# Multi Expression Programming Model for Strength Prediction of Fly-Ash-Treated Alkali-Contaminated Soils

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## Abstract

**:**

_{kaolin}and UCS

_{BC}soils was also studied. Sufficient laboratory test data comprising 384 data points were collected, and multi expression programming (MEP) was used to create tree-based models for yielding simple prediction equations to compute the UCS

_{kaolin}and UCS

_{BC}soils. The experimental results reflected that alkali contamination resulted in reduced UCS (36% and 46%, respectively) for the kaolin and BC soil, whereas the addition of FA resulted in a linear rise in the UCS. The optimal dosage was found to be 20%, and the increase in UCS may be attributed to the alkali-induced pozzolanic reaction and subsequent gain of the UCS due to the formation of calcium-based hydration compounds (with FA addition). Furthermore, the developed models showed reliable performance in the training and validation stages in terms of regression slopes, R, MAE, RMSE, and RSE indices. Models were also validated using parametric and sensitivity analysis which yielded comparable variation while the contribution of each input was consistent with the available literature.

## 1. Introduction

_{kaolin}and UCS

_{BC}soils was also evaluated for the aforementioned varying curing periods.

## 2. Materials and Methods

#### 2.1. Laboratory Studies

#### 2.2. MEP Model Development

_{kaolin}and UCS

_{BC}soil was performed in the Multi-Expression Programming X (MEPX version 2021.08.28.0-beta) by incorporating experimental records, as shown in Table 3. Sufficient laboratory test data of 384 different soils for the UCS prediction of FA-treated alkali-contaminated soils were collected by performing an experimental study [42]. The MEP genes are the substrings of varying lengths that keep the chromosomal length constant and equivalent to the total genes on each chromosome. Each gene provides instructions for making a function or a terminal sign, whereas a gene encoding a function includes addresses to the function parameters. The function arguments always have lower parameter estimates than the location of the function on that chromosome [41]. A detailed methodology for generating equations is provided here, and details of the advanced GP approach (MEP simulation) can be found elsewhere [34,35,39,42,43,44,45].

_{kaolin}and UCS

_{BC}) used to perform strength prediction of FA-treated alkali-contaminated soils in the case of both training and testing data. The maximum as well as the minimum values of all the input and output characteristics have been tabulated in Table 4. Figure 1 shows the frequency histograms (i.e., the scatter of the data) of the input attributes considered in the current study. The curves are smooth and uniformly distributed, which shows a good type of data. In addition, standard deviation (SD), kurtosis, and skewness for all the parameters are given. A smaller SD shows that the parameters are near the respective average value. The kurtosis value represents the sharpness of the peak of a frequency distribution curve. It clarifies the shape of probability distribution [34]. It is pertinent to mention that the kurtosis value is only useful when used in conjunction with the SD value. It is possible that an attribute might have a high kurtosis (bad), but the overall standard deviation is low (good). A kurtosis value of ±1 is considered very good for most psychometric uses, but ±2 is also usually acceptable. The kurtosis values of FA dosage, alkali concentration, curing days, and UCS

_{kaolin}approach zero and therefore represent a mesokurtic distribution which can be seen in the histogram plot, i.e., Figure 1. However, the kurtosis value in the case of UCS

_{kaolin}is comparatively higher, which represents a leptokurtic distribution (Figure 1). Lastly, the skewness depicts the extent to which a distribution of values deviates from symmetry around the mean. Bryne (2010) argued that data are considered to be normal if skewness is between −2 and +2.

_{kaolin}and UCS

_{BC}. It can be seen that the impact of all the three input parameters is linearly increasing (because r-values are positive). In the case of both UCS

_{kaolin}and UCS

_{BC}, the order of increasing impact of parameters follows the order: FA dosage > alkali concentration > curing age.

