Applied Computational Intelligence and Soft Computing
Volume 2021 (2021), Article ID 6686347, 17 pages
https://doi.org/10.1155/2021/6686347

Research Article

Application of Gene Expression Programming to Evaluate Strength Characteristics of Hydrated-Lime-Activated Rice Husk Ash-Treated Expansive Soil

Kennedy C. Onyelowe,¹ Fazal E. Jalal,² Michael E. Onyia,³ Ifeanyichukwu C. Onuoha,⁴ and George U. Alaneme⁵

¹Department of Civil and Mechanical Engineering, Kampala International University, Kampala, Uganda
²Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai, China
³Department of Civil Engineering, Faculty of Engineering, University of Nigeria, Nsukka, Nigeria
⁴Department of Environmental Technology, Federal University of Technology, Owerri, Nigeria
⁵Department of Civil Engineering, Michael Okpara University of Agriculture, Umudike, Nigeria

Correspondence should be addressed to Kennedy C. Onyelowe; kennedychibuzor@kiu.ac.ug

Received 7 December 2020; Revised 24 March 2021; Accepted 26 March 2021; Published 14 April 2021

Academic Editor: Babak Daneshvar Rouyendegh (B. Erdebilli)

Copyright © 2021 Kennedy C. Onyelowe 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.

Abstract.

Gene expression programming has been applied in this work to predict the California bearing ratio (CBR), unconfined compressive strength (UCS), and resistance value (R value or Rvalue) of expansive soil treated with an improved composites of rice husk ash. Pavement foundations suffer failures due to poor design and construction, poor materials handling and utilization, and management lapses. The evolution of sustainable green materials and optimization and soft computing techniques have been deployed to improve on the deficiencies being suffered in the abovementioned areas of design and construction engineering. In this work, expansive soil classified as A-7-6 group soil was treated with hydrated-lime activated rice husk ash (HARHA) in an incremental proportion to produce 121 datasets, which were used to predict the behavior of the soil’s strength parameters utilizing the mutative and evolutionary algorithms of GEP. The input parameters were HARHA, liquid limit (), (plastic limit , plasticity index , optimum moisture content (), clay activity (AC), and (maximum dry density (δmax) while CBR, UCS, and R value were the output parameters. A multiple linear regression (MLR) was also conducted on the datasets in addition to GEP to serve as a check mechanism. At the end of the computing and iterations, MLR and GEP optimization methods proposed three equations corresponding to the output parameters of the work. The responses validation on the predicted models shows a good correlation above 0.9 and a great performance index. The predicted models’ performance has shown that GEP soft computing has predicted models that can be used in the design of CBR, UCS, and R value for soils being used as foundation materials and being treated with admixtures as a binding component.

1. Introduction

The design, construction, and monitoring of earthwork infrastructure have been of utmost importance due to the everyday failure civil engineering facilities experience [1–4]. For this reason, composite materials with special properties have been evolved to replace ordinary cement [5–8]. One such technique in the utilization of special binders is the introduction of activators to ash materials to form activated ash with the ability to resist unfavorable conditions and factors that have proven to be averse to constructed infrastructure [9–14]. However, the evolution of soft computing in engineering has added to the efficiency of designing, constructing, and monitoring of the performance of earthworks [15–19]. One such soft computing or machine learning method is gene expression programming (GEP). Invented by Cramer [20], genetic programming (GP) and gene expression programming (GEP) are the branches of genetic algorithm (GA) that is regarded as an evolutionary computing algorithm technique [20–22]. It is based on Darwin's theory of “survival of the fittest” that does not require making prior assumptions about the solution structure [23]. The working procedure of GP comprises various steps [24]: (1) create an initial population in accordance with the function and terminal settings; (2) use two key criteria, fitness function and maximum number of generations, to assess the performance of the generated population; if the performance of this population is according to the requirement or approaches the maximum number of the generation, terminate the program, otherwise, continuously generate a new population using three genetic operations of reproduction, crossover, and mutation for an amount of duration until the threshold criteria are not met. The experimental database was separated into training, validation, and testing set for the GEP analysis. In order to confirm consistent data division, many combinations of the training and testing sets were taken [25].

In Figure 1, it can be seen that input data is fed to either GP or a mathematical model that incorporates GP that yields predicted and observed values. The difference between these is residual errors which are reduced by continuing formulating in the GEP tool until an optimum model is obtained.

Figure 1: Simple working schematics for gene expression programming.

2. Materials and Methods

2.1. Preparation of Materials

Expansive clay soil was prepared and tests were conducted on both the untreated and the treated soils to determine the datasets presented in Table 1, needed for the evolutionary predictive modeling. The hydrated-lime activated rice husk ash (HARHA) is a hybrid geomaterial binder developed by blending rice husk ash with 5% by weight activator agent, which in this case is hydrated lime (Ca(OH)₂) and allowed for 48 hours. At the same time, the rice husk is an agroindustrial waste derived from the processing of rice in rice mills and homes. Through controlled direct combustion proposed by Onyelowe et al. [4], the rice husk mass is turned into ash from rice husk ash (RHA). The HARHA was used in incremental proportions to treat the clayey soil and the response behavior on different properties tested, observed, and recorded (see Table 1).

Table 1: 121 datasets of input and output parameters.

