Prediction of shear strength of soft soil using machine learning methods

Catena 166 (2018) 181–191

Contents lists available at ScienceDirect

Catena journal homepage: www.elsevier.com/locate/catena

Prediction of shear strength of soft soil using machine learning methods a

b

b

c

Binh Thai Pham , Le Hoang Son , Tuan-Anh Hoang , Duc-Manh Nguyen , Dieu Tien Bui

d,e,⁎

T

a

Geotechnical Engineering and Artificial Intelligence research group (GEOAI), University of Transport Technology, Ha Noi, Viet Nam VNU University of Science, Vietnam National University, Viet Nam Department of Geotechnical Engineering, University of Transport and Communication, Ha Noi, Viet Nam d Geographic Information Science Research Group, Ton Duc Thang University, Ho Chi Minh City, Viet Nam e Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Viet Nam b c

A R T I C LE I N FO

A B S T R A C T

Keywords: Artificial neural networks Machine learning Particle swarm optimization Strength of soft soils

Shear strength of the soil is an important engineering parameter used in the design and audit of geo-technical structures. In this research, we aim to investigate and compare the performance of four machine learning methods, Particle Swarm Optimization - Adaptive Network based Fuzzy Inference System (PANFIS), Genetic Algorithm - Adaptive Network based Fuzzy Inference System (GANFIS), Support Vector Regression (SVR), and Artificial Neural Networks (ANN), for predicting the strength of soft soils. For this purpose, case studies of 188 plastic clay soil samples collected from two major projects, Nhat Tan and Cua Dai bridges in Viet Nam have been used for generating training and testing datasets for constructing and validating the models. Validation and comparison of the models have been carried out using RMSE, and R. The results show that the PANFIS has the highest prediction capability (RMSE = 0.038 and R = 0.601), followed by the GANFIS (RMSE = 0.04 and R = 0.569), SVR (RMSE = 0.044 and R = 0.549), and ANN (RMSE = 0.059 and R = 0.49). It can be concluded that out of four models the PANFIS indicates as a promising technique for prediction of the strength of soft soils.

1. Introduction In geotechnical engineering, the shear strength of the soil is an important engineering parameter which is certainly used in the design and audit of many geo-environmental and geo-technical structures i.e. road foundations and pavements, earth dams, and retaining walls (Vanapalli and Fredlund, 2000). It is determined by two important parameters to determine the shear strength, internal friction angle and unit cohesion (Das and Sobhan, 2013), and affected by several factors namely plastic index (PI), liquid limit (LL), moisture content (W), clay content (CC), etc. (Das and Sobhan, 2013; Kaya, 2009). It increases together with the approximate volume of grouted zone for treated samples soil with cement grout in the study about effects of the permeation cement grout with fly ash on the sandy soil skeleton (Ali and Yousuf, 2016; Vanapalli and Fredlund, 2000). Many studies have been carried out for the prediction of the shear strength of soft soils. Motaghedi and Eslami (2014) proposed an analytical approach for C, ϕϕ prediction using all quantities, qc, u2, and fs considering bearing capacity mechanism of failure at cone tip and direct shear failure along the penetrometer sleeve. McGann et al. (2015) used a multiple linear regression to develop a Christchurch-specific empirical correlation for predicting soil shear wave velocities (Vs) from

⁎

cone penetration test (CPT) data. Azari et al. (2014) studied the effects of shear strength variation in the disturbed zone on the time-dependent behavior of soft soil deposits improved with vertical drains and preloading. Griffiths et al. (2016) used equivalent linear and nonlinear 1D site response analyses for the well-known Treasure Island site to demonstrate challenges associated with accurately modeling large shear strains, and subsequent surface response, at soft soil sites. Oliveira et al. (2017) investigated constitutive models to simulate the creep behavior of a soft soil in its natural state or chemically stabilized state. It has been inferred from those studies that a well-established mathematical model should be constructed in order to achieve high accuracy of prediction. In recent decades, machine learning or artificial intelligent methods have been applied widely for generating such the prediction models of material properties (Shahin et al., 2009; Pham et al., 2017; Pourghasemi and Rahmati, 2018; Shirzadi et al., 2017). Samui (2008) applied Support Vector Regression (SVR) for predicting the friction capacity of driven piles in clay soils. Behavior prediction of shallow foundations was also carried out using the Artificial Neural Network (ANN) in several studies including bearing capacity (Kuo et al., 2009; Padmini et al., 2008). Chou et al. (2016) used data mining including linear regression, classification and regression tree (CART) analysis, a

Corresponding author at: Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Viet Nam. E-mail address: [email protected] (D. Tien Bui).

https://doi.org/10.1016/j.catena.2018.04.004 Received 2 February 2018; Received in revised form 9 March 2018; Accepted 3 April 2018 0341-8162/ © 2018 Elsevier B.V. All rights reserved.

Catena 166 (2018) 181–191

B.T. Pham et al.

