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CBR Prediction of Pavement Materials in Unsoaked Condition Using LSSVM, LSTM-RNN, and ANN Approaches

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Abstract

The present research introduces the best architecture model for predicting the unsoaked California bearing ratio (CBRu) of soil by comparing the models based on the least square support vector machine (LSSVM), long- short-term memory (LSTM), and artificial neural network (ANN) approach. The two kernel functions, linear and polynomial, have been selected to create LSSVM models. The developed LSTM models have been optimized by the Adam algorithm. In the employed ANN models, the Levenberg–Marquardt (LM), BFGS Quasi-Newton (BFG), scaled conjugate gradient (SCG), gradient descent with momentum (GDM), gradient descent (GD), and gradient descent with adaptive learning (GDA) algorithms have been used in the backpropagation process. For this purpose, three databases, such as training, testing and validation, have been compiled from the published research. A laboratory database has been developed by performing laboratory experiments for soil samples collected from and around Kota, Rajasthan, used for cross-validation of the best architecture model. The statistical tools, such as root means square error (RMSE), mean absolute error (MAE), correlation coefficient (R), mean absolute percentage error (MAPE), variance accounted for (VAF), weighted mean absolute percentage error (WMAPE), Nash–Sutcliffe efficiency (NS), normalized mean bias error (NMBE), Legate and McCabe’s index (LMI), root mean square error to observation's standard deviation ratio (RSR), a20-index, index of agreement (IOA) and index of scatter (IOS) have been used to measure the performance of the models. The LSTM model MD 14 has achieved higher performance and accuracy (RMSE = 0.9127%, MAE = 0.8114%, R = 0.9863%, MAPE = 9.0772%, VAF = 97.26, WMAPE = 0.0669%, NS = 0.9708, NMBE = 0.0687%, LMI = 0.1926, RSR = 0.1708, a20-index = 93.88, IOA = 0.9037 and IOS = 0.0752) in testing phase. For the performance validation, model (MD) 14 has predicted the CBRu of the validation database. Also, model MD 14 has attained higher performance (RMSE = 1.2671%, MAE = 1.0161%, R = 0.9909) in the validation phase. By comparing the performances and performing score analysis, the LSTM model MD 14 has been recognized as the best architecture model for predicting the unsoaked CBR of soil. Moreover, model MD 14 has gained over 96% (R = 0.9689) accuracy in predicting the CBRu of laboratory-tested soil samples. The present research also represents that the nonlinear approach has achieved higher performance with a high overfitting ratio. In addition, the artificial neural network requires a large database to predict the unsoaked CBR with higher performance and the least overfitting ratio. The present research also rejects the null hypothesis of normality. Sensitivity analysis illustrates that gravel content and maximum dry density of soil affect the prediction of unsoaked CBR.

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Data Availability

The database used in this research will be provided upon request.

Abbreviations

\({C}_{C}\) :

Coefficient of curvature

\({C}_{U}\) :

Coefficient of uniformity

\({D}_{30}\) :

Grain size corresponding to 30% passing

\({D}_{50}\) :

Grain size corresponding to 50% passing

\({N}_{60}\) :

Corrected SPT-N

\({\gamma }_{d}\) :

Dry unit weight

AASHTO:

American Association of State Highways and Transportation Officials

ANFIS:

Adaptive network-based fuzzy inference system

ANN:

Artificial neural networks

ASTM:

American Standards for Testing and Materials

BFG_NN:

BFGS Quasi-Newton neural network

C + S:

Clay and sand

CBR:

California bearing ratio

CBRU :

Unsoaked CBR

CH:

Inorganic clays of high plasticity

CI:

Inorganic clays of medium plasticity

CL:

Inorganic clays of low plasticity

COD:

Coefficient of determination

CS:

Coarse sand content

CSA-LSSVM:

Coupled simulated annealing least-square support vector machine

DCPT:

Depth of penetration

DE:

Differential equation

DUW:

Dry unit weight

ENRG:

Elastic net regularization regression

ERT:

Extremely randomized trees

FD:

Frequency distribution

FS:

Fine Sand content

G:

Gravel content

GA:

Genetic algorithm

GA-ANN:

Genetic algorithm optimized artificial neural network

GD_NN:

Gradient descent neural network

GDA_NN:

Gradient descent adaptive neural network

GDM_NN:

Gradient descent with momentum neural network

GEP:

Gene expression programming

GP:

Genetic programming

GPR:

Gaussian process regression

GWO:

Grey wolves optimization

L1:

Position of 1st layer

LK-Star:

Lazy K star

LL:

Liquid limit

LLSVM-P:

Polynomial LSSVM

LM_NN:

Levenberg–Marquardt neural network

LMSR:

Least median of squares regression

M5MT:

M-5 model trees

MAE:

Mean absolute error

MARS-C:

Multivariate adaptive regression splines with piecewise cubic

MARS-L:

Multivariate adaptive regression splines with piecewise linear

MDD:

Maximum dry density

MLR:

Multilinear regression

MLR:

Multilinear regression analysis

MS:

Medium sand content

N:

Number of Datasets

NL:

Number of layers

O:

Organic content

OWC:

Optimum water content

OMC:

Open method of coordination

PI:

Plasticity Index

PL:

Plastic limit

PPV:

Peak particle velocity

R:

Correlation coefficient/performance

R2 :

Coefficient of determination

RBFNN:

Radial basis function neural network

RBN:

Radial basis networks

REPTs:

Reduced error pruning trees

RF:

Random forest

RMSE:

Root mean square error

RSS–ET:

Random subsurface-based extra tree

RSS–REPT:

Random subsurface-based reduced error pruning trees

SC:

Silt clay content

SCG_NN:

Scaled conjugate gradient neural network

SL:

Position of subsequent layers

SLRA:

Single linear regression analysis

T:

Tensile strength of geosynthetic

VAF:

Variance accounted for

WC:

Water content

WMAPE:

Weighted mean absolute percentage error

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  1. Department of Civil Engineering, Rajasthan Technical University, Kota, India

    Jitendra Khatti & Kamaldeep Singh Grover

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  1. Jitendra Khatti
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JK main author, conceptualization, literature review, manuscript preparation, application of AI models, methodological development, statistical analysis, detailing, and overall analysis. KSG Conceptualization, overall analysis, manuscript finalization, detailed review, and editing.

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Khatti, J., Grover, K.S. CBR Prediction of Pavement Materials in Unsoaked Condition Using LSSVM, LSTM-RNN, and ANN Approaches. Int. J. Pavement Res. Technol. (2023). https://doi.org/10.1007/s42947-022-00268-6

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