HARHA (%)
Input soil hydraulic-prone properties
Output soil strength properties

(%)
(%)
(%)
(%)

(g/cm³)
CBR (%)
(kN/m²)

0
66
21
45
16
2.0
1.25
8
125
11.7

0.1
66
21
45
16
1.98
1.25
8.1
125
11.7

0.2
65.7
20.9
44.8
16.1
1.96
1.27
8.2
126
11.7

0.3
65.6
20.9
44.7
16.3
1.96
1.27
8.2
126
11.7

0.4
65.3
20.8
44.5
16.3
1.93
1.28
8.3
126
11.8

0.5
65
21
44
16.4
1.9
1.30
8.5
128
12.0

0.6
64.8
20.8
44
16.4
1.88
1.31
8.55
128
12.2

0.7
64.5
20.8
43.7
16.45
1.88
1.31
8.6
128
12.2

0.8
64.1
20.8
43.3
16.47
1.87
1.33
8.6
130
12.3

0.9
63.5
20.9
42.6
16.49
1.85
1.33
8.85
130
12.6

1
63
21
42
16.5
1.8
1.35
9.2
132
13.1

1.1
62.5
20.6
41.9
16.6
1.8
1.35
9.25
132
13.3

1.2
62.1
20.3
41.8
16.7
1.81
1.36
9.4
133
13.5

1.3
61.9
20.2
41.7
16.8
1.8
1.37
9.5
133
13.6

1.4
61.7
20.1
41.6
17
1.81
1.38
9.7
134
13.8

1.5
61.5
20
41.5
17.2
1.8
1.38
9.8
134
14.2

1.6
61.4
20
41.4
17.2
1.8
1.39
9.8
136
14.4

1.7
61.3
20
41.3
17.3
1.79
1.39
9.85
137
14.8

1.8
61.3
20.1
41.2
17.5
1.81
1.4
9.92
137
14.8

1.9
61.2
20.1
41.1
17.7
1.8
1.41
9.96
138
15

2
61
20
41
17.8
1.8
1.41
10.4
138
15.3

2.1
60.9
19.9
41
17.9
1.8
1.42
10.4
139
15.6

2.2
60.7
19.7
41
17.9
1.8
1.42
10.7
139
15.7

2.3
60.6
19.6
41
18
1.8
1.425
11
140
15.8

2.4
60.4
19.4
41
18.2
1.8
1.43
11.6
141
16

2.5
60
19
41
18.3
1.8
1.43
12.0
141
16.2

2.6
59.8
19
40.8
18.35
1.79
1.435
12.1
142
16.5

2.7
59.7
19.1
40.6
18.4
1.77
1.45
12.4
142
16.8

2.8
59.5
19.1
40.4
18.45
1.75
1.455
12.9
142
17

2.9
59.2
19
40.2
18.5
1.72
1.46
13.3
143
17.1

3
59
19
40
18.5
1.7
1.46
13.8
143
17.3

3.1
58.8
19.2
39.6
18.55
1.7
1.47
13.9
144
17.4

3.2
58.4
18.9
39.5
18.6
1.7
1.475
14.2
145
17.7

3.3
57.9
19.1
38.8
18.7
1.71
1.48
14.5
146
18

3.4
57.4
19
38.4
18.75
1.69
1.484
14.7
147
18.3

3.5
57
19
38
18.8
1.7
1.49
14.8
148
18.5

3.6
56.8
18.9
37.9
18.85
1.69
1.5
15
148
18.7

3.7
56.7
19
37.7
18.9
1.65
1.51
15.3
150
18.9

3.8
56.5
18.9
37.6
18.93
1.64
1.51
15.7
151
19.1

3.9
56.3
19
37.3
18.98
1.61
1.52
15.9
152
19.2

4
56
19
37
19.0
1.6
1.52
16.0
153
19.4

4.1
55.7
19
36.7
19.0
1.59
1.53
16.3
154
19.5

4.2
54.9
18.7
36.2
19.0
1.57
1.54
16.8
156
19.6

4.3
54.1
18.5
35.6
19.0
1.55
1.55
17.5
157
19.7

4.4
53.6
18.4
35.2
19.0
1.52
1.56
17.8
158
19.7

4.5
53
18
35
19.0
1.5
1.57
18.0
159
19.8

4.6
52.8
18
34.8
18.98
1.5
1.58
18.1
160
20

4.7
52.7
18
34.7
18.96
1.5
1.59
18.3
160
20

4.8
52.6
18.1
34.5
18.93
1.5
1.60
18.8
162
20.1

4.9
52.3
18
34.3
18.91
1.5
1.61
19.5
163
20.2

5
52
18
34
18.9
1.5
1.61
19.8
164
20.4

5.1
51.5
17.7
33.8
18.88
1.48
1.62
19.9
165
20.4

5.2
51.1
17.7
33.4
18.86
1.46
1.63
20
166
20.5

5.3
50.8
18.1
32.7
18.84
1.43
1.64
20.3
167
20.5

5.4
50.3
18
32.3
18.82
1.41
1.65
20.9
168
20.6

5.5
50
18
32
18.8
1.4
1.65
21.7
168
20.6

5.6
49.9
18
31.9
18.78
1.4
1.66
21.9
169
20.7

5.7
49.6
17.9
31.7
18.75
1.41
1.67
22.1
170
20.8

5.8
49.4
17.9
31.5
18.71
1.42
1.67
22.3
171
20.8

5.9
49.1
17.7
31.4
18.65
1.41
1.68
22.5
172
20.9

6
49
18
31
18.6
1.4
1.69
22.8
172
20.9

6.1
48.6
17.8
30.8
18.55
1.38
1.7
23.1
173
21

6.2
48.3
17.6
30.7
18.48
1.37
1.71
23.3
173
21.1

6.3
47.7
17.3
30.4
18.6
1.35
1.72
23.7
174
21.2

6.4
