ANN prediction of some geotechnical properties of soil from their index ...

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Arab J Geosci DOI 10.1007/s12517-014-1304-3

ORIGINAL PAPER

ANN prediction of some geotechnical properties of soil from their index parameters Parichehr Tizpa & Reza Jamshidi Chenari & Mehran Karimpour Fard & Sandro Lemos Machado

Received: 30 September 2013 / Accepted: 22 January 2014 # Saudi Society for Geosciences 2014

Abstract This paper presents artificial neural network prediction models which relate compaction characteristics, permeability, and soil shear strength to soil index properties. In this study, a database including a total number of 580 data sets was compiled. The database contains the results of grain size distribution, Atterberg limits, compaction, permeability measured at different levels of compaction degree (90–100 %) and consolidated–drained triaxial compression tests. Comparison between the results of the developed models and experimental data indicates that predictions are within a confidence interval of 95 %. To evaluate the effect of each factor on these geotechnical parameters, sensitivity analysis was performed and discussed. According to the performed sensitivity analysis, Atterbeg limits and the soil fine content (silt+clay) are the most important variables in predicting the maximum dry density and optimum moisture content. Another aspect that is coherent from the sensitivity analysis is the considerable importance of the compaction degree in the prediction of the permeability coefficient. However, it can be seen that effective friction angle of shearing is highly dependent on the bulk density of soil. Keywords Artificial neural network . Compaction characteristics . Permeability . Soil shear strength . Sensitivity analysis P. Tizpa : R. Jamshidi Chenari : M. Karimpour Fard (*) Department of Civil Engineering, Faculty of Engineering, University of Guilan, P.O. Box 1841, Rasht, Iran e-mail: [email protected] R. Jamshidi Chenari e-mail: [email protected] S. Lemos Machado Department of Materials Science and Technology, Federal University of Bahia, 02 Aristides Novis St., Salvador 40210-630, BA, Brazil e-mail: [email protected]

Introduction Permeability and shear strength are two vital parameters needed for almost all geotechnical designs. These two parameters are governed by the degree of compaction. During the compaction process, the shear strength of soil increases and permeability decreases due to the reduction in the void ratio. Moreover, the shear strength of soils decreases with increasing water content. In some cases, shear strength and hydraulic conductivity requirements should be addressed simultaneously, which means they should be achieved at the peak point of compaction curve of soil. Thus, both the maximum dry density (MDD) and optimum moisture content (OMC) are essential data for earthwork projects. Since laboratory tests for determining permeability, maximum dry density, optimum moisture content, and shear strength are time-consuming, it is desirable to develop models to predict compacted soil characteristics based on the classification properties soils. Many attempts have been made to relate these key parameters to the physical properties of soils. The physical properties used generally include grain size distribution, specific gravity, and plasticity characteristics (liquid limit, plastic limit, shrinkage limit, and plasticity index). Rowan and Graham (1948), Davidson and Gardiner (1949), Turnball (1948), Jumikis (1946), Ring et al. (1962), Ramiah et al. (1970), Nagaraj (1994), etc., are among the researchers who tried to relate the compaction characteristics of soils to their index properties. The permeability of soils depends greatly on soil structure, void ratio, soil density, water content, degree of saturation, and the type of permeant which the soil is exposed to. Various relationships between the permeability and grain size distribution of the soil have been reported, such as those of Hazen (1911), Zunker (1930), Carman (1937), Burmister (1954), Michaels and Lin (1954), Olsen (1962), and Mitchell et al. (1965). Wang and Huang (1984), using a data bank including

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Arab J Geosci

Fig. 1 Data sources used to compile the database

57 synthetic soils, developed several regression equations to correlate the compaction characteristics and permeability with the soil’s index properties. Koltermann and Gorelick (1995), Boadu (2000), Chapuis (2004), Sinha and Wang (2008), and, more recently, Cote et al. (2011) developed different numerical and analytical models to estimate the hydraulic conductivity of soils based on their index parameters. In recent years, some efforts have been made to develop a correlation between the effective friction angle and the basic properties of soil. Kayadelen et al. (2009) used artificial neural network (ANN), genetic programming (GP), and adaptive neuro-fuzzy methods to predict the φ′ value of soils. Mousavi et al. (2011) used GP and orthogonal least squares algorithm to present a correlation between the internal friction angle and the physical properties of soils such as the fine and coarse content, density, and liquid limit. Sezer (2013) employed nonlinear multiple regression, neuro-fuzzy, and ANN methods to predict this soil parameter.