2.2.1. Shear strength “Shear strength (τ) of a soil mass is the internal resistance per unit area that the soil mass can offer to resist failure and sliding along any plane inside it” (Das and Sobhan, 2013). It is an important factor in analyzing the soil stability problems including slope stability, lateral pressure on earth-retaining structures, and bearing capacity. The failure of a soil mass is not due to either shear stress or maximum normal alone and because of a critical combination of shearing stress and normal stress (Das and Sobhan, 2013). Therefore, the functional relationship between shear stress and normal stress on a failure plane of a soil mass can be presented as follows:

generalized linear (GENLIN) model, chi-squared automatic interaction detection (CHAID), ANN, and SVR to identify factors influencing shear strength and to predict the peak friction angle of FRS. In prediction of shear strength of soil, there are several studies. Das et al. (2011) studied the potential of the SVM and ANN for prediction of the residual strength of soil. Kanungo et al. (2014) compared the ANN and CART techniques for predicting the shear strength parameters. Kiran et al. (2016) applied Probabilistic Neural Network (PNN) to predict the shear strength parameters of soil, viz., cohesion “c” and internal friction angle “φ” from water content (w), Plasticity Index (PI), Dry Density (DD), Gravel % (GP), Sand % (SP), Silt % (STP), and Clay % (CP) of soil. Prediction of residual strength of clay based on a new prediction model namely functional network (FN) has been investigated in Khan et al. (2016). In general, the common conclusion from the aforementioned works is that machine learning methods are efficient for prediction of shear strength of soft soils (Moavenian et al., 2016). The recent development of machine learning and optimization have resulted in some new promising soft computing methods i.e. Particle Swarm Optimization - Adaptive Network based Fuzzy Inference System (PANFIS), Genetic Algorithm - Adaptive Network based Fuzzy Inference System (GANFIS). PANFIS and GANFIS are state-of-the art methods that were formed by integrating meta-heuristic optimization algorithms and neural fuzzy models. They have proven as the powerful tools in predicting various environmental problems such as flood (Bui et al., 2016a), forest fire (Bui et al., 2017), displacement of hydropower dam (Bui et al., 2016b), and landslide (Chen et al., 2017). On the other hand, SVR and ANN are popular and efficient methods used in the shear strength modeling. However, investigation and comparison of these methods with popular machine learning methods i.e. Support Vector Regression (SVR) and Artificial Neural Networks (ANN) for the prediction of the shear strength of soft soils have not been carried out. In this study, we expand the body of knowledge thought investigating and comparing the prediction performance of PANFIS, GANFIS, SVR, and ANN for the prediction of shear strength of soft soil. The comparison of such the machine learning methods is significant for determination of an effective prediction model that can be used in practical scenarios of shear strength of soft soils. The rest of the paper is organized as follows. Section 2 presents the study sites and dataset description. Section 3 gives the background of the models including PANFIS, GANFIS, SVR, and ANN. Sections 4 and 5 demonstrate the results and discussion. Lastly, Section 5 draws conclusions and suggests further studies. It is noted that MatlabR2014b and Weka 3.8.1 were used for dataset generation and modeling.

τ = f (σ ) = σ tan φ + c,

(1)

where σ (kg/cm ) is the normal stress on the failure plane, φ is the angle of internal friction, and c (kg/cm3) is the cohesion (Das and Sobhan, 2013). In the laboratory, the parameters of shear strength (c, φ) can be determined using different experiments namely direct shear test, triaxial test, and torsional ring shear test (Das and Sobhan, 2013; Whitlow, 1990). In general, the determination of these parameters for calculating the shear strength of a soil mass is relatively complicated and costly. In this study, suppose σ = 1kg/cm2, the shear strength was calculated using the parameters (c, φ) determined by direct shear test from 188 plastic clayed soil samples as follows: 3

τ = tan φ + c, σ = 1kg / cm2 .

(2)

Data of shear strength of 188 plastic clayed soil samples is shown in Fig. 2. It shows that τ values differ from 0.104 to 0.301 (kg/cm3), the mean value is 0.197 (kg/cm3), and the standard deviation value is 0.047 (kg/cm3). 2.2.2. Moisture content “Moisture content (ω) is also referred to as water content and is defined as the ratio of the weight of water to the weight of solids in a given volume of soil” (Das and Sobhan, 2013; Whitlow, 1990). Moisture content affects the shear strength of soil as it reduces the cohesive forces between soil solids, and even causes the saturation of soils. As the moisture content increases the shear strength of soils reduces (Sharma and Bora, 2003). Thus, moisture content was taken into account as an affecting factor for predicting of the shear strength of soils in this study. Moisture content is determined in laboratory using an oven drying method or field test using alcohol burning method. Moisture content can be calculated using following equation (Das and Sobhan, 2013; Whitlow, 1990):

2. Study site and data

ω (%) = 2.1. Description of the study site

mω g Wω × 100 = × 100, Ws ms g

(3)

where Wω is the weight of water of soil sample, Ws is the weight of solids of soil sample, mω is the mass of water of soil sample, ms is the mass of the solids of soil sample, and g is the gravity acceleration (g = 9.81 m/s2). In this study, moisture content test was carried out in the laboratory, and the moisture content values of 188 samples are shown in Fig. 3a. It shows that the moisture content values vary from 24.19 to 141.83 (%), the mean value is 56.1 (%), and the standard deviation value is 19.1 (%).

In this research, plastic clay soil samples from two bridge construction projects, the Nhat Tan Bridge (Ha Noi City) and the Cua Dai Bridge (Quang Nam City) in Vietnam were used as a case study. The Nhat Tan Bridge is located in about Latitude 20°50′30″N and Longitude 106°41′37″E, whereas the Cua Dai Bridge is located in Latitude 15°53′25″E and Longitude 108°20′42″E (Red points on the map in Fig. 1). The main beam system of the Nhat Tan Bridge was designed and constructed using cable-stayed structure with five diamond towers and six spans. The whole length of the Cua Dai Bridge is 18.3 km, and the bridge part on the river is 1.481 km.