_{kaolin}and UCS

_{BC}with an optimal combination of hyperparameters are provided in Table 6. The set of hyperparameters (i.e., number of subpopulations, size of subpopulations, code length, tournament size, and number of generations) was varied in this study to achieve the optimal performance of models. A single parameter was modified whereas the rest were kept unchanged (as shown in Table 7) in an attempt to investigate the effect of different code settings on the correlation coefficient (R) and the mean squared error (MSE), as shown in Figure 2 and Figure 3, respectively.

_{kaolin}, the best performance was noted in the case of Trial 18 (R = 0.9465, Averaged MSE = 1245), wherein the number of subpopulations, size of subpopulation, code length, number of generations, and tournament size were kept as 20, 1000, 100, 150, and 6, respectively. On the other hand, in determining the UCS

_{BC}, the best performance was noted in the case of Trial 14 (R = 0.9672, Averaged MSE = 2220), wherein the number of subpopulations, size of subpopulation, code length, number of generations, and tournament size equal 100, 2000, 80, 150, and 2, respectively.

_{kaolin}(Equation (1)) and UCS

_{BC}(Equation (2)) were obtained, via C++ code, in order to predict the targeted UCS.

## 3. Results and Discussion

#### 3.1. Strength Characteristics

#### 3.1.1. Effect of Alkali Contamination

_{kaolin}and UCS

_{BC}with curing periods and alkali concentrations is presented in Figure 4. The UCS

_{kaolin}and UCS

_{BC}linearly decreased with the rise in alkali concentration, and BC soil exhibited a relatively greater fall in the UCS compared to kaolin soil. With the increase in curing periods, both the soils increased linearly for the controlled case. However, under the contaminated case, the kaolin soil exhibited a slight increase in the UCS, whereas the UCS

_{BC}remained constant at lower curing periods and was drastically reduced at higher curing periods. The variation in UCS

_{kaolin}and UCS

_{BC}in the untreated case can be attributed to their inherent mineralogical difference which enables the formation of primary hydration compounds [4]. Under a contaminated scenario, the linear decrease in UCS

_{kaolin}and UCS

_{BC}soils may be attributed to the increase in charge of clay particles with the pH of the soil. The rise in pH contributes to the subsequent dissolution of silica which varies with the size and crystallinity of quartz, a commonly found mineral in both the soils [4]. Furthermore, an increase in the UCS

_{kaolin}with the curing period may be attributed to the precipitation of hydration compounds such as nontronite and sodium silicate hydrate. Similar observations for clayey soils were made by Sivapullaiah and Reddy [4].

#### 3.1.2. Effect of FA Dosage and Curing Period

_{kaolin}and UCS

_{BC}with the alkali concentrations and FA dosage is presented in Figure 5. Considering brevity, the results pertaining to a 28-day curing period have been presented here. It is evident from the results that the FA addition has contributed sufficiently to the linear increase in the UCS

_{kaolin}and UCS

_{BC}for both the controlled and alkali-contaminated cases. In contrast to the contaminated case, the increase in the UCS

_{BC}is substantially higher with an increment of more than 900% compared to the 350% increase noted for kaolin soil. The increase in UCS

_{kaolin}and UCS

_{BC}is more pronounced at higher concentrations. The linear increase in UCS of both soils is attributed to the decrease in clay content with the FA addition [2]. The greater increment at higher concentration is attributed to the greater affinity of dissolved silica (due to higher concentration of alkali) to react with calcium from FA and subsequent formation of pozzolanic compounds. The pozzolanic compounds formed not only resist alkali attack on mineral phases of soil but also offer greater resistance to compressive loading which is manifested in the form of increased UCS [4,19].

