coastal areas or soft ground though

these areas have a weak condition The structure constructed on soft

ground are seriously damaged due to soft ground with a high water

content, low stress, and large strain undergoing large settlement

Accordingly, the properties of consolidation must be precisely

perceived to solve these problems

The ILC test has been used widely until now as most common method

for predicting the consolidation properties in softy clay However, the

period of testing is required the time more than a week to finish the ILT

test Also, It is difficult to determine the preconsolidation pressure due

to the curve of stress and strain is not appeared is to definitely

Several types of continuous consolidation test have been introduced in

recent years to overcome some of the problems associated with the ILT test Among the continuous tests, the CRSC test has been accepted widely as a standard method in foreign countries because of its many advantages

The CRSC test was first described by Hamilton and Crawford(1959) as

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

In this study, the nonlinear theory of Wissa et al (1971) was used the interpret the results of CRSC tests Wissa et al formulated a nonlinear theory based on assuming a constant coefficient of consolidation leading to a generalized, nonlinear equation for strain distribution through the specimen By assuming a constant ratio between incremental ε and increments of log σv, nonlinear theory equations were developed to compute consolidation properties for steady state an

Proceedings of The Twelfth (2002) International Offshore and Polar Engineering Conference

Kitakyushu, Japan, May 26–31, 2002

Copyright © 2002 by The International Society of Offshore and Polar Engineers

ISBN 1-880653-58-3 (Set); ISSN 1098-6189 (Set)

transient conditions If no transient conditions exist, average effective

stress and coefficient of consolidation are calculated as follows

3 / 1 2 2

ave = σ − σ ∆ u + σ ∆ u

σ (1)













−

∆

−

=

v b v v V

u t

H

C

σ

σ σ

1 log

2

log

1

2 2

(2)

where

H = current specimen height

2

1, v

v σ

σ = total stresses at two times of difference ∆ t

b

u = excess pore pressure measured at the base of the specimen

However, it is found that transient conditions that typically occur at the

start of loading and throughout higher strain rate tests in which large

excess pore pressures are generated Also, assumption of a constant

coefficient of consolidation is reasonable in the normally consolidated

stress range, it is almost not valid in the overconsolidated stress range

SELECTION OF STRAIN RATE

The CRSC tests are generally performed at much higher strain rates

than those typically encountered in the field These strain rates

determine the pore pressures that will be generated in the testing and

thus the applicability of the theory If a specimen is strained at too slow

a rate, little or no pore pressure will be generated and, the effect on the

determination of Coefficient of consolidation will be pronounced On

the other hand, if pore pressures become excessive, assumptions made

in deriving the theory will again be rendered invalid because the pore

pressure distribution will not be parabolic

In this study, the strain rates are determined from the ASTM

recommendation and Armour & Drnevich’s method The ASTM

recommendation is relies on empirical correlation between the liquid

limit of the soil and assumed parameters Also, Armour and

Drnevich(1986) proposed an empirical equation for calculating the

strain rate, as below





























−

−

=

max

1 log )

3

8

exp(

v

b o

w

o

H

k P LI

r

σ

γ (3)

in which LI is the liquidity index with soil saturated, P a is the

atmospheric pressure, k is the permeability at start of test, and o H ois

the initial thickness of specimen In this study, the permeability of the

specimen is estimated using empirical equations And the maximum

pore pressure ratio is used 30% that set by ASTM D4186

DESIGN ARTIFICIAL NEURAL NETWORK MODEL

Neural networks are computer models that mimic the knowledge

acquisition and organization skills of the human brain Since, the

characteristics of a neural network come from the activation function

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

min max

min

V V

V V A

−

−

= (4)

Training was performed iteratively until the average of sum squared error over all the training patterns was minimized Experiment were carried out using a number of combinations of input parameters to determine the neural network model that gave the smallest average of the sum square error There is currently no rule for determining the optimal number of neurons in the hidden layer other than by experiment In this study, the structure of neural network with one input layer – two hidden layer – one output layer is used ANN model was designed to build and operate a database for the physical properties of the soil and results of consolidation test, to learn the database, and to predict the properties of consolidation