2.2.3. Clay content Clays are classified as the soil solids smaller than 0.002 mm in size. In several cases, the soil solids between 0.002 and 0.005 mm in size are also considered as clays (Das and Sobhan, 2013). Clay content (μ) was considered as an affecting factor to the shear strength of soils as it develops the plasticity of soils, and as the clay content increases the shear strength of soils reduces when soils are mixed with a limited amount of water. Clay content can be determined in the laboratory using grain size distribution analyzing test through following equation (Das and Sobhan, 2013):

2.2. Data A total of 188 samples from the two bridge projects were collected and used for generating the datasets for modeling. In this prediction problem, the shear strength is the output variable whereas the input variables are moisture content, clay content, liquid limit, plastic limit, plastic index, and consistency index. 182

Catena 166 (2018) 181–191

B.T. Pham et al.

Fig. 1. Location of sample collection.

μ (%) =

M0.005 × 100, Msum

test using Atterberg tools (Das and Sobhan, 2013). In this study, Atterberg test was carried out in the laboratory to determine the LL, and the LL of 188 samples are shown in Fig. 3c. It shows that the LL values vary from 25.17 to 147.08 (%), the mean value is 59.9 (%), and the standard deviation value is 20.5 (%).

(4)

where M0.005 is the mass of soil solids passing the 0.005 mm sieve in size and Msum is the total mass of the soil sample. In this study, grain size distribution analyzing test was carried out in the laboratory to determine, and the clay content of 188 samples are shown in Fig. 3b. It shows that the clay content values differ from 11 to 87 (%), the mean value is 49.8 (%), and the standard deviation value is 17.2 (%).

2.2.5. Plastic limit Plastic Limit (PL) is an Atterberg limit defined as the moisture content at the point of transition from semisolid to plastic state (Das and Sobhan, 2013). Plastic limit is related with the shear strength of soils as it increases the shear strength decreases (Sharma and Bora, 2003). It can be determined using the laboratory test using Atterberg tools (Das and Sobhan, 2013). This limit can be calculated using following equation:

2.2.4. Liquid limit Liquid Limit (LL), which is known as one of the Atterberg limits, is defined as the moisture content at the point of transition from plastic to liquid state (Das and Sobhan, 2013). Liquid limit is related with the shear strength of soils as it increases the shear strength decreases (Sharma and Bora, 2003). This limit can be determined using the laboratory test using Atterberg tools (Das and Sobhan, 2013). It can be calculated using following equation:

LL (%) =

Wliquid Ws

× 100,

PL (%) =

Wplastic Ws

× 100,

(6)

where Wplastic is the weight of water of soil sample at the point of transition from semisolid to plastic state determined from the laboratory test using Atterberg tools (Das and Sobhan, 2013). In this study, Atterberg test was carried out in the laboratory to determine the PL, and the PL of 188 samples are shown in Fig. 3d. It shows that the PL values

(5)

where Wliquid is the weight of water of soil sample at the point of transition from plastic to liquid state determined from the laboratory

Fig. 2. Shear strength of the soil samples. 183

Catena 166 (2018) 181–191

B.T. Pham et al.

Fig. 3. Geotechnical properties of the soil samples: (a) moisture content, (b) clay content, (c) liquid limit, and (d) plastic limit.

dataset was used to test the models.

range from 13.31 to 99.33 (%), the mean value is 35.45 (%), and the standard deviation value is 13 (%).

3. Background of the method used 2.3. Data preparation for modeling

3.1. Adaptive neural fuzzy inference system

In order to generate the datasets for modeling, the strength of soil data is considered as dependent variable (Y) whereas other factors namely factors moisture content, clay content, liquid limit, plastic limit are considered as independent variables X1, X2, X3, and X4, respectively. Data presentation is shown in the form of Table 1. Data of the variables were divided into two parts such as training dataset (70%) and validating dataset (30%). Different dividing strategies of data were carried out to get the best fit for each model and the statistical values of data used for each model are shown in Table 2. Training dataset was then used to learn models whereas validating

Adaptive neuro-fuzzy inference system (ANFIS) is a neuro-fuzzy system that takes advantages of an ANN and a fuzzy system to construct a powerful and successful prediction model in many fields. ANFIS structure consists of 5 layers as follows (Fig. 4): Layer 1: consists of input for the next layers. In this study, input layer consists of 276 thirteen-dimensional samples. Layer 2: This is an adaptive step. Membership value of each controlling factor is calculated based on membership functions Cji. Gaussian function was used as membership function as shown in (Eq. 7). For each μC11(x1), there are two antecedent parameters to be tuned ci and δi

Table 1 Data presentation. No.

X1

X2

X3

X4

Y

1 2 3 4 5 6 7 8 … … … 186 187 188

54.5 23.5 42.0 41.5 15.0 11.5 17.5 32.0 … … … 55.0 20.5 20.5

86.05 140.51 55.38 94.56 131.34 125.57 147.08 97.22 … … … 65.97 77.32 109.70

45.45 97.58 35.69 60.34 84.23 76.40 99.33 58.80 … … … 29.87 41.05 61.43

80.29 134.39 51.61 87.67 121.34 125.42 141.83 86.98 … … … 62.63 71.36 99.22

0.16 0.17 0.18 0.16 0.14 0.11 0.14 0.16 … … … 0.14 0.14 0.14

μC11 (x) = exp ⎛− ⎝ ⎜

(ci − x ) 2 ⎞ . 2δi 2 ⎠ ⎟

(7)

Layer 3: Preliminary weights were calculated in this layer by using

wi = μCi1 (x1) ∗μCi2 (x2)…∗μCim (xm).