47.2
17
30.2
18.44
1.33
1.73
23.8
175
21.4

6.5
47
17
30
18.4
1.3
1.74
24.0
175
21.5

6.6
46.8
17.1
29.7
18.4
1.31
1.75
24.3
176
21.6

6.7
46.5
16.8
29.7
18.41
1.31
1.76
24.9
177
21.8

6.8
45.6
15.9
29.7
18.4
1.3
1.77
25.2
177
21.9

6.9
45.2
15.9
29.3
18.41
1.3
1.78
25.5
178
22.0

7
45
16
29
18.4
1.3
1.78
25.9
179
22.0

7.1
44.8
16.3
28.5
18.39
1.29
1.79
26.2
180
22.1

7.2
44.3
16.1
28.2
18.37
1.27
1.8
26.6
181
22.3

7.3
43.7
15.9
27.8
18.35
1.26
1.81
27
182
22.4

7.4
43.4
16
27.4
18.32
1.23
1.83
27.3
183
22.5

7.5
43
16
27
18.3
1.2
1.84
27.6
183
22.6

7.6
42.8
15.9
26.9
18.29
1.19
1.85
27.7
184
22.7

7.7
42.4
16
26.4
18.28
1.18
1.86
28.3
184
22.8

7.8
41.8
15.4
26.4
18.26
1.16
1.87
28.5
183
22.8

7.9
41.5
15.4
26.1
18.23
1.14
1.87
28.7
184
22.9

8
41
15
26
18.2
1.13
1.88
29.0
185
22.9

8.1
40.7
14.9
25.8
18.2
1.12
1.88
29.3
186
23

8.2
40.3
15
25.3
18.2
1.11
1.89
29.9
187
23.2

8.3
39.8
15.1
24.7
18.2
1.11
1.90
30.4
188
23.3

8.4
39.3
15
24.3
18.21
1.1
1.90
30.7
189
23.5

8.5
39
15
24
18.2
1.0
1.91
31.2
190
23.6

8.6
38.8
15
23.8
18.2
1.0
1.92
31.5
191
23.7

8.7
38.3
14.9
23.4
18.2
1.0
1.93
32.1
192
23.8

8.8
37.9
15.2
22.7
18.2
1.0
1.94
32.4
193
23.9

8.9
37.5
15.2
22.3
18.2
1.0
1.95
33.5
194
24

9
37
15
22
18.2
1.0
1.96
34.0
195
24.0

9.1
37
15
22
18.19
1.0
1.962
34.5
196
24.1

9.2
37
15
22
18.18
1.0
1.964
34.8
197
24.2

9.3
37
15
22
18.16
1.0
1.966
35.2
198
24.3

9.4
37
15
22
18.13
1.0
1.969
35.8
199
24.4

9.5
37
15
22
18.1
1.0
1.97
36.0
200
24.5

9.6
36.8
15.1
21.7
18
0.99
1.972
36.5
202
24.6

9.7
36.7
15.1
21.6
17.92
0.98
1.973
36.9
204
24.7

9.8
36.5
15.1
21.4
17.93
0.97
1.975
37.6
208
24.8

9.9
36.3
15.2
21.1
17.91
0.94
1.977
37.8
208
24.8

10
36
15
21
17.9
0.9
1.98
38.0
210
24.9

10.1
35.7
14.9
20.8
17.88
0.88
1.98
38.3
213
25.1

10.2
35.5
15.1
20.4
17.84
0.86
1.982
38.5
214
25.3

10.3
34.6
14.9
19.7
17.79
0.84
1.984
38.9
215
25.4

10.4
33.3
14
19.3
17.73
0.82
1.987
39.6
218
25.4

10.5
33
14
19
17.7
0.8
1.99
40.0
220
25.5

10.6
32.8
14
18.8
17.7
0.79
1.99
41.1
222
25.8

10.7
32.4
13.9
18.5
17.71
0.78
1.99
42.4
223
26.2

10.8
31.5
13.9
17.6
17.71
0.75
1.99
43.2
225
26.3

10.9
31.1
14
17.1
17.7
0.72
1.99
43.5
228
26.5

11
31
14
17
17.7
0.7
1.99
44.0
230
26.8

11.1
30.7
13.9
16.8
17.68
0.7
1.99
44.0
231
26.8

11.2
30.3
13.7
16.6
17.63
0.71
1.99
44.5
232
26.8

11.3
29.8
13.4
16.4
17.57
0.71
1.99
44.6
232
26.9

11.4
29.4
13.2
16.2
17.53
0.71
1.98
44.6
232
26.9

11.5
29
13
16
17.5
0.7
1.97
43.8
225
26.9

11.6
28.7
12.8
15.9
17.5
0.69
1.97
43.8
224
26.9

11.7
28.5
13
15.5
17.4
0.67
1.96
43.7
223
27.0

11.8
27.8
13
14.8
17.3
0.65
1.96
43.6
222
27.0

11.9
27.6
13.2
14.4
17.2
0.62
1.95
43.5
221
27.0

12
27
13
14
17.1
0.6
1.95
43.4
221
27.0

2.2. Model Method

In Figure 2, the flowchart of the gene expression programming method and execution is presented. The 121 input and output datasets were deployed to the GeneXpro software computing platform to generate the predicted outputs and the models from that operation. Several trials or iterations were carried out to achieve the best fit.

Figure 2: Flowchart of the GEP model execution.

