Applied Computational Intelligence and Soft Computing

Applied Computational Intelligence and Soft Computing / 2021 / Article

Research Article | Open Access

Volume 2021 |Article ID 5992628 | https://doi.org/10.1155/2021/5992628

Ahmed M. Ebid, Light I. Nwobia, Kennedy C. Onyelowe, Frank I. Aneke, "Predicting Nanobinder-Improved Unsaturated Soil Consistency Limits Using Genetic Programming and Artificial Neural Networks", Applied Computational Intelligence and Soft Computing, vol. 2021, Article ID 5992628, 13 pages, 2021. https://doi.org/10.1155/2021/5992628

Predicting Nanobinder-Improved Unsaturated Soil Consistency Limits Using Genetic Programming and Artificial Neural Networks

Academic Editor: Cheng-Jian Lin
Received14 Jun 2021
Accepted16 Jul 2021
Published27 Jul 2021

Abstract

Unsaturated soils used as compacted subgrade, backfill, or foundation materials react unfavorably under hydraulically bound environments due to swell and shrink cycles in response to seasonal changes. To overcome these undesirable conditions, additive stabilization processes are used to improve the volume change phenomenon in soils. However, the use of supplementary binders made from solid waste base powder materials has become necessary to deal with the hazards of greenhouse due to ordinary cement use. Meanwhile, several studies are being carried out to design infrastructures even with the limitations of insufficient or lack of equipment needed for efficient design performance. Intelligent prediction techniques have been used to overcome this shortcoming as the primary purpose of this research work. Therefore, in this work, genetic programming (GP) and artificial neural network (ANN) have been used to predict the consistency limits, i.e., liquid limits, plastic limit, and plasticity index of unsaturated soil treated with a composite binder known as hybrid cement (HC) made from blending nanostructured quarry fines (NQF) and hydrated-lime-activated nanostructured rice husk ash (HANRHA). The database needed for the prediction operation was generated from several experiments corresponding with treatment dosages of HANRHA between 0 and 12% at a rate of 0.1%. The results of the stabilization exercise showed substantial development on the soil properties examined, while the prediction exercise showed that ANN outclassed GP in terms of performance evaluation, which was conducted using sum of squared error (SSE) and coefficient of determination (R2) indices. Generally, nanostructuring of the component binder material has contributed to the success achieved in both soil improvement and efficiency of the models predicted.

1. Introduction

1.1. Soil Improvement and Stabilization Techniques and Purposes

Overall, a number of benefits ranging from economy and environmental friendliness have triggered the physical, chemical, mechanical, biological, or combined practice of changing a natural soil to meet an engineering purpose. Soil improvement encompasses enhancing its bearing capabilities, tensile strength, and general performance for geotechnical and structural applications [1]. Soil stabilization therefore leads to improved soil strength, durability stiffness, and reduction in soil plasticity and swelling/shrinkage tendencies. Various techniques have been used for soil stabilization based on studies involving various materials such as sodium hydroxide additives, fly ash geopolymeric binders, ashes, and cementitious binders so as to ascertain their suitability as soil stabilizers. Generally, soil stabilization can be categorized into mechanical stabilization and chemical stabilization. Mechanical stabilization induces changes in soil gradation by blending it with other types of soils of various specifications and properties. This leads to a compacted soil mass, which can play more severe or critical roles when used as a foundation or structural material. Conversely, chemical stabilization involves the adjustment of soil properties by the inclusion of chemically active materials for improved performance. The technology and techniques of soil stabilization are dynamic as additional stabilization products are being explored [2]. The products, mostly called nontraditional stabilizers, have been categorized into five groups by Scholen [3], namely: electrolytes, enzymes, mineral pitches, clay fillers, and acrylic polymers [2].

