Estimating compaction parameters of marl soils using multi...

Journal of the Balkan Tribological Association Vol. 20, No 2, 170-198 (2014)

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Estimating compaction parameters of marl soils using multi-layer perceptron neural networks

A. MAJIDIa, G. LASHGARIPOURa,, Z. SHOAIEb, M. NORUZI NASHLAJIc, Y. FIROUZEIa

a Department of Geology, Faculty of Sciences, Ferdowsi University of Mashhad (FUM), Mashhad, Iran, Email: [email protected]. b Head of Soil Conservation and Watershed Management Research Institute (SCWMRI) Tehran, Iran. Email: [email protected]. c Department of Computer, Faculty of Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran. Email: [email protected]. ABSTRACT

The compaction parameters of fine-grained soils, maximum dry density

(MDD) and optimum moisture content (OMC) are fundamental data required for the design, construction and choosing construction materials. This paper presents two multi-layer perceptron (MLP) artificial neural network (ANN) models to estimate the MDD and OMC of marl soils. Marl soil is a fine-grained soil. The Levenberg-Marquadt learning algorithm was used to train the networks. Existing models estimate soil compaction parameters based on physical and soil index parameters. The present study considers the effects of chemical factors on the behavior and characteristics of fine-grained soils along with the common soil index parameters. The model used test results from 60 marl soil samples taken from marl formations in the Neogene basin in central Iran. The models were designed to use different input data sets and structures to determine which soil properties and ANN structures correlate well with the compaction parameters. Electrical conductivity (EC) of saturated soil was a new input parameter used in addition to the physical and soil index parameters that include the Atterberg limit, and the activity and content of the clay, silt and sand. The results show that inclusion of EC improved the accuracy of the models. It was found that the

For correspondence


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accuracy of the generalizations and estimations of the ANN models was further increased by clustering data before the data division stage. Keywords: Artificial neural network, Marl soil, Electrical conductivity of saturated soil, Soil compaction parameters, Fine-grained soil.

1. INTRODUCTION

Marl formations are widely distributed throughout Iran and the Middle East.

Marl soils are fine-grained and generally considered to be natural foundation and building materials. The compaction parameters of fine-grained soil are maximum dry density (MDD) and optimum moisture content (OMC). These are fundamental data required for design and construction, when choosing construction materials and for preparation of soil samples for different tests. The standard Proctor and modified Proctor tests are common methods for measuring these two parameters in a laboratory [4].

Measuring the compaction parameters of fine-gained soils in a laboratory is lengthy and requires a large amount of soil. This has prompted much research to develop methods to rapidly and accurately estimate soil compaction parameters indirectly using easily available parameters. A great deal of consideration has been given to correlating compaction parameters with physical and soil index properties. Previous studies have attempted to correlate soil index properties with compaction parameters using regression models [6, 8, 13-15, 21, 28].

Over the past two decades, new methods based on artificial intelligence, such as artificial neural networks (ANNs), have attracted attention. ANNs are information-processing systems with architectures that essentially mimic the biological system of the brain [10]. They have been useful in place of conventional mathematical models for analyzing complex relationships involving a multitude of variables. ANNs have been used to estimate and predict soil properties and behavior [36], pile capacity [23], earth retaining structures [12], slope stability [19], liquefaction potential [11] and the behavior of expansive soil [3, 25].

Researchers have also used ANN models to estimate soil compaction parameters [18, 21, 26, 27, 33]. The majority of these prediction models utilize physical and common soil index properties, such as liquid limit, plastic limit,


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plasticity index, mean grain size, effective grain size, soil activity and specific gravity. Few correlations have been developed to predict the compaction properties of fine-grained and clayey soils compacted using the modified Proctor rather than the standard Proctor test [8].

The present study applied ANN models to estimate the compaction parameters of marl soils at standard Proctor compaction energy with an emphasis on the effect of electrical conductivity (EC) of saturated soil as a chemical parameter on model accuracy. The difference between this study and previous studies lays in the usage of EC with other common soil parameters to estimate the compaction parameters of marl soils.

The data was collected from 60 marl soil samples taken from the Qom and Upper Red marl formations in the Neogene basin in central Iran. Fig.1 shows the basin of studied and the distribution of the Qom and Upper Red formations outcrops in the central basin of Iran. Laboratory tests were conducted according to ASTM standards. The standard Proctor test was used and soil classification was carried out according to the Unified Soil Classification System.