3. Results and Discussion

3.1. Pearson Correlation

Pearson’s correlation matrix [26] was generated from the given data comprising seven input and three output parameters using the data analysis capabilities of Microsoft Excel. The correlation matrix is defined as a square, symmetrical matrix with the (ij)th element equal to the correlation coefficient R_ij among the (i)th and the (j)th variable. The diagonal members (correlations of variables with each other) are always equal to one [27]. Thus, the left-hand nine columns of this correlation matrix represent qualitatively the correlations between the input soil hydraulic-prone properties (HARHA, , , , , AC, δmax) and output soil strength properties, i.e., CBR, UCS28, and RValue (Table 2). The range of correlation factors varies from −1 and 1 (0 represents no correlation, whereas ±1 shows greater correlation). A positive value suggests that the respective increase or decrease is linear among the two variables simultaneously. It is indicated in Table 2 that the CBR, UCS₂₈, and RValue have a correlation coefficient above 0.90 for all input parameters with the exception of for the last two outputs (0.134 and 0.363), respectively. Thus, a high correlation exists in this correlation matrix for the considered input and out parameters. In Figure 3 was presented the frequency histograms of the input variables: (a) HARHA; (b) ; (c) ; (d) ; (e) ; (f) AC; (g) δmax; and output variables (h) CBR; (i) UCS₂₈; (j) RValue.

Table 2: Pearson correlation matrix for input and output parameters.

HARHA

AC
δmax
CBR
UCS₂₈
RValue

HARHA
1

−0.99724
1

−0.98926
0.991515
1

−0.99652
0.999411
0.986472
1

0.201388
−0.1435
−0.17491
−0.1348
1

AC
−0.99388
0.997543
0.984584
0.998142
−0.12039
1

δmax
0.985771
−0.98176
−0.97696
−0.98026
0.23936
−0.97417
1

CBR
0.991609
−0.99425
−0.98026
−0.99514
0.097679
−0.9951
0.969326
1

UCS₂₈
0.990886
−0.99098
−0.97628
−0.99206
0.134931
−0.99283
0.967127
0.996459
1

RValue
0.984407
−0.9721
−0.96953
−0.97003
0.363941
−0.96588
0.972762
0.96009
0.967161
1

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

Figure 3: Frequency histograms of the input and output variables: (a) HARHA; (b); (c); (d); (e); (f) AC; (g) δmax; (h) CBR; (i) UCS₂₈; (j) RValue. Note: the input parameters are illustrated in blue while the output variables are expressed as green histograms.

3.2. Gene Expression Programming

The performance of a developed GEP model using a database is affected by the sample size and its variable distributions, which agrees with the findings of Gandomi and Roke [25]. Thus, the frequency histograms for all the input parameters (HARHA, , , , , AC, and δmax) and output values (CBR, UCS28, and RValue) are visualized in Figure 3. It can be seen that the bell-shaped curve indicates even distribution of the data. This diagram is often used for the initial assessment of geochronological data, which involves relatively large sets of data, according to Sircombe [28]. All the data is seen to exhibit even sample distributions and follow a symmetrical pattern such that the display of the histograms straightforward.

The descriptive statistics of the input and out parameters are tabulated in Table 3. This statistical summary shows the minimum and maximum ranges for all input and output parameters. The standard deviation (SD), Kurtosis, and skewness are also given for each parameter, which agrees with Edjabou et al. [29]. A low SD means that most of the values are close to the average (, , AC, δmax, and RValue), whereas a larger SD means that the numbers are more spread out (, , CBR, and UCS₂₈). Skewness quantifies the asymmetry of the probability distribution of a real-valued random variable with respect to its mean. It can be positive, zero, negative, or undefined [30]. The negative values generally suggest that the tail is extended on the left side of the distribution curve (, , , , AC, δmax, and RValue), while positively skewed shows that the tail is on the right side (CBR and UCS₂₈), which is reflected from the frequency histograms given in Figure 3 and the variable importance presented in Figures 4–6. Like skewness, kurtosis explains the shape of a probability distribution [31]. The Pearson measure of kurtosis of a given univariate normal distribution is generally taken as 3. Kurtosis values below 3 are called platykurtic, meaning that the distribution produces fewer and less extreme outliers than does the normal distribution, for instance, a uniform distribution, that is reflected in Figure 3.

Table 3: Statistical parameters of the input and output parameters.

Input soil hydraulic-prone properties
Output soil strength properties

AC
δmax
CBR
UCS₂₈
RValue

Min.
27.00
12.80
14.00
16.00
0.60
1.25
8.00
125.00
11.70

Max.
66.00
21.00
45.00
19.00
2.00
1.99
44.60
232.00
27.00

Sum
5808
2078
3730
2181
163
204
2904
20917
2481

Mean
48.00
17.17
30.82
18.02
1.35
1.69
24.00
172.87
20.50

Median
49.00
17.70
31.00
18.20
1.40
1.69
22.80
172.00
20.90

SD
11.49
2.40
9.11
0.77
0.40
0.24
11.69
31.53
4.46

Kurtosis
−1.25
−1.24
−1.25
0.24
−1.18
−1.42
−1.17
−1.04
−0.79

Skewness
−0.13
−0.06
−0.14
−0.94
−0.21
−0.17
0.30
0.26
−0.44

Figure 4: CBR variable importance of observed values and the input variable; (d0) HARHA; (d1) ; (d2) ; (d3) ; (d4) ; (d5) AC; (d6) δmax.

Figure 5: UCS variable importance of observed values and the input variable; (d0) HARHA; (d1) ; (d2) ; (d3) ; (d4) ; (d5) AC; (d6) δmax.

Figure 6: R value variable importance of observed values and the input variable; (d0) HARHA; (d1) ; (d2) ; (d3) ; (d4) ; (d5) AC; (d6) δmax.