Materials and methods Database A database including a total number of 580 data sets was compiled, in which 155 data sets were used for modeling the

permeability, 320 data sets for modeling MDD and OMC, and 105 cases for modeling effective friction angle of shearing. Different types of soils were used in these tests; therefore, the results of this research could be valid for all types of soils. As presented in Fig. 1, the database is obtained from different sources, mainly from the geotechnical engineering laboratory of the Federal University of Bahia (UFBA), Brazil. Also, other cases from Wang and Huang (1984) and Mousavi et al (2011) were added to the former source. For each data set, the values of permeability, OMC, MDD, compaction degree, friction angle, and soil index properties (grain size curve, Atterbeg limits, and specific density) were available. Table 1 gives the descriptive statistics of the variables used for the compaction characteristics and permeability model developments. The variation ranges of the parameters used for effective friction angle model are summarized in Table 2. It is noteworthy that the gravel content (Gc) was a coarse aggregate having a particle size coarser than 4.75 mm, and the grain size of sand content (Sc) ranged from 4.75 to 0.075 mm. As well, particles smaller than 0.075 mm were named as fine content (Fc). In addition, a quantity called fineness modulus (FM) is also computed. The value of fineness modulus multiplied by 100 is equal to the sum of the percentages of particles coarser than 3/4 in., 3/8 in., no. 4, and no. 100 mm. Note that the friction angle values in the database were determined by consolidated–drained triaxial tests. Modeling method Artificial neural networks were employed to develop prediction models. To evaluate the importance of each factor on the prediction models, a set of sensitivity analyses have been performed. Artificial neural networks are information-processing systems whose architectures essentially mimic the biological system of the brain (Goh 1994). ANNs have been successfully applied to link independent variables to a series of dependent ones, mainly where it is diverse to establish numerical equations. The use of ANNs has increased during the last decades in various fields of geotechnical engineering, such as liquefaction (Ural and Saka 1998; Najjar and Ali 1998), foundation settlements (Sivakugan et al. 1998), reinforced soil (Ghiassian et al. 2006), and compaction characteristics of soils (Sinha and

Table 1 Descriptive statistics of the variables used for MDD, OMC, and permeability model Parameter

Gc (%)

Sc (%)

Fc (%)

FM

LL (%)

PL (%)

Gs

Cd (%)

MDD (kN/m3)

OMC (%)

Ka (cm/s)

Minimum Maximum Mean Standard deviation

0 67 7.39 10.15

0 100 40.05 21.13

0 100 52.31 22.83

0.01 4.22 1.71 1.17

0 495 77.58 104.48

0 47 24.60 10.47

2.42 3.02 2.70 0.06

90 100 95 4.04

12.43 27.35 17.31 1.97

5.81 37.13 17.44 5.67

2.50E−11 1.70E−03 3.49E−05 1.91E−04

a

Permeability

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Arab J Geosci Table 2 Descriptive statistics of the variables used for effective friction angle model Parameter

Cc (%)

Fc (%)

γ LL (kN/m3) (%)

Shearing rate φ (deg) (mm/min)