#### 3.2. Comparison between Experimental and Predicted Results

_{kaolin}and UCS

_{BC}, using a variety of performance indices. To evaluate the prediction efficiency and accuracy of the proposed MEP models using MEPX software, eight analytical standard indicators, namely regression line slope, correlation coefficient (R), root mean squared error (RMSE), mean absolute error (MAE), root squared error (RSE), relative root mean square error (RRMSE), Nash–Sutcliffe efficiency (NSE) and performance index (ρ) were used in this study [46,47]. These performance measures are defined by the following Equation (3) to Equation (9):

_{i}and P

_{i}are the ith actual and predicted output values, respectively; ${\overline{E}}_{i}$ and ${\overline{P}}_{i}$ are the average values of the actual and predicted output values, respectively; and n is the number of samples. In addition, the objective function (OBF), as given in Equation (10), shall have a minimum value for better formulation of the model. A smaller OBF helps in overcoming the overfitting problem. A value approaching zero exhibits an excellent predictive capability.

_{kaolin}and UCS

_{BC}in the training and validation phases, as well as the efficacy metrics (i.e., slope, R, RMSE, MAE, RSE, RRMSE, and ρ), are shown in Figure 6a,b, respectively. The 45° regression line with a horizontal axis depicts the ideally fit (1:1) line having an inclination corresponding to 1 [49,50]. For good, reliable, and highly correlated models, the dispersion pattern of the data points should be closer to the diagonal line crossing the origin, with a trend line of slope approximately equaling unity, R-value greater than 0.8, and reduced error measurements (i.e., R, RMSE, MAE, RSE, RRMSE, and ρ), as shown in Figure 6 and Table 8. For both the kaolin and BC soil, the slopes of the trend lines are closer to 1 (0.90: training, 1.01: validation; 0.97: training, 0.96: validation, respectively). In addition, the R is above 0.8 (closer to 1) for both types of soils, which reflects a reasonably strong correlation between the model predicted outputs (i.e., UCS

_{kaolin}and UCS

_{BC}) and experimental observations. Furthermore, the OBF value of kaolin soil was 0.025694481, whereas that of BC soil was 0.025050897 in the current study.

_{kaolin}model has MSE and MAE equaling 1245 and 19.6 and 2220 MPa and 30 for the training and validation phases, respectively. Likewise, the discussed attributes are also lower for the optimized UCS

_{BC}model. Furthermore, for both optimized models, the RSE tends to approach zero in each phase (i.e., training and validation), confirming their superior functionality. The consistent and accurate performance of the developed models is due to the structural flow of the MEP algorithm. The MEP follows the reproduction procedure to move the relevant information to the subsequent generation and uses the mutation function for optimization inside the chosen chromosomes.

_{kaolin}model (Figure 7a) are −160 kPa and 100 kPa, respectively, and are ±130 kPa for the UCS

_{BC}model (Figure 7b). The majority of the error readings run along the x-axis, indicating a significant frequency of low error values. In conjunction with significantly higher correlations and reduced error measurements, the proposed models could be advantageously employed for the prediction of UCS

_{kaolin}and UCS

_{BC}, assisting practitioners and designers to save time and skip costly laboratory tests.

_{kaolin}and UCS

_{BC}can be seen in Figure 8a,b, respectively. In each case, the modeled values of the training and validation phases almost go along the observed (experimental) output, which shows the efficiency and accuracy of the formulated MEP models.

_{kaolin}and UCS

_{BC}soil, which will aid in avoiding the heavy testing process.

#### 3.3. Model Validity

_{kaolin}and UCS

_{BC}shown as sensitivity and parametric analysis.

#### Sensitivity Analysis and Parametric Study of MEP Model

_{i}). Next, the second independent variable was changed and the output was monitored.