Fig 1 Flow chart for programming of the artificial neural network

VERIFICATIONS OF MANN MODEL

In 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

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

Class Range of values Water content (%) 33.9 ~ 142.8

Liquid limit (%) 38.0 ~ 120.2

Plasticity index 16.6 ~ 74.2

Specific gravity 2.42 ~ 2.70

Initial void ratio 0.924 ~ 3.499

Dry unit eight (g/cm3) 0.542 ~ 1.367

60% particle size subject to a grain size

distribution curve (mm) 0.0046 ~ 0.075

Passing the # 200 (%) 60.0 ~ 99.8

Clay fraction < 2µ 0 ~ 45.0

Present effective vertical pressure (kg / cm2) 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

Iteration Number (N)

1E-005

0.0001

0.001

0.01

0.1

Fig 2 Variation of the learning error with Iteration Number

Factor

0 4 8 12 16

Wn LL PI LI Gs e o r d D60 #200 2 µ Po r

Fig 3 Relative importance of the input parameter on the pre-consolidation pressure ratio

In order to verify the reliance of the ANN model, the measure value, which have not been included in database, are also inferred to compare with the predicted value Properties of the soil used for verification of the ANN models are summarized in Table 2

Table 2 Properties of the soil used for verification of the MANN models

o

d

γ (g/cm3 ) 0.668 0.891 1.249 60

Passing the # 200 (%) 89.0 82.9 99.1 Clay fraction < 2µ (%) 26.0 32.0 16.0 0

p (kg / cm2) 0.28 1.46 0.19 Strain rates (%/min) 0.02 0.04 0.05 Fig 4 shows the results of the preconsolidation pressure ratio(P C(CRS) P C(ILC)) and compression index ratio(C C(CRS) C C(ILC)) 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

0 0.4 0.8 1.2 1.6 2

Measured Value

0

0.4

0.8

1.2

1.6

2

Preconsolidation Stress Ratio Compression Index Ratio

Fig 4 Comparison between the predicted and measured values

TEST PROGRAM

To investigate the applicability of MANN model, consolidation tests

were performed on undisturbed samples obtained in-situ by using both

ILC test equipment and CRSC test equipment The CRSC test was

performed with strain rates that determined by various estimate

methods The soil samples used in this study were obtained from

marine clayey soil deposit at the offshore area of Ha-dong in Korea

The physical properties of this clay are presented in Table 3

Table 3 Properties of the soil and strain rate used for the test

Class D Range of value

o

d

γ (g/cm3 ) 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 (kg / cm2) 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, taken with 76mm diameter piston sampler ILC test were loaded in steps using a load increment ratio of 1.0 which was maintained for 24 hours The CRSC tests were carried out after confirming full saturation using B value, and were performed with the strain rate selected as illustrated in Table 3

TEST RESULTS AND DISCUSSIONS

In Fig 5 a comparison is made between the measured values from the test and the predicted values using ANN model for the sample D There appeared to be an almost nonlinear relationship between preconsolidation pressure ratio and strain rate, where the results show a similar tendency With the result, the preconsolidation pressure ratio increases as the increase of strain rate and their trends are similar to those of the previous research In the case of sample D, the predicted values of ANN model are slightly different from the field data In particular, these differences are increase at the high strain rate range The reason is that ANN model has not a lot of database on the high strain rate To eliminate this effect should be collected database

Strain Rate (%/min)

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Predicted Value Measured Value

PR = 34.36 * r 2 + 1.87 * r + 1.00

R 2 = 0.98

Fig 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

0.02 0.04 0.06 0.08 0.1

Strain Rate(%/min)

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

ASTM Armour ANN Model

Fig 6 Preconsolidation pressure ratio with strain rate that

determined by various estimation methods

CONCLUSIONS

A rational approach has been developed to estimate the strain rate for

use in the CRSC test The following conclusions have been derived

from this research

The main factors on the preconsolidation pressure ratio are liquid index

and strain rate from various parametric studies

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

REFERENCES

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Constant Rate of Strain Consolidation Test," Consolidation of soils :

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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

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