2. MATERIALS AND METHODS 2.1. DATA PROCESSING

The nature and characteristics of the mother rocks mean that marl soils are

fine-grained (mostly clay and silt) with some soluble salts, particularly carbonates, sulfates, and chlorides [9, 22, 29]. Chemical parameters like soluble salts influence soil compaction characterizations [2, 5, 7], consistency limits [37], shear strength [35], dispersion potential [1], and geotechnical properties [24].

This indicates that chemical parameters can be effective for estimation of marl soil compaction parameters. The compaction parameters of soils are influenced by grain size distribution and consistency [18]. Most previously published models used characteristics of soil that were either physical parameters or elated to soil water content (index parameters).


173

Fig. 1. The distribution of Upper red and Qom formation outcrops in central basin of Iran.

Test results from the 60 samples of marl soil were used to verify the accuracy of the models. EC was applied as an input parameter for the ANNs because it shows the total anions and cations soluble in soil and can be measured relatively quickly and easily [31, 30]. The model input variables chosen for the present study were liquid limit (LL), plasticity limit (PL), plasticity index (PI), clay content(C), silt content (M), sand content (S), activity (A) and EC. The target or output variables chosen were maximum dry density (MDD) and optimum moisture content (OMC).The statistical features of the soil parameters are

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175

Table 2. Input parameter groups for ANN models.

2.2. DATA DIVISION

For ANN modeling, data are routinely randomly divided into training, testing

and validation sets [18]. The network is trained using the first group of data. The training set is also used to adjust the connection weights. The validation set is used to check the performance of the network at various stages of learning; training is stopped early if the model attempts to over-fit the training data. Once training has been successful, the testing set is used to evaluate the performance of the model.Recent studies have shown that the way the data is divided can have a significant effect on the performance of ANN models [32].

ANNs perform best when they do not extrapolate beyond the extreme values of the data used for training and validation [18].Consequently, to develop the best ANN model given the available data, the training and validation sets should contain all representative patterns present in the data as a whole. If all patterns present in the data are represented in the training and validation sets, the toughest evaluation of generalization by the model will occur when all representative patterns (and not just a subset) are also contained in the validation data [32].

The most effective approach is to enter random but homogenized data into the neural network. The samples in the present study, based on the input and target

Input Parameters PL LL PI S M C A EC

Group % % % % % % mS/cm

Cat-1 * * * * * * *

Cat-2 * * * * * *

Cat-3 * * * * *

Cat-4 * * * * * * *

Cat-5 * * * * * *

Cat-6 * * * * *

Cat-7 * * * *

Cat-8 * * * *

Cat-9 * * * * * *

Cat-10 * * * *

Cat-11 * * * *


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variables, were primarily clustered using hierarchical and k-means methods and optimized by the discriminator method. Each group randomly then extracted its share of data from each cluster. This produced data sets that were both random and homogeneous.

Prior to the distribution of data into the three network input groups, the data was clustered into 2 to 6 clusters. A comparison of the results of the different clusters determined the best clustering method, the most suitable number of clusters for coherency of the data and the most accurate model for estimating soil compaction parameters. The effect of clustering methods on the accuracy and efficiency of the ANN was also determined. In the data distribution phase, about 75% of samples in all clusters were placed in the training group, 15% in testing group and 10% in the validation group.

By omitting the effect of range and scale and by considering the data used in the network to be dimensionless, the speed and accuracy of the training phase and output model increased. The variables must be scaled to be commensurate with the limits of the transfer function used in the output layer [21]. In the present study, data was scaled for the range (-1, 1) and the hyperbolic tangent sigmoid function was used as the transfer function. In order to do so, before applying the ANN to the data, the input and output data were normalized using the following equation: (1)

Where Xnor is the normalized value of the observed value, Xi is the real value

of the variable, and Xmin and Xmax are the minimum and maximum values of the input data sets, respectively. When the function of the network was complete, the model outputs were denormalized and returned to natural form. 2.3. DEVELOPMENT OF ANN MODELS 2.3.1. NETWORK STRUCTURE

ANNs have found acceptance in disciplines that deal with complex real world

problems [18]. ANN modeling is a computer methodology that simulates

min

max min

2( )1i

nor

x xx

x x


177

important feature of the human nervous system; the ability to solve problems by applying information gained from past experience to new problems or case scenarios. An ANN uses simple computational elements (artificial neurons) connected by variable weights. ANN modeling consists of training and testing steps. During training, the network uses inductive learning to learn from the set of examples called the training set. Test data cannot be used in the training step. The multilayer perceptron (MLP) structure is commonly used for prediction [17].

A network consists of layers of parallel processing elements with each layer being fully-connected to the preceding layer by interconnection strengths, or weights (W). A multilayer feed-forward network consists of an input layer, one or more hidden layers, and an output layer (Fig.3).Computations take place only in the hidden and output layers [16, 20].