## 4. Conclusions

_{kaolin}and UCS

_{BC}) to overcome the demerits of laborious laboratory testing, cost, and time. The following conclusions can be drawn from the study:

- The inundation of kaolin and BC soils in alkali solution caused the UCS property to decrease. The higher concentrations posed a significant impact in lowering the UCS
_{kaolin}and UCS_{BC}. On the contrary, the FA treatment of alkali-contaminated soils resulted in a linear increase in the UCS_{kaolin}and UCS_{BC}, and an increase of 7-fold was witnessed for the BC soil. Hence, it is concluded that the alkali contamination acted as an activator for a subsequent pozzolanic reaction when FA was incorporated. - In order to obtain the optimal MEP model for predicting the UCS
_{kaolin}and UCS_{BC}, a total of 18 trials (each) were undertaken while considering the variation in (a) number of subpopulations, (b) subpopulation size, (c) code length, (d) tournament size, and (e) number of generations. The corresponding performance of all the trials was evaluated using a variety of performance indices, i.e., correlation coefficient and averaged MSE value. The best MEP model (kaolin and BC soil) was achieved in the case of 20 and 70 subpopulations, 1000 and 50 subpopulation size, 100 each code length, 6 each tournament size, 150 and 100 number of generations, 0.9465 and 0.9538 R-value, and 1245 kPa and 4400 kPa averaged MSE value, respectively. - Simple regression equations developed in this study (Equations (1) and (2)) for kaolin and BC contaminated soils can readily be used to forecast the UCS property. The equations have been generated from relatively high accuracy models evaluated using R, MAE, RMSE, and RSE (0.937, 19.6, 18.271, 0.128 and 0.956, 30, 17.151, 0.108) for the training data of kaolin and BC soils, respectively.
- The generated models were evaluated using parametric and sensitivity analysis as second-level validation. The results obtained from the parametric study manifested a variation in UCS conforming to the literature for kaolin and BC soil with the change in the given input parameters. The sensitivity analysis of kaolin soil showed that curing period and alkali concentration had comparable contributions, followed by the FA dosage, whereas for BC, soil the following increasing trend was observed: curing period > alkali concentration > FA dosage.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Frequency histograms of the input and output parameters: (

**a**) fly ash dosage (%), (

**b**) alkali concentration (N), (

**c**) curing age (days), (

**d**) UCS

_{kaolin}, and (

**e**) UCS

_{BC}.

**Figure 2.**Comparison of normalized averaged MSE and correlation for the developed MEP model for kaolin soil.

**Figure 3.**Comparison of normalized averaged MSE and correlation for the developed MEP model for BC soil.

**Figure 4.**The variation in UCS

_{kaolin}and UCS

_{BC}with curing period and concentration of alkali after a 28-day curing period.

**Figure 6.**Comparison of experimental and predicted results to evaluate the UCS in the case of (

**a**) kaolin soil and (

**b**) BC soil.

**Figure 7.**Error analysis of the developed models to evaluate the UCS in the case of (

**a**) kaolin soil and (

**b**) BC soil.

**Figure 8.**Tracing of experimental results by predicted values to evaluate the UCS in the case of (

**a**) kaolin soil and (

**b**) BC soil.

**Figure 10.**Parametric study of input variables for kaolin and BC soil MEP models: (

**a**,

**d**) fly ash dosage, (

**b**,

**e**) alkali concentration, and (

**c**,

**f**) curing period.

Property | Kaolin Soil | BC Soil |
---|---|---|

Specific gravity | 2.56 | 2.65 |

pH | 7.3 | 7.1 |

USCS classification | CH | CH |

Liquid limit (%) | 41 | 62 |

Plasticity index (%) | 19 | 28 |

Optimum moisture content (%) | 17 | 23 |

Maximum dry density (g/cc) | 1.81 | 1.67 |

Chemical Constituents | Value (%) |
---|---|

Silica (SiO_{2}) | 62.9 |

Alumina (Al_{2}O_{3}) | 21.7 |

Ferric oxide (Fe_{2}O_{3}) | 4.5 |

Calcium oxide (CaO) | 6.8 |

Magnesia (MgO) | 1.08 |

Titanium (TiO_{2}) | 0.06 |

Potash (K_{2}O) | 0.04 |

Sulfur (SO_{3}) | 0.7 |

Loss on ignition | 2.21 |

S. No. | Fly Ash Dosage (%) | Alkali Concentration (N) | Curing Age (Days) | UCS_{BC} (kPa) | UCS_{kaolin} (kPa) |
---|---|---|---|---|---|