(8)

Layer 4:

wi =

wi . sum (wi )

(9)

Layer 5:

fi = wi (a0 + 184

∑ (ai xi).

(10)

Catena 166 (2018) 181–191

B.T. Pham et al.

Table 2 Data generation and analysis. No.

1 2 3 4

Values

Minimum Maximum Mean Standard deviation

Training dataset (70%)

Testing dataset (30%)

PANFIS

GANFIS

SVR

ANN

PANFIS

GANFIS

SVR

ANN

0.104 0.301 0.199 0.048

0.104 0.301 0.195 0.048

0.104 0.301 0.196 0.045

0.104 0.293 0.201 0.044

0.104 0.283 0.190 0.044

0.104 0.294 0.2 0.046

0.104 0.293 0.199 0.053

0.104 0.301 0.187 0.053

Fig. 4. Basic structure of ANFIS.

Fig. 5. Methodology chart of the study.

Rule k: IF x1 is Ck1 AND x2 is Ck2….AND xm is Ckm THEN fk

Output value is generated as summation of fi and goes through defuzzification process to return final value. ANFIS uses the fuzzy rules in the following forms:

= a 0k +

m

∑i =1

a ik x i

where xi is controlling factors such as Clay content, Plastic limit, and Liquid limit, Ck1 is the linguistic label, μCji(x) is membership value that 185

Catena 166 (2018) 181–191

B.T. Pham et al.

3.3. Genetic algorithm Genetic Algorithm (GA) is an optimization algorithm and search engine based on the principles of genetic and natural selection (Johari et al., 2011). GA starts with the creation of a group of solutions (population of individuals) - each solution is represented by a chromosome (Chromosome). Individuals in the population are used to create new other individuals. This is done with the expectation that the new population outperforms the old one. Individuals selected to create new individuals - offspring - are selected based on their level of adaptation the higher adaptation the individuals are, the more likely they are used to reproduce. This process is repeated until the conditions set are satisfied. Natural genetic processes used in this algorithm are: selection, crossover, and mutation (Johari et al., 2011).

Fig. 6. RMSE analysis of the PANFIS and GANFIS.

defines how much factor (x) belong to Cji, and ai is parameter of linear function to measure y.

3.4. Support vector regression Support Vector Regression (SVR) uses the same principles as SVR for classification except a new type of loss function. Considering a regression problem with a given training data set, expressed in a vector space, where each material is a point. This method finds the best flat that can divide the points in the space into two distinct classes, corresponding to class + and class − (binary classification). The quality of this hyperplane is determined by the distance (called boundary) of the nearest data point of each layer to this plane. Therefore, the larger the boundary indicates the better the decision plane and the more accurate the classification. The goal of the SVR method is to find the maximum boundary distance (Basak et al., 2007). In this study, we determine the values for SVR parameters through the trial-error process.

3.2. Particle swarm optimization Particle Swarm Optimization (PSO) is based on the idea of swarm intelligence to find optimal solutions in a given search space (Poli et al., 2007). PSO is initialized by a random group of individuals and then optimized by updating generations. In each generation, each individual is updated by two best positions. The first value is the best position an individual has reached so far, called Pbest. The other optimal solution that this individual pursues is the overall optimal solution of Gbest, which is the best position in the entire search of the entire population from the past to the present. In the other words, each individual of the population updates their position according to their best position and swarm's best position (Zhou et al., 2011). In this research, Root Mean Square Error (RMSE) is used as the objective function. The lower the RMSE indicates the more accuracy the model. The PSO algorithm will evaluate the objective function to determine if the criteria are met or not.

3.5. Artificial Neural Networks Artificial Neural Networks (ANN) is a popular machine learning techniques which is based on biologically the process of information of the human brain. It gives the decision by detecting and analyzing the relationships and patterns in data itself (Behrang et al., 2010). In this study, multi-layered perceptron neural network was selected as a regression method for prediction of strength of soft soils. Using the sigmoid function, the neurons compute the weights of the inputs using the activation function:

n

RMSE = Sqrt ∑ ((pri − yi )2 / n),

(11)

i=1

where pri is the predicted value from the model, yi is the measure of the shear strength of the soil, n is the number of input data. If the criteria at position xi are not met, the next position will be generated with another velocity of a particle. The formulas are as follow:

vi k + 1 = ωvi + ac1 r1 (pbesti − x i ) + ac2 r2 (gbesti − x i ),

(12)

x i k + 1 = x i + vi k + 1

(13)

yj = f j (x ) =

1 , 1 + e−x

(14)

where x = (x1, x2, …, xk) are inputs (landslide influencing factors) and yj are the outputs (landslide or non-landslide variables).