Various combinations of network structure were examined to find the optimum ANN model. ANN (i, j, k) denotes a network structure with i, j and k neurons in the input, hidden and output layers, respectively. Fig. 3 illustrates a 3-layer neural network consisting of layers i, j and k, with the interconnection weights Wij and Wjk between the layers of neurons. The initially-estimated weights are progressively corrected during training as the predicted outputs are compared with known outputs; any errors are back propagated to determine the appropriate weight adjustments necessary to minimize the errors. Throughout ANN simulation, adaptive learning rates are used to increase the speed of training and solving local minima. For each epoch, if performance decreases toward the target, then the learning rate increases by the learning rate increment and if performance increases, the learning rate is adjusted by the learning rate decrement [16, 20].

Determining the best structure is difficult in ANN modeling. It consists of determining the optimum number of hidden layers and selecting the number of neurons in the hidden layer(s). There is no generally-accepted rule for determination of the best ANN topology [18, 20]. The number of input and output neurons is predetermined prior to network modeling. They are typically determined from the selected input variables and the desired target variable(s). The number of hidden layers and hidden neurons can be determined using trial-and-error. The number of hidden layers and its neurons is determined by training several networks with different numbers of hidden neurons and comparing the predicted results with the target [16, 18, 20].


178

Fig. 3. Typical 3-layer fully connected network.

Researchers have employed the feed-forward MLP with the Levenberg-Marquart training algorithm, which is an approximation of Newton’s method to adjust weights of an ANN model because it is more powerful than conventional gradient descent techniques [16, 20].This type of network was used in the present study. The tangent sigmoid function was used as the activation function.

To evaluate the impact of different structures on the accuracy and efficiency of the model, networks with one or two hidden layers, each with 3 to 12 neurons, were created. This was done to accommodate the number of input parameters and to avoid complication of the model. For each target (MDD and OMC), 100 ANNs with different structures were created. The number of input layer neurons in these networks equaled the number of input variables and the number of output layer neurons equaled the number of target variables. Each network for each input parameter set was based on one of the two data clustering methods with 2 to 6 clusters; this created 10 combinations or arrangements for training, validation and testing, for a total of 1000 runs. There were 11 groups of input parameters, thus, 11000 ANN models were created to predict each target parameter.

2.4. EVALUATION CRITERIA


179

The results obtained from each model were evaluated to quantitatively assess their predictive abilities. Different criteria that are primarily based on statistics exist by which to evaluate the accuracy and efficiency of and to compare models. The correlation coefficient for the real values and those estimated by the model is the most common comparison index. This index is a general criterion and cannot be solely considered proper for assessment of the function of the model for estimation. In this study, the correlation coefficient was combined with the mean square error (MSE), root mean square error (RMSE), coefficient of determination (R2), mean bias error (MBE), mean absolute relative error (MARE) and model efficiency coefficient (MEC). The relations for calculation of the indices are:

(2) (3)

(4) (5)

(6) (7)

Where n is the number of samples, Oi is the measured data, Pi is the estimated data, Ō is the mean of the measured data and P̅ is the mean of the estimated data. In the evaluation process, when the values for MARE, MBE, RMSE and MSE approach zero and R and R2 approach unity, the accuracy of the model increased. The more positive and closer to unity was the value for MEC, the better the efficiency of the model. Positive values for MBE indicated over-estimation and negative values indicated under-estimation of parameters by the model.

3. RESULTS AND DISCUSSION

To produce the best ANN to estimate compaction parameters MDD and OMC of marl soils, the effect of network structure, composition of the input parameters

2

1

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2

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1

1( )

n

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MBE O Pn

1

1 ni i

i i

O PMARE

n O

1

2 2

1 1

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( ) ( )

n

i ii

n n

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O O P P

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1

2

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O O


180

and generalized data by clustering (before feeding the network) were studied. The distinction between this study and past studies is the use of EC as a chemical parameter in addition to other physical and common soil index parameters to estimate MDD and OMC. Accurate predictions and the ability to generalize were achieved by appropriate normalization and by clustering data before the data division stage. Table 2 shows the 11 combinations of the 8 parameters selected to feed the networks. Concurrent evaluation of the effect of various combinations of input parameters and different network structures on the accuracy and efficiency of the ANN models made it possible to select the best combinations of the input parameters and network structure. A total of 11000 ANN models with different structures and combinations of input parameters were created to estimate each target parameter (MDD and OMC). The best model was specified for each input parameter set as that with the lowest MSE.