Attempts have been made to determine the relative efficiencies of calcium chloride solution, sodium hydroxide solution, and lime precipitation in stabilizing the expansive soil by comparing the physicochemical and index properties, oedometer swell potentials, and unconfined compressive strength of treated soil samples [4]. In the aforementioned study, the relative efficiencies of hydrated lime and precipitated lime in stabilizing the expansive soil were explored. It was observed from laboratory works that treating the expansive soils with calcium chloride and sodium hydroxide solutions solely enhanced only the short-term reactions, whereas the combined treatment of the expansive soil with calcium chloride and sodium hydroxide solutions gave rise to lime precipitation, which could trigger both short-term lime-changing and long-term soil-lime pozzolanic reactions. Soil stabilization could also be performed using microbially induced calcium carbonate precipitation (MICP). In fact, most authors argue that relative to the conventional cementation methods, MICP provides an alternative and environmentally friendly method for soil improvement [57]. Appreciable improvement in shear strength, ductility, and failure strain has been achieved with fiber addition in the MICP-treated sand [8, 9]. In addition, it was observed in ref. [10] that the cohesion and angle of internal friction of fiber-reinforced sand blended at varying fiber ratios improved significantly. Conclusively, the inclusion of fibers improved the ductility of the soil by hampering the loss of post-peak strength [11].

Likewise, in their study, Zhao et al. [12] gave a clear insight into the mechanical and physical properties of the natural, fiber, and soil stabilized with chemical additives in heavy-haul railway embankment. They conducted a series of triaxial compression tests on the stabilized samples under various preparation conditions, including water content, compaction degree, confining pressure, fiber content, fiber length, stabilizer content, and curing time. The results of their investigation further confirmed that the shear strength of natural soils assumes a clear improvement after fiber addition and chemical additive stabilization. They, however, discovered brittle behaviour of the stabilized material. The mixing of additives, which will release aluminum, calcium, silicon, and other important soil nutrients, helps in closing spaces or voids that exist in the soil matrix [13]. Onyelowe et al. [13] added that there is a corresponding displacement reaction based on the metallic order in the electrochemical series, which follows the formation of important nutrients. Hence, there is a calcination reaction involved in the soil stabilization process, whereby calcium displaces the hydrogen ions of the dipole-adsorbed moisture and displaces the sodium ion needed for the swelling potential of clayey soils. This general process results in the pozzolanic reaction, which ultimately produces calcium alumina-silica hydrate. These processes and responses are responsible for soil stabilization.

1.2. Use of Nanostructured Materials for Improving the Consistency Limits and Other Important Parameters of Unsaturated Soils

Soil stabilization using nanostructured materials not only positively influences the shear or compressive strength properties of unsaturated treated soils alone but also enhances the strength with which soil materials are held together or the resistance of soil to deformation and rupture, known as soil consistency [13]. The water contents at which the soil changes from one state to the other are known as consistency limits, which are categorized into liquid limit, shrinkage limit, and plastic limit. The field of nanotechnology is one promising area that has offered unquantifiable soil-improvement options for geotechnical and structural engineers. Nanomaterials constitute usually a small proportion of the overall soil matrix and have a size in the range of 1 to 100 nm [1, 14]. In their experimental studies performed using laboratory samples with varying quantities of silt soils and nanoclay, Bahari et al. [15] remarked that the use of nanoclay in silt stabilization will enhance the consistency limit and other critical soil parameters. The optimum moisture content, maximum dry unit weight, and plasticity index have been reported to be affected by the addition of lime or cement [16]. It is equally reported that clayey admixtures with liquid limit in the range of 40% to 60% could be obtained with the addition of 4% to 12% cement [17]. Also, the study further stated that clayey admixtures with liquid limits over 60% could only attain this with appreciable uneconomical amounts of cement. Asma Muhmed and Wanatowski [18] evaluated the effects of hydrated lime on the strength and microstructure of lime-treated clays. In order to confirm such effects, they carried out a series of laboratory tests to determine the Atterberg limits, compaction tests, unconfined compressive strength tests, and scanning electron microscopy using the kaolin clay mixed with 5% hydrated lime. They stated that the inclusion of lime aids in the lowering of the plasticity of kaolin. The estimation of clay content is critical for large-scale soil heterogeneity modelling and prediction [16, 19]. The combined influence of all these parameters as they affect each other or a combination of one another still needs to be explored.

1.3. Evolutionary Computation Techniques for Predicting Consistency Limit: Genetic Programming and Artificial Neural Networks

Recently, significant use of evolutionary computation, a family of population-based trial-and-error problem solvers with a metaheuristic or stochastic optimization character for global optimization inspired by biological evolution, a field of artificial intelligence and soft computing, has emerged [20]. Because of their excellent ability to produce highly optimized solutions in many problem sets, evolutionary computation is linked to biology systems that are in turn linked to the theory of dynamical systems, as they are used to predict the behaviour of the system in the future space. Artificial intelligence has many advantages over the existing methods for use in civil engineering, development, and practice [21].