To select the most appropriate GEP estimation model for HARHA treated expansive soils, several models with a varying number of genes were generated by employing a set of genetic operators (mutation, transposition, and crossover). Originally, a model composed of two genes with additional linking functions and head sizes of four (head size, H = 4) was selected and run a number of times. After that, the parameters were altered, in a stepwise order, by increasing the number of genes to three, head size to eight (head size, H = 8), number of chromosomes to 50, and weights of function sets. The program was run various times for different models, and the predicted final models were checked and compared with regard to their performance. Furthermore, the parameters such as mutation rate, inversion, and points of recombination were chosen on the basis of past studies [32–34] and then assessed to obtain their optimum impact. After running several trials, the final mathematical model was obtained, for which the selected parameters including detailed information of the general, numerical constants, and the genetic operators, are listed in Table 4. The final prediction model was chosen on the basis of criteria of the best fitness and lesser complexity of the mathematical formulation, while the expression trees (ETs) are illustrated in Figures 7–9 for the model outcomes CBR, UCS28, and RValue, respectively.

Table 4: Parameters setting for GEP algorithms.

Parameters
Settings

CBR, UCS₂₈, RValue

General

Training records
81

Validation/Testing records
40

Number of chromosomes
50

Number of genes
3

Head size
8

Linking function
Addition

Function set
+, −, ×, ÷, exp, Sqrt, ln

Numerical constants

Constants per gene
10

Type of data
Floating point

Maximum complexity
10

Ephemeral random constant
[−10, 10]

Genetic operators

Mutation
0.00138

Inversion rate
0.00546

IS transposition rate
0.00546

RIS transposition rate
0.00546

One-point recombination rate
0.00277

Two-point recombination rate
0.00277

Gene recombination rate
0.00277

Uniform recombination
0.00755

(a)

(b)

(c)

Figure 7: Expression tree of the model formulated for CBR (where d0: HARHA, d1: , d2: , d3: , d4: , d5: AC, d6: δmax, Sub-ET1 C6: 438.77, Sub-ET1 C1: 5.829, Sub-ET2 C1: -3341.12, Sub-ET3 C1: 0.6831).

(a)

(b)

(c)

Figure 8: Expression tree of the model formulated for UCS (where d0: HARHA, d1: , d2: , d3: , d4: , d5: AC, d6: δmax, Sub-ET1 C9: -9.177, Sub-ET1 C1: -9.522, Sub-ET1 C6: -4.669, Sub-ET2 C3: 5.995, Sub-ET2 C8: 0.07915, Sub-ET3 C4: 5.3481, and Sub-ET3 C1: 3.479).

(a)

(b)

(c)

Figure 9: Expression tree of the model formulated for R value (where d0: HARHA, d1: , d2: , d3: , d4: , d5: AC, d6: δmax, Sub-ET2 C7: 1.4413, Sub-ET3 C2: -12.398, Sub-ET3 C6: 3.212).

In order to formulate the three models for the respective output parameters, initially, the input parameters were selected from the extensive experimental study, which is given below:

where CBR is California bearing ratio, UCS₂₈ is unconfined compression strength after 28 days, RValue is resistance value, HARHA is hydrated lime activated rice husk ash, is the liquid limit, is the plastic limit, is the plasticity index, is the optimum moisture content, AC is the activity value, and δmax is the maximum dry density.

The K-expressions and the genes nodal values for the ET of the modeled parameters of strength are presented as follows.

3.2.1. California Bearing Ratio

 Sqrt.Sqrt.+.−.−.−.+..d5.d5.d4.c6.c1.d4.d1.d6.d3 + .Sqrt.−.d0.+.+.−.+.c1.d3.d0.d2.d1.c1.d2.d1.d6 + .+.d6./.Exp./.c1.Ln.d2.d1.d5.d1.d2.d2.d5.d5.d4

Numerical Constants:

 Gene 1

 c0 = 6.01733451338237 c1 = 5.82940372479169 c2 = 11.2892741508225 c3 = −1.38096255378887 c4 = −7.16238898892178 c5 = 6.36524552140873 c6 = 438.770447855123 c7 = −3.76850684316538 c8 = −3.92196417126987 c9 = 5.34226508377331

 Gene 2

 c0 = 5.61693166905728 c1 = −33451.121590902 c2 = 9.04538102359081 c3 = 4.02193288475646 c4 = 7.06854457228309 c5 = −5.52471996798914 c6 = 9.28254036072878 c7 = −9.37192907498398 c8 = 7.87691579943236 c9 = 7.84859767448958

 Gene 3

 c0 = 9.3145542771691 c1 = 0.683142490481803 c2 = 0.65507980590228 c3 = 2.23527237769707 c4 = 2.1560127041438 c5 = −3.4600786347084 c6 = −0.443433942686239 c7 = 6.32145146031068 c8 = −243.307901242103 c9 = 3.60334589462102

3.2.2. Unconfined Compressive Strength

 .−.c9.+.d0.c1.Exp..d5.c6.d0.d0.d0.d3.d4.d2.c4 + ./.c3.Sqrt.d5./.−.+.d4.d0.c8.d5.d6.d0.c8.c1.d0 + −.+.+.+.−.d3.Sqrt.−.c4.d2.d4.d0.d1.c1.d5.d0.d1

Numerical Constants:

 Gene 1

 c0 = 9.40635120700705 c1 = −9.52207061952574 c2 = -6.06555375835444 c3 = 8.41547898800623 c4 = 6.96584978789636 c5 = 4.43152256843776 c6 = −4.66996057039345 c7 = −1.44721823786126 c8 = 2.64381847590564 c9 = −9.17752843515198

 Gene 2

 c0 = −6.69023712881863E-02 c1 = 1.7045835749382 c2 = 3.74612759288614 c3 = 5.99579447574825 c4 = −4.96296086938292 c5 = −3.58989226966155 c6 = −0.914639728995636 c7 = −6.71803949095126 c8 = 7.91580822137299E-02 c9 = −0.480693990905484