Tables 3 and 4 show the results for estimation of MDD using ANN models for each of the best networks, including the best combination of input parameters, network structure, clustering method and optimum number of clusters. Tables 5 and 6 show the results for estimation of OMC. MD-iH and MD-iK denote the best models to estimate MDD according to the ith input data set (Table 2) using the hierarchical and k-means methods, respectively.OM-iH and OM-iK denote the best models for estimation of OMC according to the ith input data set (Table 2) using the hierarchical and k-means methods, respectively.

For each best network, the evaluation and efficiency criteria for the training, validation and testing stages of the models were calculated. The performance statistics of the ANN models to estimate MDD are summarized in Tables 7 and 8 and to estimate OMC in Tables 9 and 10.The final best model was determined using the RMSE, R2 and MEC values for the testing and training stages. Figs. 4 and 5 depict the changes in R2 and RMSE, respectively, for optimum networks.

Tables 7 and 8 indicate that model MD-8K had the best values for RMSE, R2 and MEC to estimate MDD. The values for RMSE, R2 and MEC were 0.03, 0.80 and 0.80 for training and 0.03, .093 and 0.78 for the testing stage, respectively. MD-4K belongs to the eighth group of input variables (Cat-8) clustered using the k-means method. The network structure of this model contained two hidden layers; the numbers of neurons in the first layer were 9 and in the second layer were 4.


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Table 3. Results for best networks using hierarchical clustering to estimate MDD. Optimum Structural Network

Model Input Parameter No. of mid. Layers

No. of neurons Optimum clusters

Group Layer 1 Layer 2 (Hierarchical method)

MD-1H Cat-1 2 3 12 2

MD-2H Cat-2 2 4 9 2

MD-3H Cat-3 2 3 10 2

MD-4H Cat-4 2 7 6 4

MD-5H Cat-5 2 6 5 2

MD-6H Cat-6 2 11 10 2

MD-7H Cat-7 2 3 4 2

MD-8H Cat-8 2 3 4 2

MD-9H Cat-9 2 7 12 2

MD-10H Cat-10 2 5 10 3

MD-11H Cat-11 2 9 3 2

Table 4. Results for best networks using k-means clustering to estimate MDD. Optimum Structural Network



Group Layer1 Layer 2 (k-means method)

MD-1K Cat-1 2 3 6 3

MD-2K Cat-2 2 3 5 3

MD-3K Cat-3 2 6 11 6

MD-4K Cat-4 2 7 10 3

MD-5K Cat-5 2 7 3 3

MD-6K Cat-6 2 8 4 2

MD-7K Cat-7 1 8 0 3

MD-8K Cat-8 2 9 4 3

MD-9K Cat-9 2 7 4 6

MD-10K Cat-10 2 3 12 6

MD-11K Cat-11 1 12 0 2


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Table 5. Results for best networks using hierarchical clustering to estimate OMC Optimum Structural Network



Group Layer 1 Layer 2 (Hierarchical method)

OM-1H Cat-1 2 9 10 3

OM-2H Cat-2 2 12 5 4

OM-3H Cat-3 1 8 0 3

OM-4H Cat-4 2 10 12 2

OM-5H Cat-5 2 7 11 3

OM-6H Cat-6 2 8 4 2

OM-7H Cat-7 2 6 5 4

OM-8H Cat-8 1 7 0 2

OM-9H Cat-9 2 7 6 2

OM-10H Cat-10 2 5 10 3

OM-11H Cat-11 2 5 9 4

Table 6. Results for best networks using k-means clustering to estimate OMC Optimum Structural Network

Model Input Parameter No. of mid No. of neurons Optimum clusters

Group Layers Layer 1 Layer 2 (k-means method)

OM-1K Cat-1 2 12 10 3

OM-2K Cat-2 2 4 12 3

OM-3K Cat-3 2 6 4 3

OM-4K Cat-4 2 11 4 3

OM-5K Cat-5 2 6 10 2

OM-6K Cat-6 2 11 8 3

OM-7K Cat-7 2 7 10 3

OM-8K Cat-8 2 10 12 6

OM-9K Cat-9 2 9 12 3

OM-10K Cat-10 2 8 12 6

OM-11K Cat-11 2 5 7 3


183


184


185


186


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(a)

(b) Fig.4. Variation in (a) R2and (b) RMSE of ANN models to estimate OMC.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

R2

ANN Modle (OMC)

R2

Train Test

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

RMSE

ANN Modle (OMC)

RMSE

Train Test


188

(a)

(b) Fig.5. Variation in (a) R2and (b) RMSE of ANN model to estimate MDD.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