3.6. Quality assessment The accuracy of a model is assessed by Root Mean Square Error (RMSE) and R (correlation coefficient). These three indicators are popular in model validation. The formulas are as follow:

where Xik is the position of individual i at generation k, Vik is the velocity of individual i at generation k, Xik+1 is the position of individual i at generation k + 1, Vik+1 is the velocity of individual i at generation k + 1, Pbest is best location of individual i in the swarm, and Gbest is the best location of the all individuals in the swarm. If the criteria are met or the model reaches the iteration, the algorithm stops.

n

RMSE = Sqrt ∑ ((pri − yi )2 / n),

(15)

i=1

Table 3 Validation of the PANFIS with different values of initial weight. Validation criteria

R RMSE

Initial weight 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.59 0.0365

0.591 0.0364

0.554 0.0374

0.601 0.034

0.593 0.0361

0.538 0.0392

0.588 0.0363

0.598 0.0342

0.533 0.0359

0.533 0.0359

186

Catena 166 (2018) 181–191

B.T. Pham et al.

Table 4 Validation of the GANFIS with different values of Gamma. Validation criteria

Gamma

R RMSE

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.538 0.037

0.572 0.0352

0.533 0.0359

0.5777 0.035

0.582 0.0354

0.45 0.038

0.59 0.035

0.248 0.194

0.513 0.0366

0.543 0.0356

Table 5 Validation of the SVR with different values of Gamma. Validation criteria

Gamma

R RMSE

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.549 0.044

0.5341 0.0445

0.5333 0.0444

0.519 0.0449

0.4858 0.0461

0.4719 0.0467

0.4356 0.048

0.3905 0.0495

0.3457 0.051

0.329 0.0517

Table 6 Validation of the ANN with different numbers of hidden neurons. Validation criteria

Number of hidden neurons

R RMSE

1

2

3

4

5

6

7

8

9

10

0.3226 0.0545

0.36 0.0534

0.1594 0.0614

0.4754 0.0564

0.3992 0.0519

0.4935 0.0472

0.4681 0.05

0.4473 0.0648

0.4385 0.0675

0.36 0.0645

Fig. 7. RMSE analysis of the models using the training dataset: (a) PANFIS, (b) GANFIS, (c) SVR, and (d) ANN. n

Using training dataset, the four models, PANFIS, GANFIS, SVR, and ANN were trained and constructed for predicting of strength of soils. For the PANFIS, an initial FIS model was first generated with initial parameters, in which, a FIS structure was created based on a number of membership functions. Thereafter, the PSO is then used to search the most suitable antecedent parameters and consequent parameters for training the ANFIS. Fitness function (RMSE) was used evaluate the performance of the model for 500 iterations (Fig. 6). In learning the PSO, initial parameter such as inertia weight was set as “0.4” to give the best RMSE (Table 3). Finally, the PANFIS model was constructed as the stopping criteria or the RMSE is optimized. In term of

∑ (pri − pr )(yi − y ) R=

i=1 n

n

∑ (pri − pr )2

∑ (yi − y )

i=1

i=1

, (16)

where yi and y are respectively the measure and mean values of soil shear strength, pri and pr are output values from the model. 4. Results and analysis Methodological flow chart of this research is shown in Fig. 5. 187

Catena 166 (2018) 181–191

B.T. Pham et al.

Fig. 8. RMSE analysis of the models using the testing dataset: (a) PANFIS, (b) GANFIS, (c) SVR, and (d) ANN.

In term of the R analysis, the results of the training dataset (Fig. 9) indicate that the R values of four models vary from 0.637 to 0.817 indicating that all four models has a goodness of fit with the data used; however, the RANFIS (R = 0.817) has the highest goodness of fit, followed by the GANFIS (R = 0.654), the SVR (R = 0.64), and the ANN (R = 0.637), respectively. For the testing dataset (Fig. 10), out of four models the PANFIS (R = 0.601), GANFIS (R = 0.569), and SVR (R = 0.549) have acceptable capability for predicting the strength of soft soils, and the ANN (R = 0.49) has a bit poor capability in this study.

GANFIS, the process is similar to the PANFIS; however, the GA was used to find the most suitable antecedent parameters and consequent parameters for training the ANFIS instead of the PSO. In learning the GA, initial parameters namely crossover percentage, mutation percentage, Gama, mutation rate were selected as “0.4”, “0.7” (Table 4), “0.7”, and “0.5”, respectively. Fitness function (RMSE) in the GA was used for 500 iterations (Fig. 6). The stopping criteria or the RMSE is applied to construct the final GANFIS. For the SVR, kernel function of RBF is used to train the model especially learning parameters such as gamma, nu selected as “0.1” (Table 5), and “0.5” (Thomas et al., 2017), respectively. Regarding the ANN, the artificial network is constructed with 4 input neurons, 6 hidden neurons, and 1 output neuron (Table 6). A trial-and-error test is applied to determine the values of initial parameters of the models. Validation was carried out to test the performance of the models for prediction of strength of soils using different criteria such as RMSE and R. Both training and validating datasets were used in this task. While training dataset was used to test the goodness of fit of the models with data used, validating dataset was used to validate the predictive capability of the models. Validation and comparison of the models have been done using RMSE and R criteria, and the results are shown in Figs. 7, 8, 9, and 10. According to the validation results using RMSE criteria (Figs. 7 and 8), it can be observed that the RMSE values of the models varies from 0.027 to 0.0359 for the training dataset which are smaller than standard deviation of the training dataset used for the corresponding models (Table 2) indicating that all models have good performance; however, the PANFIS has the highest value of RMSE compared with other models (GANFIS, SVR, and ANN) indicating that the PANFIS has the best goodness of fit with the data used compared with other models. Similarly, RMSE values of PANFIS, GANFIS, SVR, and ANN are 0.038, 0.04, 0.044, and 0.047, respectively which are smaller than standard deviation of the testing dataset used for the corresponding models. Those results indicate that these four models perform well for prediction of strength of soft soils in this study but the PANFIS outperforms the other models (GANFIS, SVR, and ANN).