Minimum Maximum Mean Standard deviation

1 85 38.37 21.54

15 99 63.16 21.08

14.11 21.54 17.64 1.52

0.024 0.350 0.240 0.142

1 105 45.34 18.75

19 35.27 27.49 3.26

Wang 2008; Gunaydın 2009). In this study, a multilayer perceptron network has been utilized to present the prediction models. A multilayer perceptron (MLP) is a feed-forward artificial neural network model that maps sets of input data onto a set of appropriate outputs. MLP utilizes a supervised learning technique called back-propagation for training the network. In the application of MLP, data are categorized as input layer, output layer, and one or more hidden layers. The input patterns are fed to the network for feed-forward computations to calculate output patterns. The output patterns are compared with corresponding output patterns and the summation of the square of the errors is calculated. The errors are then back-propagated through the network using the gradient-descent rule to modify the weights and minimize the summed squared errors. Figure 2 illustrates the typical ANN structure and the relation between the input and output parameters. In this study, a MLP network consisting of three hidden layers with nine, ten, and one neurons for the first, second, and third hidden layers, respectively, has been used. The number of neurons in the hidden layer was determined by training several networks with different numbers of hidden neurons and comparing the predicted results with the desired output.

Fig. 2 Typical structure of ANN

Fig. 3 Comparison between the predicted values of MDD and the actual data

Since the manner in which the database is used in the training and testing sets has a significant effect on the results, the database was divided into several combinations of training and testing sets until a robust representation of the whole population was achieved. To select an optimal combination of training and testing sets, a statistical analysis considering the maximum, minimum, mean, and standard deviation was performed on the input and output parameters. The aim of the analysis was to ensure that the statistical properties of the data in each of the subsets were as close to each other as possible and therefore represented the same statistical population (Rezania et al. 2008). Sensitivity analysis concerns the mathematical model representation of a physical system and attempts to evaluate the

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Fig. 4 Comparison between the predicted values of OMC and the actual data

sensitivity of the output patterns to variations of input patterns. The main issues in designing methods for regression sensitivity analysis are the choice of perturbation scheme and the way to assess and measure any influence. An appropriate method for perturbation is to delete observations individually or in groups. This approach is known as case deletion and aims to assess the influence of an observation on the final results. In this research, the type of sensitivity analysis was ANNbased. At the first step, a MLP network was trained in the case of each parameter with all data. In the trained network, each neuron in a specific layer is connected to other neurons via weighted connections in which scalar weights show the strength of the connections. In the second step, one of the inputs is removed from the ANN model by setting its scalar weight to zero and then an output is achieved. In this way, all the weighted connections between this variable and other variables will be dropped from the model; therefore, the effect of the removed input on the prediction of outputs could be pictured.

Fig. 5 Comparison of the ANN results on MDD model by excluding each parameter

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Fig. 6 Comparison of the ANN results on OMC model by excluding each parameter

Xn

Evaluation method Different statistical approaches were used to evaluate the performance of the prediction model. These parameters were coefficient of determination (COD), root mean squared error (RMSE), and coefficient of residual mass (CRM). The following equations are the mathematical expressions of these parameters.

COD ¼ 1 − Xi¼1 n

ðM i −Pi Þ

i¼1

RMSE ¼

ð1Þ

M 1 −M

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Xn ðPi −M i Þ2 i¼1 n

 100

ð2Þ

Table 3 Summary of the ANN’s performance Outputs

Statistics

Total

Ex. w1a (Gc)

Ex. w2 (Sc)

Ex. w3 (Fc)

Ex. w4 (Gs)

Ex. w5 (LL)

Ex. w6 (PL)

MDD

COD RMSE CRM COD RMSE CRM

0.92 54.42 1.50E−04 0.92 199.11 4.92E−05

0.57 128.23 3.30E−02 0.84 236.89 1.40E−04

0.57 184.29 8.40E−02 0.83 245.06 6.80E−05

0.67 390.94 2.1E−01 0.83 246.76 1.30E−03

0.64 162.58 −1.40E−02 0.85 223.39 −8.70E−05

0.74 387.32 2.10E−01 0.61 373.11 4.50E−04

0.42 235.57 −8.70E−02 0.65 355.93 5.90E−04

OMC

Ex. excluding a

Scalar weights

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Fig. 7 Comparison between the predicted values of permeability coefficient and the actual data