 Gene 3

 c0 = 8.17865535447249 c1 = 3.47497553241407 c2 = −6.28205053865169 c3 = −7.01719634907071 c4 = 5.34816290007036 c5 = 6.77358317819758 c6 = −4.4777053132725 c7 = −9.76500747703482 c8 = 8.85799737540819 c9 = 2.08953825495163

3.2.3. Resistance Value (R value)

 Sqrt../.Sqrt.Exp.d6.+.d5.d1.d4.d5.c5.d4.c5.d1.c7.d1 + /..d6.d0.Ln.+.−.+.d4.d5.c7.d4.c4.c1.d2.d1.d3 + +.Ln./.+./.−.+..d4.d3.d0.d2.c2.d4.d4.c6.c7

Numerical Constants:

 Gene 1

 c0 = −5.76100955229347 c1 = 4.89717612231819 c2 = −3.93536179692984 c3 = 3.23796197393719 c4 = −6.77412671285134 c5 = 3.29407635731071 c6 = 2.38074892422254 c7 = −3.36100344859157 c8 = 7.98272652363659 c9 = 3.71135593737602

 Gene 2

 c0 = -5.65450864340739 c1 = −7.65190588091678E-02 c2 = 0.593482469817356 c3 = −0.21698660237434 c4 = −7.5964995269631 c5 = −6.84987945188757 c6 = 3.66069521164586 c7 = 1.44131669080772 c8 = −7.00961638233589 c9 = 8.11291842097232

 Gene 3

 c0 = 2.97519449316012 c1 = −2.45399334696493 c2 = −12.3985913762825 c3 = 3.00576799829096 c4 = −6.60390026551103 c5 = 5.46067690054018 c6 = 3.21220500714347 c7 = 3.68913754692221 c8 = −10.8087886989959 c9 = −6.13330484939116

It has been reported earlier that multilinear regression (MLR) was conducted to evaluate quantitatively the relationships between the input soil hydraulic-prone properties and output soil strength properties, i.e., CBR, UCS28, and RValue. Each output value was defined as a combination of the six soil parameters (HARHA, , , , , AC, and δmax, respectively), and the following equations were derived:

These are useful tools to estimate the soil strength properties based on easily determinable geotechnical indices for HARHA treated expansive soils. However, these MLR equations can only be employed in the case when the points show linearly changing behavior [27]. These equations were derived from making a comparison with the developed GEP models for CBR, UCS28, and RValue.

Using the expression trees given from Figures 6–9 for evaluating the CBR, UCS28, and RValue of soils, respectively, decoding was done to derive the three simple mathematical expressions (equations (5)–(7)) as follows:

The comparisons between the predicted and the observed expansive soil parameters are shown in Figure 10. The indicators indicate high accuracy can be observed for CBR, UCS28, and RValue, with higher R² values for GEP formulated models. This suggests that the prediction of the output parameters using the proposed model is in good agreement with the testing data.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 10: Experimental versus predicted values of CBR, UCS, and R values for models formulated using GEP and MLR, respectively.

It can be seen in Figure 11 that the range of error distribution for CBR and RValue is significantly lower in contrast to that of UCS₂₈. It could be attributed to the larger SD value and range of data for the UCS₂₈, as reflected in Table 1. In addition, the GEP proposed models exhibit superior performance for CBR and RValue cases in comparison with the respective MLR plots. However, the results of GEP are not better than that of the MLR model in terms of error distribution which is shown in Figures 7(c) and 7(d), respectively.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 11: Error distribution diagram for CBR, UCS, and R value generated models using GEP and MLR, respectively.

Finally, the summary of statistical performance is listed in Table 5. Variety of performance indices have been determined, including root mean square error (RMSE), mean absolute error (MAE), root square error (RSE), Nash–Sutcliffe efficiency (NSE), relative root mean square error (RRMSE), coefficient of correlation (R), performance index (ρ), and objective function (OBF) to evaluate the performance of developed CBR, UCS, and R value GEP models. The following equations were used to calculate the performance indices. The RMSE errors are squared, implying that relatively a much larger weight is assigned to the larger errors. High R values and low RRMSE values achieve a high degree of accuracy, which agrees with the results of Gandomi and Roke [25]. The proposed models indicate that the MAE, RMSE, RSE, and RRMSE values are significantly lower while the NSE and R values are larger for the CBR and Rvalue, which shows superior model performance. However, these values are vice versa in the case of UCS₂₈ that leads to lower performance. Similarly, the performance indices and OBF values are well within allowable limits in the literature [32, 35, 36]. These results further show that the proposed models of CBR and RValue using GEP were much better than for the case of UCS₂₈, thereby achieving reliable and accurate results. The range of data for the input parameters of UCS₂₈ is several times greater than those of CBR and RValue, which is also reflected in Table 2. So, GEP models were used to formulate simple mathematical equations which can be readily employed to predict CBR, UCS28, and RValue values, as mentioned earlier in detail.where

where ei and are the i number of experimental and predicted outputs, respectively; and are the average values of the experimental and predicted output values, respectively, and n is total the number of samples.

Table 5: Statistical calculations, performance indices, and objective functions of the GEP models for CBR, UCS, and R value.