Studies have shown that a combination of AI algorithms can boost the prediction efficiency [22]. Overall, the fields of statistics, numerics, and optimization are critical aspects that facilitate understanding the data, describing the properties of a dataset, finding relationships and patterns in the data, as well as choosing and implementing the suitable AI model. At the moment, many evolutionary computation techniques such as artificial neural network (ANN), fuzzy logic (FL), adaptive neurofuzzy inference system (ANFIS), support vector machine (SVM), genetic programming, and genetic algorithm have been applied to predict and forecast critical engineering parameters [2327]. Among these machine learning methods, ANN models and genetic programming (GP) techniques have proven very useful owing to their robust computational abilities, with each of the models having their various performance capability with respect to the problem being solved or data being analyzed. ANN is based on an assembly of connected units or nodes called artificial neurons, which roughly model the neurons in a biological brain with each connection, like the synapses in a biological brain, transmitting a signal to other neurons, whereas the GP technique evolves programs, starting from a population of unfit or random programs, fit for a particular task by employing the roles of operations analogous to natural genetic processes to the population of programs. ANNs make their predictions by adjusting the weights via a series of repeatedly presented examples of input and output variables to minimize an error value existing between the theoretical result and the ANN-predicted result [28]. ANNs have been successfully applied in pile capacity prediction, modelling soil behaviour, site characterization, earth retaining structures, settlement of structures, slope stability, design of tunnels and underground openings, liquefaction, soil permeability and hydraulic conductivity, soil compaction, soil swelling, and soil classification problems [29]. The use of ANN models has also reflected in the prediction of various mechanical and physical properties of soil such as consistency limits and other strength properties of stabilized soils [3033]. Moreover, evolutionary predictions of the physical and mechanical properties of improved soils, such as unconfined compressive strength (UCS), internal friction, and coefficients of uniformity and gradation, with respect to the percentage of admixture contact (such as cement content) have been carried out by many emerging researchers without particular interest on the prediction of consistency limit [3336]. Likewise, in reference [37], the authors predicted the performance characteristics of stabilized soils by utilizing a variant of genetic programming, namely, linear genetic programming (LGP), and a hybrid search algorithm coupling LGP and simulated annealing (SA), called LGP/SA. In their own efforts, Naderi et al. [38] proposed two numerical models by employing GP for the estimation of soil compaction parameters. However, their input variables were the soil classification properties and the output variables were the optimum moisture content (OMC) and maximum dry density (MDD).

It is certain that the use of nanobinders for improving the critical soil parameters like Atterberg limits of unsaturated soils has not been fully evaluated. In addition, there has not been also an evolutionary computation approach that compares the performances of the GP and ANN models in predicting soil consistency limits (liquid limit, plastic limit, and plasticity index) using the effects induced by the nanobinder hybrid cement, which affects the clay content and clay activity with other strength properties of the soil medium. The current study has employed the use of GP and ANN models to predict the consistency limits, viz, plastic limit (Wp), liquid limit (WL) and plasticity index (Ip), of nanobinder-improved soil from experimentally measured physical and mechanical properties such as hybrid cement percent by weight (Hc), clay activity (Ac), and clay content (C) in addition to the already experimentally estimated predicted values, and compares the same.

2. Methodology

2.1. Materials Preparation

The soil was collected from a depth of 0.5 meters (to avoid debris) from the borrow pit at Ohia (marked red) located in Umuahia, as shown in the GIS map in Figure 1; sundried for 3 days; and stored for the experiment. Rice husk ash generated by combusting rice husk was obtained from farm dumpsites and local rice mills in Abakaliki, where the people’s primary occupation is rice farming. This agro-industrial waste disposal is a huge environmental problem in Ebonyi state, Nigeria, due to the lack of waste management system. The rice husk ash (RHA) was further pulverized to fineness and sieved with 200 nm sieves to obtain nanostructured or nanotextured rice husk ash (NRHA). Further and in order to improve the binding ability of the NRHA, 5% by weight NRHA of hydrated lime (Ca(OH)2) was blended with NRHA and allowed to react for 48 hours to obtain hydrated-lime-activated nanotextured rice husk ash (HANRHA). Also, nanotextured quarry fines (NQF) was obtained by completely crushing quarry dust to fineness and passing the powder through 200 nm sieves. Finally, a cementing composite, which for the purpose of this work was called hybrid cement (HC), was generated by mixing HANRHA and NQF in a ratio of 1 : 0.1%. These experimental materials were characterized and stored for use in the stabilization process.