1 | 0 | 0 | 1 | 280 | 255 |

2 | 0 | 0 | 1 | 271 | 261 |

3 | 0 | 0 | 1 | 269 | 259 |

4 | 0 | 0 | 1 | 286 | 275 |

5 | 0 | 0 | 1 | 278 | 268 |

6 | 0 | 0 | 1 | 288 | 277 |

7 | 0 | 0 | 7 | 272 | 262 |

8 | 0 | 0 | 7 | 274 | 264 |

9 | 0 | 0 | 7 | 281 | 270 |

10 | 0 | 0 | 7 | 286 | 275 |

11 | 0 | 0 | 7 | 289 | 278 |

12 | 0 | 0 | 7 | 280 | 269 |

13 | 0 | 0 | 14 | 300 | 265 |

14 | 0 | 0 | 14 | 280 | 262 |

15 | 0 | 0 | 14 | 298 | 279 |

16 | 0 | 0 | 14 | 285 | 266 |

17 | 0 | 0 | 14 | 301 | 281 |

18 | 0 | 0 | 14 | 296 | 277 |

19 | 0 | 0 | 28 | 310 | 270 |

20 | 0 | 0 | 28 | 286 | 267 |

21 | 0 | 0 | 28 | 296 | 277 |

22 | 0 | 0 | 28 | 308 | 288 |

23 | 0 | 0 | 28 | 301 | 281 |

24 | 0 | 0 | 28 | 296 | 276 |

25 | 0 | 1 | 1 | 267 | 236 |

26 | 0 | 1 | 1 | 260 | 231 |

⁝ | ⁝ | ⁝ | ⁝ | ⁝ | ⁝ |

378 | 20 | 4 | 14 | 631 | 851 |

379 | 20 | 4 | 28 | 729 | 998 |

380 | 20 | 4 | 28 | 732 | 987 |

381 | 20 | 4 | 28 | 750 | 996 |

382 | 20 | 4 | 28 | 745 | 1040 |

383 | 20 | 4 | 28 | 732 | 1012 |

384 | 20 | 4 | 28 | 740 | 1004 |

Fly Ash Dosage (%) | Alkali Concentration (N) | Curing Age (Days) | UCS_{BC} (kPa) | UCS_{kaolin} (kPa) | |
---|---|---|---|---|---|

Minimum | 0 | 0 | 1 | 44 | 119 |

Maximum | 20 | 4 | 28 | 750 | 1040 |

Mean | 11.25 | 1.75 | 12.5 | 379.51 | 369.06 |

Median | 12.5 | 1.5 | 10.5 | 365 | 325.5 |

SD | 7.40 | 1.48 | 10.06 | 109.14 | 183.30 |

Kurtosis | −1.1537 | −1.1537 | −1.1427 | 1.1374 | 2.2691 |

Skewness | −0.4364 | 0.4364 | 0.5025 | 0.8667 | 1.4534 |

**Table 5.**Pearson correlation coefficient values for the input parameters and the UCS of alkali-contaminated soils.

Fly Ash Dosage (%) | Alkali Concentration (N) | Curing (Days) | UCS_{kaolin,BC} (kPa) | |
---|---|---|---|---|

Fly ash dosage (%) | 1 | |||

Alkali concentration (N) | 0 | 1 | ||

Curing age (days) | 0 | 0 | 1 | |

UCS_{kaolin} (kPa) | 0.589906 | 0.508303 | 0.185189 | 1 |

UCS_{BC} (kPa) | 0.724809 | 0.270496 | 0.321986 | 1 |

**Table 6.**Parameter setting for MEP algorithm settings for strength prediction of fly-ash-treated alkali-contaminated soils.