5. Discussion Determination of shear strength of soft soil is important task for audit and design of geotechnical structures and constructions. On the other hand, the experiment of shear strength is time-consuming and needs costly laboratory equipment (Vanapalli et al., 1996). Thus, prediction of shear strength using advanced machine learning techniques is effective solution for quickly determination and low cost experiment. Only few studies have been done to predict the properties of soft soil using machine learning techniques (Chou et al., 2016; Samui, 2008). Moreover, the prediction of shear strength of soft soil using these techniques is still limited and required more advanced techniques for better predictive capability. In this study, four advanced machine learning methods PANFIS, GANFIS, SVR, and ANN were used and applied for better prediction of the shear strength of soft soil. Based on the analysis of validation results of the models, it can be observed that out of four models the PANFIS, GANFIS, and SVR has acceptable capability for the prediction of the strength of soft soils while the ANN has a slightly poor performance in this study. However, the PANFIS has the highest performance, followed by the GANFIS, the SVR, and the ANN, respectively. It can be seen the reasonability of the obtained results is that the PANFIS and GANFIS used PSO and GA optimization techniques which can help in reducing the RMSE of prediction; however, the PSO is more effective than the GA. In term of the comparison results of the SVR and ANN, the 188

Catena 166 (2018) 181–191

B.T. Pham et al.

Fig. 9. Correlation results analysis of the models using the training dataset: (a) PANFIS, (b) GANFIS, (c) SVR, and (d) ANN.

models used. In this study, these four models indicated acceptable capability of prediction; however, their capability might be improved by providing more number of data so that the models might be more regressive and by applying over-sampling or under-sampling methods (He et al., 2008) to deal with imbalanced data sets. In addition, the use of different combination of inputs might give the different prediction outcomes of the models which should be taken into account for further studies. In fact, soil is very complicated material which is not easy to predict their properties. Even so, determination of their properties in laboratory is sometimes not very much accurate due to many affecting factors (namely experimental conditions, equipment, experience of testers, etc.). In this study, the advanced machine learning models predicted the shear strength of soft soil with average error rates (4.2%), which are lower than standard deviation, are acceptable for geotechnical problems. Thus, these machine learning techniques might also be used to predict other properties of soft soil.

optimization used to solve the constrained quadratic programming function in the SVR is more optimal and global than the one in the ANN (Samui, 2008). Moreover, the SVR is better than the ANN in generalization capability as it has ability to deal with overtraining problems. In addition, the ANN is controlled by many parameters (number of hidden layers, learning rate, number of training epochs, number of hidden nodes, momentum term, weight initialization techniques, and transfer functions) which is difficult to be optimized simultaneously during learning model (Samui, 2008). This result is in agreement with another study carried out by Das et al. (2011) who stated that the SVM model is better than the ANN models in prediction of residual strength of soft soil. Although the ANN has the lowest predictive capability in prediction of shear strength of soil in this study, its potential has been proven by Kanungo et al. (2014) who stated that the ANN is a promising method for prediction of soil shear strength parameters. Even though machine learning techniques such as PANFIS, GANFIS, SVR, and ANN are advanced methods in prediction problems, their performance depends significantly on the quality of data used (Mair et al., 2000). In geotechnical problems, the use of variables determined from various experiments on various samples of the same soils can cause the bias of outcomes which can affect the performance of the

6. Conclusion This 189

research

investigated

and

compared

the

prediction

Catena 166 (2018) 181–191

B.T. Pham et al.

Fig. 10. Correlation results analysis of the models using the testing dataset: (a) PANFIS, (b) GANFIS, (c) SVR, and (d) ANN.

researches should consider newer algorithms for optimizing the ANFIS model such as the fuzzy clustering (Son et al., 2011, 2012a, 2012b, 2013; Son, 2014, 2015; Wijayanto et al., 2016), and newer machine learning algorithms i.e. Bagging framework (Pham et al., 2018a), ensembles (Chen et al., 2018), and advanced decision trees (Khosravi et al., 2018; Pham et al., 2018b). Despite the limitation, the results of this study is helpful for geotechnical engineer to predict the strength of soft soils for carrying out the audit of geotechnical structures and constructions in practice as the input variables such as CC, W, LL, and PL are available. It will also help to reduce the cost of construction due to reduction of the cost of laboratorial experiments.

performance of the four machine learning methods PANFIS, GANFIS, SVR, and ANN for predicting the strength of soft soils. The plastic clay soil data were provided from the two projects, the Nhat Tan and the Cua Dai bridges in Viet Nam. PANFIS and GANFIS are relative new fuzzy inference systems that have rarely explored for predicting the strength of soft soil, whereas SVR and ANN are popular and efficient machine learning in soil strength modeling. The result shows that the prediction quality of the strength of soft soils is strongly influenced by the method used. Among the four models, PANFIS and GANFIS have the highest prediction performance; therefore we conclude that PANFIS and GANFIS are valid tools for predicting the strength of soft soils. The main advantage of PANFIS and GANFIS is that the two models were constructed and then optimized by two meta-heuristic optimization algorithms, PSO and GA, autonomously. Therefore, these may guarantee that the parameters of the inference rules for predicting the strength of soft soil of the two models are optimized. Among the two models, PANFIS and GANFIS, the PANFIS performed better. This is because PSO has a strong global search ability with a quick convergence (Zhou et al., 2011). As a result, PSO searched and found the optimized parameters better than that of GA in the GANFIS model. The limitation of this research is that only two meta-heuristic optimization algorithms, PSO and GA were investigated. Therefore, future