2.2. Experimental Methods

The material-handling conditions of the British Standard International (BSI) (BS1377, 1990) were adhered to in characterizing the reference soil. Under the above standard conditions, the distribution of particles of the soil, compaction, consistency limits, specific gravity, and potential for swelling were determined. In order to determine the composition of oxides of the constituent cementitious composite binder materials (NRHA, NQF, and HC), X-ray fluorescence (XRF) tests were carried out adhering to the standard conditions of ASTM E1621-13 (2013), and in order to achieve more reliable and accurate outcomes, the specimens were prepared and mixed to considerable homogeneity. Also, the ultraviolet-visible spectrophotometer test was conducted on the soil, NRHA, and NQF to determine the textured absorbance of nanoparticle exposures. Furthermore, generated HC stabilization exercise of the soil was conducted adhering to the standard conditions of the BS1924 (1990) and a series of data values were generated for various proportions of HC between 0% and 12% by weight of dry soil at the rate of 0.1%. The studied parameters of the treated soil were as follows: the predictors: clay content (C) and clay activity (Ac); the targets: liquid limit (WL), plastic limit (Wp), and plasticity index (Ip). Furthermore, the generated datasets (see Table 1) were deployed in the intelligent forecasting exercise employing the genetic programming (GP) and artificial neural network techniques.


HcCAcWLWpIp

Training dataset
0.0670.2351.3100.4650.1680.297
0.0650.2351.3000.4700.1700.300
0.1040.2390.8200.3330.1400.193
0.0640.2351.3300.4720.1700.302
0.0930.2381.0000.3700.1500.220
0.1170.2400.6700.2850.1300.155
0.0800.2371.1300.4100.1500.260
0.0790.2371.1400.4150.1540.261
0.0350.2321.7000.5700.1900.380
0.0780.2361.1600.4180.1540.264
0.0550.2341.4000.5000.1800.320
0.0210.2311.8000.6090.1990.410
0.0470.2331.5000.5270.1800.347
0.0080.2311.8700.6410.2080.433
0.0280.2321.7500.5950.1910.404
0.0030.2301.9600.6560.2090.447
0.0500.2341.5000.5200.1800.340
0.0990.2390.9400.3630.1520.211
0.0830.2371.1100.3980.1510.247
0.0890.2381.0000.3750.1520.223
0.0120.2311.8100.6210.2030.418
0.0370.2331.6500.5670.1900.377
0.0960.2380.9900.3680.1510.217
0.0760.2361.1900.4280.1590.269
0.0480.2341.5000.5260.1810.345
0.0260.2321.7900.5980.1900.408
0.0310.2321.7000.5880.1920.396
0.1080.2400.7500.3150.1390.176
0.0070.2311.8800.6450.2080.437
0.0020.2301.9600.6570.2090.448
0.0360.2321.6900.5680.1890.379
0.0600.2351.4000.4900.1800.310
0.1190.2410.6200.2760.1320.144
0.0680.2351.3000.4560.1590.297
0.1000.2390.9000.3600.1500.210
0.0580.2341.4200.4940.1790.315
0.0090.2311.8500.6350.2090.426
0.0010.2301.9800.6600.2100.450
0.0000.2302.0000.6600.2100.450
0.1090.2400.7200.3110.1400.171
0.0700.2361.3000.4500.1600.290
0.0410.2331.5900.5570.1900.367
0.0730.2361.2600.4370.1590.278
0.0340.2321.6900.5740.1900.384
0.1020.2390.8600.3550.1510.204
0.0170.2311.7900.6130.2000.413
0.0300.2321.7000.5900.1900.400
0.0440.2331.5200.5360.1840.352
0.0520.2341.4600.5110.1770.334
0.0180.2311.8100.6130.2010.412
0.0200.2311.8000.6100.2000.410
0.0740.2361.2300.4340.1600.274
0.0160.2311.8000.6140.2000.414
0.0900.2381.0000.3700.1500.220
0.0660.2351.3100.4680.1710.297
0.0820.2371.1100.4030.1500.253
0.0980.2380.9700.3650.1510.214
0.0330.2321.7100.5790.1910.388
0.0870.2371.0000.3830.1490.234
0.0590.2351.4100.4910.1770.314
0.0290.2321.7200.5920.1900.402
0.1050.2390.8000.3300.1400.190
0.0710.2361.2900.4480.1630.285
0.0230.2321.8000.6060.1960.410
0.0880.2371.0000.3790.1520.227
0.0130.2311.8000.6190.2020.417
0.1010.2390.8800.3570.1490.208
0.0570.2341.4100.4960.1790.317
0.0970.2380.9800.3670.1510.216
0.0390.2331.6100.5630.1900.373
0.0190.2311.8000.6120.2010.411
0.0770.2361.1800.4240.1600.264
0.1070.2390.7800.3240.1390.185
0.0560.2341.4000.4990.1800.319
0.0400.2331.6000.5600.1900.370
0.0220.2321.8000.6070.1970.410
0.0490.2341.5000.5230.1800.343
0.0420.2331.5700.5490.1870.362
0.0380.2331.6400.5650.1890.376
0.0720.2361.2700.4430.1610.282
0.0950.2381.0000.3700.1500.220