Xn

ðPi Þ CRM ¼ 1 − Xni¼1 ðM i Þ i¼1

ð3Þ

where Mi and Pi are the measured and predicted values, respectively, M is the mean of the measured values, and n is the number of samples. The RMSE is the variance of the residual error and should be minimized when the outputs fit a set of data. In the case of a perfect fitting, the RMSE is zero. The lower the RMSE, the higher is the accuracy of the model predictions. The coefficient of residual mass, CRM, is an analysis of the difference between the measured and predicted values. The optimum value of CRM is zero. Positive values of CRM indicate underestimation and vice versa.

(PL). The only output was MDD. Hence, the input layer has six neurons and the output layer has one neuron. Among 320 measured data sets, 290 sets (90 %) have been used for training and 30 sets (10 %) have been used for testing the model. Figure 3 shows the predicted values of MDD versus the experimental data. As is clear from the graphs, the MLP model gives very reliable estimates of the maximum dry density. A similar ANN structure with the same input parameters (Gc, Sc, Fc, Gs, LL, PL) has been used to estimate OMC. Figure 4 shows a comparison between the results of the developed ANN model and the experimental data. The obtained values of COD and RMSE demonstrate the accuracy of the developed model. The results of the sensitivity analysis performed on the MDD prediction model is presented in Fig. 5. In each graph, one input variable is excluded (by setting its scalar weight to zero) and the ANN model is trained for the five remaining input parameters. As is obvious from the graphs, excluding each parameter causes some extra scatter in the prediction model for MDD. The results of the sensitivity analysis performed on the OMC prediction model are also presented in Fig. 6. The graphs illustrate that LL and PL are the most important variables in the prediction of OMC. Moreover, it can be seen easily that removing Fc leads to perturbation in the results. Table 3 also presents a summary of ANN performance. Based on the results, in the case of MDD, excluding Fc from ANN increases the RMSE to 390.9, indicating the significant role of this parameter on the ANN predictions. Also, a CRM of 0.21 shows an underestimation of the MDD. LL and PL are the other important parameters in the prediction of MDD. Moreover, it is clear from the results that excluding Gs and PL causes an overestimation of the ANN prediction. Considering the OMC results, Fc, LL, and PL are the most important variables in the ANN prediction. ANN prediction model for permeability

Results and discussions ANN prediction model for MDD and OMC Six input variables were used for the ANN model for MDD, including gravel content (Gc), sand content (Sc), fine content (Fc), specific density (Gs), liquid limit (LL), and plastic limit

Six input variables were used for the ANN model for permeability coefficient, including FM, LL, gravel content (Gc), sand content (Sc), fine content (Fc), and compaction degree (Cd). The only output was LogK. Thus, the input layer has six neurons and the output layer has one neuron. Among 155 measured data sets, 140 sets (90 %) have been used for training and 15 sets (10 %) have been used for testing the model. Figure 6 shows the

Table 4 Summary of the permeability model performance Output

Statistics

Total

Ex. w1 (Gc)

Ex. w2 (Sc)

Ex. w3 (Fc)

Ex. w4 (FM)

Ex. w5 (LL)

Ex. w6 (Cd)

LogK

COD RMSE CRM

0.99 17.69 1.27E−05

0.51 152.86 1.01E−01

0.54 125.42 4.90E−02

0.78 95.57 −2.80E−02

0.88 119.11 −1.35E−01

0.33 214.17 2.20E−01

0.48 431.38 5.73E−01

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Fig. 8 Comparison of the ANN results on permeability model by excluding each parameter