Acknowledgements The authors are greatly indebted to Prof. Dao Van Dong, Rector and the GEOAI group, University of Transport Technology, Vietnam for your ultimate supports of this research. References Ali, H.A., Yousuf, Y.M., 2016. Improvement of shear strength of sandy soil by cement

190

Catena 166 (2018) 181–191

B.T. Pham et al. grout with fly ash. J. Eng. 22, 16–34. Azari, B., Fatahi, B., Khabbaz, H., 2014. Assessment of the elastic-viscoplastic behavior of soft soils improved with vertical drains capturing reduced shear strength of a disturbed zone. Int. J. Geomech. 16, B4014001. Basak, D., Pal, S., Patranabis, D.C., 2007. Support vector regression. Neural Inf. Process. Lett. Rev. 11, 203–224. Behrang, M., Assareh, E., Ghanbarzadeh, A., Noghrehabadi, A., 2010. The potential of different artificial neural network (ANN) techniques in daily global solar radiation modeling based on meteorological data. Sol. Energy 84, 1468–1480. Bui, D.T., et al., 2016a. Hybrid artificial intelligence approach based on neural fuzzy inference model and metaheuristic optimization for flood susceptibility modeling in a high-frequency tropical cyclone area using GIS. J. Hydrol. 540, 317–330. Bui, K.-T.T., Bui, D.T., Zou, J., Van Doan, C., Revhaug, I., 2016b. A novel hybrid artificial intelligent approach based on neural fuzzy inference model and particle swarm optimization for horizontal displacement modeling of hydropower dam. Neural Comput. & Applic. 1–12. http://dx.doi.org/10.1007/s00521-016-2666-0. Bui, D.T., et al., 2017. A hybrid artificial intelligence approach using GIS-based neuralfuzzy inference system and particle swarm optimization for forest fire susceptibility modeling at a tropical area. Agric. For. Meteorol. 233, 32–44. Chen, W., Panahi, M., Pourghasemi, H.R., 2017. Performance evaluation of GIS-based new ensemble data mining techniques of adaptive neuro-fuzzy inference system (ANFIS) with genetic algorithm (GA), differential evolution (DE), and particle swarm optimization (PSO) for landslide spatial modelling. Catena 157, 310–324. Chen, W., Xie, X., Peng, J., Shahabi, H., Hong, H., Bui, D.T., ... Zhu, A.X., 2018. GIS-based landslide susceptibility evaluation using a novel hybrid integration approach of bivariate statistical based random forest method. Catena 164, 135–149. Chou, J.-S., Yang, K.-H., Lin, J.-Y., 2016. Peak shear strength of discrete fiber-reinforced soils computed by machine learning and metaensemble methods. J. Comput. Civ. Eng. 30, 04016036. Das, B.M., Sobhan, K., 2013. Principles of Geotechnical Engineering. Cengage Learning. Das, S., Samui, P., Khan, S., Sivakugan, N., 2011. Machine learning techniques applied to prediction of residual strength of clay. Open Geosci. 3, 449–461. Griffiths, S.C., Cox, B.R., Rathje, E.M., 2016. Challenges associated with site response analyses for soft soils subjected to high-intensity input ground motions. Soil Dyn. Earthq. Eng. 85, 1–10. He, H., Bai, Y., Garcia, E.A., Li, S., 2008. ADASYN: Adaptive synthetic sampling approach for imbalanced learning, Neural Networks, 2008. In: IJCNN 2008. (IEEE World Congress on Computational Intelligence). IEEE International Joint Conference on. IEEE, pp. 1322–1328. Johari, A., Javadi, A., Habibagahi, G., 2011. Modelling the mechanical behaviour of unsaturated soils using a genetic algorithm-based neural network. Comput. Geotech. 38, 2–13. Kanungo, D., Sharma, S., Pain, A., 2014. Artificial Neural Network (ANN) and Regression Tree (CART) applications for the indirect estimation of unsaturated soil shear strength parameters. Front. Earth Sci. 8, 439–456. Kaya, A., 2009. Residual and fully softened strength evaluation of soils using artificial neural networks. Geotech. Geol. Eng. 27, 281–288. Khan, S., Suman, S., Pavani, M., Das, S., 2016. Prediction of the residual strength of clay using functional networks. Geosci. Front. 7, 67–74. Khosravi, K., Pham, B.T., Chapi, K., Shirzadi, A., Shahabi, H., Revhaug, I., Prakash, I., Bui, D.T., 2018. A comparative assessment of decision trees algorithms for flash flood susceptibility modeling at Haraz watershed, northern Iran. Sci. Total Environ. 627, 744–755. Kiran, S., Lal, B., Tripathy, S., 2016. Shear strength prediction of soil based on probabilistic neural network. Indian J. Sci. Technol. 9. Kuo, Y., Jaksa, M., Lyamin, A., Kaggwa, W., 2009. ANN-based model for predicting the bearing capacity of strip footing on multi-layered cohesive soil. Comput. Geotech. 36, 503–516. Mair, C., et al., 2000. An investigation of machine learning based prediction systems. J. Syst. Softw. 53, 23–29. McGann, C.R., Bradley, B.A., Taylor, M.L., Wotherspoon, L.M., Cubrinovski, M., 2015. Development of an empirical correlation for predicting shear wave velocity of