Validation dataset
0.0630.2351.3500.4770.1730.304
0.0100.2311.8000.6300.2100.420
0.0320.2321.7000.5840.1890.395
0.0750.2361.2000.4300.1600.270
0.1120.2400.7100.3030.1370.166
0.0690.2361.3000.4520.1590.293
0.0050.2301.9000.6500.2100.440
0.1110.2400.7000.3070.1390.168
0.0910.2381.0000.3700.1500.220
0.0850.2371.0000.3900.1500.240
0.0840.2371.1000.3930.1500.243
0.0060.2311.8800.6480.2080.440
0.0530.2341.4300.5080.1810.327
0.0940.2381.0000.3700.1500.220
0.0540.2341.4100.5030.1800.323
0.0450.2331.5000.5300.1800.350
0.1150.2400.7000.2900.1300.160
0.0860.2371.0000.3880.1500.238
0.1060.2390.7900.3280.1400.188
0.1180.2410.6500.2780.1300.148
0.1140.2400.7100.2940.1320.162
0.0620.2351.3700.4830.1760.307
0.1130.2400.7100.2980.1340.164
0.0040.2301.9300.6530.2080.445
0.0110.2311.8000.6250.2060.419
0.1030.2390.8400.3460.1490.197
0.0240.2321.8000.6040.1940.410
0.0430.2331.5500.5410.1850.356
0.1100.2400.7000.3100.1400.170
0.1200.2410.6000.2700.1300.140
0.0510.2341.4800.5150.1770.338
0.0270.2321.7700.5970.1910.406
0.0250.2321.8000.6000.1900.410
0.0920.2381.0000.3700.1500.220
0.0140.2311.8100.6170.2010.416
0.1160.2400.6900.2870.1280.159
0.0150.2311.8000.6150.2000.415
0.0810.2371.1200.4070.1490.258
0.0460.2331.5000.5280.1800.348
0.0610.2351.3800.4860.1780.308

2.3. Statistical Analysis and Research Model Program
2.3.1. Collected Database

A total of 121 soil samples were tested to determine the following physical and mechanical properties:(i)Hybrid cement percent by weight (HC)(ii)Clay content (C)(iii)Clay activity (Ac)(iv)Liquid limit (WL)(v)Plastic limit (Wp)Plasticity index (Ip)

The measured data were divided into training set (81 records) and validation set (40 records). Table 1 includes the complete dataset, while Table 2 summarizes their statistical characteristics.