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1.0

R2

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R2

Train Test

0.00

0.01

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RMSE

Train Test


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Tables 9 and 10 shows that model OM-2H had the best values for RMSE, R2 and MEC to estimate OMC. The values for RMSE, R2 and MEC were 0.66, 0.82 and 0.82 for training and 0.50, 0.97 and 0.90 for testing, respectively. OM-2H belongs to the second group of input variables (Cat-2) that were clustered using the hierarchical method. The network structure for this model had two hidden layers; the numbers of neurons in the first layer were 12 and in the second layer were 5. The results in Tables 7 through 10 indicate that the best predictions (lowest RMSE and highest R2 and MEC) belonged to the variable groups containing the EC variable. Note that the results for most variable groups were at valid and acceptable levels (for example, MD-7H and OM-3H).

This result indicates that conventional soil parameters (Atterberg limits, plasticity index, graining and activity) were appropriate parameters for estimating compaction parameters of the fine-grained soils. When the evaluation criteria for variable groups included EC, however, the results were more accurate, especially for the prediction of MDD. The significant and sensitive role of EC in the prediction of compaction parameters (particularly MDD) of marl soil is evident. The use of EC with the commonly-used parameters resulted in higher accuracy for estimation of the compaction parameters of the marl soils.

The results also indicated that clustering performed before the data are divided, can have a significant effect on model performance (forming the input and output generalization data). In this study, the results indicate that the best estimations were for inputs in 3 to 4 clusters that were clustered before division of input parameters. The accuracy of the proposed models was verified by comparing the actual and estimated values for OMC and MDD for the training and testing data. The relative errors were calculated using Eq. (8). The comparisons are shown in Figs. 6 and 7. (8)

1

n

i ii

i

RO P

EO


190

Fig. 6. Actual MDD versus predicted MDDp obtained by ANN model (MD-8K).

1.5

1.6

1.7

1.8

1.9

2.0

2.1

1.5 1.6 1.7 1.8 1.9 2.0 2.1

Act

ual

val

ues

of

MD

D (

gr/c

m3)

Estimated values of MDD (gr/cm3)

Sample

-5%

5%

Line 1:1

1.58

1.62

1.66

1.70

1.74

1.78

1.82

1.86

1.90

S1 S3 S5 S7 S9 S11 S13 S15 S17 S19 S21 S23 S25 S27 S29 S31 S33 S35 S37 S39 S41 S43 S45 S47 S49

MD

D (

gr/c

m3)

Sample

Actual Estim.


191

Fig. 7. Actual OMC versus predicted OMCp obtained by ANN model (OM-2H).

The average error for MDD was about 1.5%; the maximum error was 4% and minimum error was 0.03%. The RSME for MDD was 0.03. The average error for OMC was about 2.8%. The maximum error was 8.5% and minimum error was 0.1%. The RSME for OMC was 0.6.

10

12

14

16

18

20

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24

10 12 14 16 18 20 22 24

Act

ual

val

ues

of

OM

C (

%)

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-33

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-35

S-3

6S

-37

S-3

8S

-39

S-4

0S

-41

OM

C (

%)

Sample

Estim. Actual


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4. CONCLUSION This paper presents ANN models that estimate the compaction parameters of

marl soils (fine-grained soils) based on the electrical conductivity of saturated soil and common soil parameters using the standard Proctor compaction test. A total of 60 marl soil samples were collected from the Neogene basin in central Iran. Their Atterberg limits (LL and PL), grain size distribution, EC and Proctor parameters were determined by laboratory testing.

The results showed that the most significant variables influencing OMC and MDD were the Atterberg limits, clay and silt fractions and EC. The EC is a new chemical input variable in the estimation of marl soil compaction parameters. The results of model evaluation criteria showed that utilization of EC increased the accuracy and performance of the ANN models for estimation of MDD and OMC.

The data set was clustered using the k-means and hierarchical methods and then divided randomly into training, testing and validation sets. It was found that the generalization ability and estimated accuracy of ANN models increased when the data was clustered. The network structures of the proposed ANN models for estimating OMC and MDD indicate the complexity of the relationships between the input parameters and OMC.

The proposed ANN models can be applied to standard Proctor compaction data sets for marl soils that the input data are within the variation ranges given in Table 1. These models can be used for assessment of the preliminary design phases and feasibility studies to obtain reliable information for site investigation projects and to estimate test results before they are conducted.

ACKNOWLEDGEMENT

This work was financed by the Soil Conservation and Watershed Management Research Institute (SCWMRI) of Iran. The authors wish to thank SCWMRI for their financial support of this study.


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