Christchurch soils from cone penetration test data. Soil Dyn. Earthq. Eng. 75, 66–75. Moavenian, M., Nazem, M., Carter, J., Randolph, M., 2016. Numerical analysis of penetrometers free-falling into soil with shear strength increasing linearly with depth. Comput. Geotech. 72, 57–66. Motaghedi, H., Eslami, A., 2014. Analytical approach for determination of soil shear strength parameters from CPT and CPTu data. Arab. J. Sci. Eng. 39, 4363–4376. Oliveira, P.J.V., Correia, A.A., Lemos, L.J., 2017. Numerical prediction of the creep behaviour of an unstabilised and a chemically stabilised soft soil. Comput. Geotech. 87, 20–31. Padmini, D., Ilamparuthi, K., Sudheer, K., 2008. Ultimate bearing capacity prediction of shallow foundations on cohesionless soils using neurofuzzy models. Comput. Geotech. 35, 33–46. Pham, B.T., Bui, D.T., Prakash, I., Dholakia, M.B., 2017. Hybrid integration of Multilayer Perceptron Neural Networks and machine learning ensembles for landslide susceptibility assessment at Himalayan area (India) using GIS. Catena 149, 52–63. Pham, B.T., Bui, D.T., Prakash, I., 2018a. Bagging based support vector machines for spatial prediction of landslides (Environ. Earth Sci.). 77 (4), 146. Pham, B.T., Prakash, I., Bui, D.T., 2018b. Spatial prediction of landslides using a hybrid machine learning approach based on random subspace and classification and regression trees. Geomorphology 303, 256–270. Poli, R., Kennedy, J., Blackwell, T., 2007. Particle swarm optimization. Swarm Intell. 1, 33–57. Pourghasemi, H.R., Rahmati, O., 2018. Prediction of the landslide susceptibility: which algorithm, which precision? Catena 162, 177–192. Samui, P., 2008. Prediction of friction capacity of driven piles in clay using the support vector machine. Can. Geotech. J. 45, 288–295. Shahin, M.A., Jaksa, M.B., Maier, H.R., 2009. Recent advances and future challenges for artificial neural systems in geotechnical engineering applications. Adv. Artif. Neural Syst. 2009, 5. Sharma, B., Bora, P.K., 2003. Plastic limit, liquid limit and undrained shear strength of soil—reappraisal. J. Geotech. Geoenviron. 129, 774–777. Shirzadi, A., Shahabi, H., Chapi, K., Bui, D.T., Pham, B.T., Shahedi, K., Ahmad, B.B., 2017. A comparative study between popular statistical and machine learning methods for simulating volume of landslides. Catena 157, 213–226. Son, L.H., 2014. Enhancing clustering quality of geo-demographic analysis using context fuzzy clustering type-2 and particle swarm optimization. Appl. Soft Comput. 22, 566–584. Son, L.H., 2015. A novel kernel fuzzy clustering algorithm for geo-demographic analysis. Inf. Sci. 317 (C), 202–223. Son, L.H., et al., 2011. Developing JSG framework and applications in COMGIS project. Int. J. Comput. Inf. Syst. Ind. Manag. Appl. 3, 108–118. Son, L.H., Cuong, B.C., Lanzi, P.L., Thong, N.T., 2012a. A novel intuitionistic fuzzy clustering method for geo-demographic analysis. Expert Syst. Appl. 39 (10), 9848–9859. Son, L.H., Lanzi, P.L., Cuong, B.C., Hung, H.A., 2012b. Data mining in GIS: a novel context-based fuzzy geographically weighted clustering algorithm. Int. J. Mach. Learn. Comput. 2 (3), 235. Son, L.H., Cuong, B.C., Long, H.V., 2013. Spatial interaction–modification model and applications to geo-demographic analysis. Knowl.-Based Syst. 49, 152–170. Thomas, S., Pillai, G., Pal, K., 2017. Prediction of peak ground acceleration using ϵ-SVR, νSVR and Ls-SVR algorithm. Geomatics Nat. Hazards Risk 8, 177–193. Vanapalli, S., Fredlund, D., 2000. Comparison of different procedures to predict unsaturated soil shear strength. Adv. Unsaturated Geotech. 195–209. Vanapalli, S., Fredlund, D., Pufahl, D., Clifton, A., 1996. Model for the prediction of shear strength with respect to soil suction. Can. Geotech. J. 33, 379–392. Whitlow, R., 1990. Basic Soil Mechanics. Wijayanto, A.W., Purwarianti, A., Son, L.H., 2016. Fuzzy geographically weighted clustering using artificial bee colony: an efficient geo-demographic analysis algorithm and applications to the analysis of crime behavior in population. Appl. Intell. 44 (2), 377–398. Zhou, D., et al., 2011. Randomization in particle swarm optimization for global search ability. Expert Syst. Appl. 38, 15356–15364.

191