HcCAcWLWpIp

Training set
Max.0.000.230.620.280.130.14
Min0.120.242.000.660.210.45
Avg0.060.231.390.490.170.32
SD0.030.000.370.110.020.08
Var0.580.010.270.220.130.27

Validation set
Max.0.000.230.600.270.130.14
Min0.120.241.930.650.210.45
Avg0.070.241.260.460.170.29
SD0.040.000.430.130.030.10
Var0.580.010.340.280.160.35

2.3.2. Research Model Program

Both the GP and ANN techniques were used to predict the consistency limits of the tested soil. Two GP models and one ANN model were developed to predict the values of liquid limit (WL), plastic limit (Wp), and plastic index (Ip) using the measured hybrid cement percent by weight (HC), clay content (C), and clay activity (Ac). The developed GP models started with the simplest (two levels of complexity) and stopped at three levels of complexity because the accuracy of the models could not be improved any further. The ANN model was developed to compare the accuracies of both techniques; it was based on a simple back-propagation network without hidden layers with a linear activation function (y = x). For all models, the prediction accuracy was evaluated in terms of sum of squared error (SSE). Simple formulas allow for limited rooms for the most effective variables, whereas complicated formulas allow for more rooms for less effective variables. Hence, the considered variables could be ranked according to their impact on the output. Table 3 shows the characteristics of the developed GP models, while Figure 1 shows the layout of the developed ANN model.


Model no.No. of levelsUsed variablesPopulation sizeSurvivor sizeNo. of generationsMutation present

12Hc, C, Ac, WL, Wp, Ip, 1, 3, 5, 7, 1150,00015,0001005%
23100,00030,000200

The following section discusses the results of each model. The accuracies of the developed models were evaluated by comparing the (SSE) between the predicted and calculated consistency limit values. The results of all developed models are summarized in Table 4.


Property% passing 0.075 mmNMCLLPLPISPSGAASHTOMDDOMC

Value4514662145231.24A-7-61.2516
Unit%%%%%%g/cm3%

3. Results and Discussion

3.1. Preliminary Classifications

Table 4 and Figure 2 show the preliminary properties of the soil, which show the soil’s potential for swelling, high plasticity, and lack of strength to be used as a foundation material. Figures 35 present the ultraviolet-visible spectrophotometric nanographs of soil, NRHA, and NQF, respectively, which show the absorbance of the HC constituent materials and their ability to form a homogeneous mixture with soil in the HC composite. It also shows the ability of the materials to form nucleating surfaces in order to react by ion exchange and hydration. Finally, the compaction characteristics of the lateritic soil sample are presented in Figure 6 [13].

From the results of previous research [13], it was observed that “RHA exhibited gel-like porous-valve structure at a magnification level of 100 micrometers. Additionally, the presence of bigger voids could be observed in the SEM micrograph, which illustrates the light-weight structure and porous structure of the agricultural waste. Similarly, the SEM image of the soil depicts a laminar structure with dispersive, larger, and thinner clay platelets. The smectites are seen to conform plate-like structures with the presence of thin hairline cracks. Additionally, the aggregates are mostly arranged in a face-to-face contact style.” These morphological characteristics contribute to the reactive and pozzolanic capacity of the test materials in their nanoscale texture used in this study.

Table 5 shows the aluminosilicate composition of the experimental materials from XRF tests. This shows that the HC, presently obtained from blending HANRHA and NQF, is observed with the highest aluminosilicate content of 97.15% compared to NQF with 87.74% and NRHA with 83.97% corresponding to the total compositions of Al2O3, SiO2, and Fe2O3. Accordingly, the supplementary cementitious material (SCM) design conditions proposed by ASTM C618 (1978) show that HC is highly cementitious and can be utilized as a binder in the soil treatment experiment. From the foregoing requirements, it can be seen that HC is a hybridized composite of NRHA and NQF with higher capacity to bind materials. It can be observed that the increased varying proportion of the multiple binders consistently improved the studied treated soil parameters, which was due to the hydration, pozzolanic reaction, cation exchange, and densification of the treated soil with increased binders and fundamentally due to the nanostructuring of the binder constituents, thereby increasing the reactive surface. The increased nucleating and reactive surface achieved through nanotexturing of the quarry dust and RHA through complete pulverization and nanosieving has proven to be of great significance to the geotechnics of this exercise. This linear improvement on the studied parameters of the unsaturated soil has a huge influence on the performance of the proposed models.