GEP model
Dataset
Statistical parameters

MAE
RSE
RMSE
NSE
R
RRMSE
ρ
OBF

CBR
Training
0.5
0.003
4.94
0.997
0.998
0.202
0.101
0.028

Testing
0.3
0.011
3.69
0.989
0.996
0.271
0.136

Validation
0.5
0.011
5.49
0.989
0.996
0.167
0.084

UCS₂₈
Training
7.8
0.151
13.06
0.849
0.924
0.076
0.040
0.013

Testing
2.7
0.970
12.21
0.903
0.971
0.081
0.041

Validation
13.7
0.647
13.61
0.353
0.624
0.067
0.041

RValue
Training
0.2
0.003
4.49
0.997
0.998
0.222
0.111
0.032

Testing
0.2
0.007
4.22
0.992
0.997
0.238
0.119

Validation
0.1
0.012
4.72
0.988
0.994
0.193
0.097

4. Conclusions

From the gene expression programming of California bearing ratio, unconfined compressive strength and resistance value of hydrated-lime modified expansive soil with input parameters; HARHA, liquid limit (), (plastic limit , plasticity index , optimum moisture content (), clay activity (AC), (maximum dry density (δmax), CBR, UCS, and R value generated from series of laboratory exercise which produced 121 datasets, the following can be concluded:

(1)The A-7-6 expansive soil and hydrated-lime activated rice husk were blended in varying proportions of the additive to the soil, and the modified blend specimens were tested to get the liquid limit, plastic limit, plasticity index, optimum moisture content, clay activity, maximum density, California bearing ration, unconfined compressive strength, and resistance value responses.(2)The responses were deployed to both MLR and GEP evolutionary operations to model the output parameters: CBR, UCS, and R value.(3)The outcome of the GEP training, testing, and validation of the datasets showed a consistent agreement between the MLR and GEP.(4)Three model equations were formed, each of MLR and GEP under optimized conditions, and the agreement between the predicted models and the generated datasets is above 0.9.(5)Generally, the GEP showed that design, construction, performance, and infrastructure management could be predicted with perfect accuracy using the gene expression programming soft computing method for sustainable earthworks and other engineering operations. This can be easily implemented when the treatment materials for construction are similar in properties to the ones used in this project and also when similar numbers of predictor parameters are used in proposing the model.(6)Lastly, it can be recommended to have more multiple experiments to generate upwards of a thousand datasets for a perfect and more reliable outcome.

Data Availability

The data used in the study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

References

K. C. Onyelowe, T. Amhadi, C. Ezugwu et al., “Strength of pozzolan soil blend in chemically improved lateritic soil for pavement base material purpose,” International Journal of Low-Carbon Technologies, vol. 14, no. 3, pp. 410–416, 2019.

K. C. Onyelowe, E. Onukwugha, A. B. Salahudeen et al., “Microstructural and mineralogical analysis of weak erodible soil for gully site study and solutions,” NIPES Journal of Science and Technology Research, vol. 1, no. 3, pp. 24–37, 2019.

K. Onyelowe et al., “Sorptivity, swelling, shrinkage, compression and durability of quarry dust treated soft soils for moisture bound pavement geotechnics,” Journal of Materials Research and Technology, vol. 8, no. 4, pp. 3529–3538, 2019.

K. C. Onyelowe, F. D. A. Onyelowe, D. Bui Van et al., “Valorization and sequestration of hydrogen gas from biomass combustion in solid waste incineration NaOH oxides of carbon entrapment model (SWI-NaOH-OCE Model),” Materials Science for Energy Technologies, vol. 3, pp. 250–254, 2020.

K. C. Onyelowe, D. Bui Van, M. O. Idrees et al., “An experimental study on compaction behaviour of lateritic soils treated with quarry dust based geopolymer cement,” The Journal of Solid Waste Technology and Management, 2021, In press.

K. C. Onyelowe, M. E. Onyia, E. R. Onukwugha et al., “Atterberg limits of modified compacted clayey soil for sustainable green subgrade structure,” Jurnal Kejuruteraan, 2021, In press.

K. C. Onyelowe, D. Bui Van, L. Dao-Phuc et al., “Evaluation of index and compaction properties of lateritic soils treated with quarry dust based geopolymer cement for subgrade purpose,” Epitőanyag– Journal of Silicate Based and Composite Materials, vol. 72, no. 1, pp. 12–15, 2020.

K. C. Onyelowe, M. E. Onyia, F. D. A. Onyelowe et al., “Critical state desiccation induced shrinkage of biomass treated compacted soil as pavement foundation Epitőanyag–,” Journal of Silicate Based and Composite Materials, vol. 72, no. 2, pp. 40–47, 2020.

K. C. Onyelowe, E. J. Fazal, E. O. Michael, C. O. Ifeanyichukwu, U. A. George, and I. Chidozie, “Artificial intelligence prediction model for swelling potential of soil and quicklime activated rice husk ash blend for sustainable construction,” Jurnal Kejuruteraan, 2021, In press.

K. C. Onyelowe, M. E. Onyia, D. Bui Van et al., “Shrinkage parameters of modified compacted clayey soil for sustainable earthworks,” Jurnal Kejuruteraan, vol. 33, no. 1, pp. 133–140, 2021, In press.

K. C. Onyelowe, F. A. Deborah, and D. Bui Van, “Overview of ash as supplementary cementitious silicate-based composite and construction material,” Epitőanyag–Journal of Silicate Based and Composite Materials, vol. 72, no. 3, pp. 80–85, 2020.

K. C. Onyelowe, D. Bui Van, C. Ikpa et al., “Resilient modulus and deviatoric stress of cemented soils treated with crushed waste ceramics (CWC) for pavement subgrade construction,” Epitőanyag–Journal of Silicate Based and Composite Materials, vol. 72, no. 3, pp. 86–90, 2020.

K. C. Onyelowe, M. E. Onyia, E. R. Onukwugha, O. C. Nnadi, I. C. Onuoha, and F. E. Jalal, “Polynomial relationship of compaction properties of silicate-based RHA modified expansive soil for pavement subgrade purposes,” Epitőanyag–Journal of Silicate Based and Composite Materials, vol. 72, no. 6, pp. 223–228, 2020.