predicted values of LogK versus the experimental data. Figure 7 shows an almost perfect prediction of hydraulic conductivity based on the employed index parameters; however, in the testing cases, the predictions exhibit a higher scatter. Table 4 and Fig. 8 illustrate the results of the sensitivity analysis performed on the permeability prediction model. In accordance with Table 4, removing Cd increases the RMSE to 431.4, which indicates that the compaction degree is of great importance in predicting the permeability of soils. In this case, the obtained value for CRM shows an overestimation of permeability. As is clear from the results, Gc, Sc, and LL are the other important variables in the ANN prediction model. Another aspect that is obvious from the results is that excluding Fc and FM causes an underestimation of the ANN model. As mentioned above, the degree of compaction has the highest effect on the prediction of permeability coefficient. It is well known that the volume of voids decreases due to an increase in the degree of compaction, which causes the permeability of a soil to decrease. Boynton and Daniel (1985)

conducted hydraulic conductivity tests on compacted clays. They plotted the variation of permeability at different densities (Fig. 9). As could be seen, for the same soil, permeability could be changed almost in one order of magnitude. AhangarAsr et al. (2011) have presented the same results for the effects of compaction degree on the permeability of soils. The results of their parametric analysis show a decreasing trend for permeability by increasing the degree of compaction. In addition, Mesri and Olson (1971), by comparing the permeability of different type of clays, stated that the size and arrangement of particles have a significant effect on the permeability coefficient. According to their studies, decreasing the void ratio, which is a result of increasing the compaction degree, will cause the permeability of soils to decline. ANN prediction model for effective friction angle Five input variables were used for the ANN model for effective friction angle of shearing, including coarse content (Cc),

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Arab J Geosci Fig. 9 Variation of the permeability at different dry densities (Boynton and Daniel 1985)

fine content (Fc), liquid limit (LL), soil bulk density (γ), and shearing rate (Sr). The only output was φ′. Thus, the input layer has six neurons and the output layer has one neuron. Among 105 measured data sets, 95 sets (90 %) have been used for training and 10 sets (10 %) have been used for testing the model. Figure 10 shows the predicted values of φ′ versus the experimental data. Table 5 and Fig. 11 also present the results of the sensitivity analysis performed on the ANN model of effective friction angle. It can be concluded from the results that the soil bulk density has the highest influence on the prediction of the effective friction angle. Another aspect that is coherent from Table 5 Summary of the effective friction angle model performance Ex. w2 Ex. w3 Ex. w4 (Fc) (γ) (LL)

Ex. w5 (Sr)

0.97 0.27 0.06 0.01 0.18 51.63 517.71 723.03 3600.2 452.82 0.0018 −0.06 −0.08 4.61 0.01

0.67 340.93 0.1

Output Statistics Total φ Fig. 10 Comparison between the predicted values of effective friction angle and the actual data

COD RMSE CRM

Ex. w1 (Cc)

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Fig. 11 Comparison of the ANN results on friction angle model by excluding each parameter

the result is that excluding the soil bulk density increases the value of CRM significantly and leads to an underestimation of effective friction angle. Also, the sensitivity analysis conducted by Mousavi et al. (2011) indicates the importance of the bulk density on the friction angle of soils.

Summary and conclusion This paper presents a set of ANN models for predicting the compaction characteristics, permeability, and effective friction angle of shearing based on the soil index properties. Since laboratory tests to determine these key parameters are laborious and time-consuming, it is desirable to develop prediction models to estimate these parameters based on index parameters which are easy to measure. To do this, the databank of geotechnical laboratory of the Federal

University of Bahia (UFBA), Brazil was utilized; however some other experimental data cases from the literature were added to this data bank. The results of the prediction models have been compared with the experimental data. Comparison of the results demonstrates that the developed ANN models provide highly accurate predictions and that the existing models can be improved with increasing the database. A major strength of the ANN prediction models is their ability to improve as more data become available without repeating the development procedures from the beginning. Furthermore, a set of sensitivity analyses have been performed to illustrate the influence of each parameter on the ANN’s performance. To evaluate the performance of the prediction models, three statistical approaches have been utilized: coefficient of determination (COD), root mean squared error (RMSE), and coefficient of residual mass (CRM).

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