MaterialsOxides’ composition (content by weight, %)
SiO2Al2O3CaOFe2O3MgOK2ONa2OTiO2LOIP2O5SO3IRFree CaO

Clay soil12.4518.092.3010.664.8912.1034.330.075.11
NRHA57.4822.724.563.774.652.760.013.170.88
NQF62.4818.724.836.542.563.180.291.01
HC66.527.81.32.851.50.030.02

IR is insoluble residue; LOI is loss on ignition.
3.2. Prediction of Consistency Limits Value Using Both GP and ANN
3.2.1. Model (1):GP of Two Levels of Complexity

With only two levels of complexity, this model is the simplest one. Equations (1)–(3) present the output formulas for (WL), (Wp), and (Ip), respectively, while Figures 7(a), 8(a), and 9(a) show their performance fitness, respectively. The total set error % values for (WL), (Wp), and (Ip) are (2.3%), (2.5%), and (1.8%), respectively, while the (R2) values are (0.992), (0.969), and (0.997), respectively (see Table 6). These models’ behaviours agree with the predictive model performance of the works of Onyelowe et al. [13, 33], Elbosraty et al. [39], and Onyelowe and Shakeri [20].


Soil propertyModel no.Output formulaError %R2
TrainingValidationTotalTrainingValidationTotal

WL1Equation (1)2.02.92.30.9930.9910.992
2Equation (4)1.62.01.70.9960.9940.995
3Equation (7)1.21.21.20.9990.9970.998

Wp1Equation (2)2.32.92.50.9720.9670.969
2Equation (5)2.12.72.30.9750.9700.972
3Equation (8)1.92.22.00.9820.9770.979

Ip1Equation (3)1.71.91.80.9980.9960997
2Equation (6)1.51.81.60.9980.9960.997
3Equation (9)1.51.51.50.9990.9970.998

3.2.2. Model (2): GP of Three Levels of Complexity

The next step was to increase the level of complexity to enhance the prediction accuracy; hence, three levels of complexity were used in this model. The outputs are illustrated in Equations (4)–(6), and their fitnesses are shown in Figures 7(b), 8(b), and 9(b). The error % and (R2) values were improved to (1.7%) − (0.995), (2.3%) − (0.972), and (1.6%) − (0.997) for the total datasets, respectively (see Table 6). These models’ behaviours agree with the predictive model performance of the works of Onyelowe et al. [13], Onyelowe and Shakeri [20], and ELbosraty et al. [39]. The closed-form equations show the influence of the studied variables of this model and their usefulness in the design, construction, and monitoring of the performance of the subgrade infrastructure.

3.2.3. Model (3): Back-Propagation ANN

Finally, a simple back-propagation ANN was used to compare the accuracies of both techniques. The used network layout and its connection weights are illustrated in Figure 10. Since the used ANN has a linear activation function, it is equivalent to a set multivariable linear equations as shown in Equations (7)–(9). The total dataset error % values for these equations are (1.2%), (2.0%), and (1.5%), and the (R2) values are (0.998), (0.979), and (0.998), respectively (see Table 6). The relations between calculated and predicted values are shown in Figures 7(c), 8(c), and 9(c). These performance indices agree with the findings of Onyelowe et al. [26, 40] with performance deficiencies less than 2% and accuracy of above 95%. It shows that the ANN-predicted models are sufficiently reliable to be used in subgrade designs and construction.

4. Conclusions

This research presents three models (two GP models and one ANN model) to predict the consistency limit values of liquid limit (WL), plastic limit (Wp), and plasticity index (Ip) using the measured hybrid cement percent by weight (HC), clay content (C), and clay activity (Ac). The results of comparing the accuracies of the developed models could be concluded in the following points:(i)The prediction accuracies of all models are very close (between 97.5% and 98.5%), which gives an advantage to the first model (the simplest one).(ii)The outputs of the first model indicated that the WL values were governed by Ac and HC, while the Wp values depended only on Ac, and finally, the Ip values were controlled by Ac and C values.(iii)Although the third model used a very simple ANN configuration (no hidden layers and linear activation function), it was still able to determine the relations between the inputs and the outputs accurately. It showed an accuracy level slightly higher than the GP models.(iv)values of Ip were predicted independently of the WL and Wp values in the three models to increase the prediction accuracy by avoiding the error commutations from the developed formulas for WL and Wp. However, the developed formula for Ip in the third model satisfies the relation Ip = WL − Wp.(v)Like any other regression technique, the generated formulas are valid within the considered range of parameter values; beyond this range, the prediction accuracy should be verified.

Data Availability

The underlying data supporting the results of this study have been reported in the manuscript.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this article.

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Copyright © 2021 Ahmed M. Ebid et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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