D. Bui Van, K. C. Onyelowe, M. Onyia et al., “Strength and consistency behaviour of replacement of cement with silicate-based geopolymer cement modified soft soil treated with crushed waste glasses for pavement underlain,” Epitőanyag–Journal of Silicate Based and Composite Materials, vol. 72, no. 6, pp. 186–197, 2020.

A. B. Salahudeen, J. A. Sadeeq, A. Badamasi, and K. C. Onyelowe, “Prediction of unconfined compressive strength of treated expansive clay using back-propagation artificial neural networks,” Nigerian Journal of Engineering, vol. 27, no. 1, pp. 45–58, 2020.

G. U. Alaneme, K. C. Onyelowe, M. E. Onyia et al., “Modelling of the swelling potential of soil treated with quicklime-activated rice husk ash using fuzzy logic,” Umudike Journal of Engineering and Technology (UJET), vol. 6, no. 1, pp. 1–12, 2020.

G. U. Alaneme, K. C. Onyelowe, M. E. Onyia et al., “Modeling volume change properties of hydrated-lime activated rice husk ash (HARHA) modified soft soil for construction purposes by artificial neural network (ANN),” Umudike Journal of Engineering and Technology (UJET), vol. 6, no. 1, pp. 1–12, 2020.

G. U. Alaneme, K. C. Onyelowe, M. E. Onyia et al., “Comparative modelling of strength properties of hydrated-lime activated rice-husk-ash (HARHA) modified soft soil for pavement construction purposes by artificial neural network (ANN) and fuzzy logic (FL),” Jurnal Kejuruteraan, 2021, In press).

K. C. Onyelowe and M. E. Onyia, “Analytics of swelling potential on highly expansive (plastic) clayey soils behavior for sustainable admixture stabilization,” Jurnal Kejuruteraan, 2021, In press.

R. S. Faradondeh, D. J. Armaghani, M. Monjezi, and E. T. Mohamad, “Genetic programming and gene expression programming for flyrock assessment due to mine blasting,” International Journal of Rock Mechanics and Mining Sciences, vol. 88, pp. 254–264, 2016.

C. Ferreira, “Gene expression programming in problem solving,” Soft Computing and Industry, Springer, Berlin, Germany, 2002.

J. R. Koza and J. R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT press, Cambridge, MA, USA, 1992.

Z. L. Cheng, W. H. Zhou, and A. Garg, “Genetic programming model for estimating soil suction in shallow soil layers in the vicinity of a tree,” Engineering Geology, vol. 268, Article ID 105506, 2020.

A. Garg, A. Garg, and K. Tai, “A multi-gene genetic programming model for estimating stress-dependent soil retention curves,” Computational Geosciences, vol. 18, pp. 45–56, 2014.

A. H. Gandomi and D. A. Roke, “Assessment of artificial neural network and genetic programming as predictive tools,” Advances in Engineering Software, vol. 88, pp. 63–72, 2015.

K. Pearson, “X. On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling,” The London, Edinburgh and Dublin Philosophical Magazine and Journal of Sciences, vol. 50, pp. 157–175, 1900.

J. Gravier, V. Vignal, S. Bissey-Breton, and J. Farre, “The use of linear regression methods and Pearson’s correlation matrix to identify mechanical-physical-chemical parameters controlling the micro-electrochemical behavior of machined copper,” Corrosion Science, vol. 50, pp. 2885–2894, 2008.

K. N. Sircombe, “Age display: an EXCEL workbook to evaluate and display univariance geochronological data using binned frequency histograms and probability density distributions,” Computers and Geosciences, vol. 30, no. 1, pp. 21–31, 2004.

M. E. Edjabou, J. A. Martin-Fernandez, C. Scheutz, and T. F. Astrup, “Statistical analysis of solid waste composition data: arithmetic mean, standard deviation and correlation coefficients,” Waste Management, vol. 68, pp. 13–23, 2017.

C. Sharma and C. Ojha, “Statistical parameters of hydrometeorological variables: standard deviation, SNR, skewness and kurtosis,” Advances in Water Resources Engineering and Management, Springer, Berlin, Germany, 2020.

M. K. Cain, Z. Zhang, and K. H. Yuan, “Univariate and multivariate skewness and kurtosis for measuring nonnormality: prevalence, influence and estimation,” Behavior Research Methods, vol. 49, pp. 1716–1735, 2017.

M. F. Iqbal, Q. F. Liu, I. Azim et al., “Prediction of mechanical properties of green concrete incorporating waste foundry sand based on gene expression programming,” Journal of Hazardous Materials, vol. 384, Article ID 121322, 2020.

G. B. Jumaa and A. R. Yousef, “Predicting shear capacity of FRP-reinforced concrete beams without stirrups by artificial neural networks, gene expression programming and regression analysis,” Advances in Civil Engineering, vol. 2018, Article ID 5157824, 2018.

M. F. Javed, M. N. Amin, M. I. Shah et al., “Applications of gene expression programming and regression techniques for estimating compressive strength of bagasse ash-based concrete,” Crystals, vol. 10, p. 737, 2020.

M. I. Shah, M. F. Javed, and T. Abunama, “Proposed formulation of surface water quality and modeling using gene expression, machine learning and regression techniques,” Environmental Science and Pollution Research, vol. 28, pp. 13202–13220, 2021.

K. C. Onyelowe, M. Onyia, E. R. Onukwugha, D. Bui Van, J. Obimba-Wogu, and C. Ikpa, “Mechanical properties of fly ash modified asphalt treated with crushed waste glasses as fillers for sustainable pavements,” Epitőanyag–Journal of Silicate Based and Composite Materials, vol. 72, no. 6, pp. 219–222, 2020.