Parameters | Kaolin Soil | BC Soil |
---|---|---|

Number of subpopulations | 20 | 100 |

Subpopulation size | 1000 | 2000 |

Code length | 100 | 80 |

Crossover probability | 0.9 | 0.9 |

Crossover type | Uniform | |

Mutation probability | 0.001 | |

Tournament size | 2 | |

Operators | 0.5 | |

Variables | 0.5 | |

Constants | 0 | |

Number of generations | 150 | |

Function set | +, −, ×, / | |

Terminal set | Problem input | |

Replication number | 10 | |

Error measure | Mean squared error | |

Problem type | Regression | |

Simplified | Yes | |

Random seed | 0 | |

Number of runs | 10 | |

Number of threads | 1 |

MEP Trial | No. of Subpopulation | Subpopulation Size | Code Length | No. of Generations | Tournament Size | R^{2} | R | Avg. MSE | Time (min) |
---|---|---|---|---|---|---|---|---|---|

Kaolin Soil | |||||||||

1 | 10 | 100 | 20 | 100 | 2 | 68.54 | 82.79 | 8148 | 1 |

2 | 20 | 69.28 | 83.23 | 7489 | 1 | ||||

3 | 70 | 66.27 | 81.41 | 7177 | 2 | ||||

4 | 100 | 66.27 | 81.41 | 4436 | 3 | ||||

5 | 200 | 64.57 | 80.36 | 5209 | 6 | ||||

6 | 100 | 500 | 77.20 | 87.86 | 2937 | 25 | |||

7 | 1000 | 79.09 | 88.93 | 2521 | 48 | ||||

8 | 1500 | 78.89 | 88.82 | 2562 | 72 | ||||

9 | 2000 | 80.34 | 89.63 | 2485 | 85 | ||||

10 | 30 | 82.60 | 90.88 | 2109 | 130 | ||||

11 | 50 | 83.66 | 91.47 | 1951 | 220 | ||||

12 | 80 | 87.19 | 93.38 | 1527 | 300 | ||||

13 | 100 | 87.65 | 93.62 | 1474 | 429 | ||||

14 | 150 | 88.98 | 94.33 | 1455 | 667 | ||||

15 | 200 | 88.00 | 93.81 | 1315 | 925 | ||||

16 | 20 | 1000 | 150 | 87.19 | 93.37 | 1551 | 40 | ||

17 | 4 | 89.33 | 94.51 | 1895 | 106 | ||||

18 | 6 | 89.58 | 94.65 | 1245 | 102 | ||||

BC Soil | |||||||||

1 | 10 | 100 | 20 | 100 | 2 | 72.45 | 85.12 | 14,697 | 1 |

2 | 20 | 2 | 78.02 | 88.33 | 10,980 | 1 | |||

3 | 70 | 2 | 77.81 | 88.21 | 11,187 | 2 | |||

4 | 100 | 2 | 77.56 | 88.07 | 9578 | 3 | |||

5 | 200 | 2 | 76.39 | 87.40 | 9804 | 8 | |||

6 | 100 | 500 | 2 | 79.19 | 88.99 | 8733 | 23 | ||

7 | 1000 | 2 | 80.26 | 89.59 | 8486 | 52 | |||

8 | 1500 | 2 | 81.13 | 90.07 | 8105 | 100 | |||

9 | 2000 | 2 | 80.88 | 89.93 | 8026 | 145 | |||

10 | 30 | 2 | 79.26 | 89.03 | 7993 | 190 | |||

11 | 50 | 2 | 78.80 | 88.77 | 7256 | 330 | |||

12 | 80 | 2 | 80.55 | 89.75 | 6592 | 357 | |||

13 | 100 | 2 | 80.00 | 89.44 | 7633 | 393 | |||

14 | 80 | 150 | 2 | 93.54 | 96.72 | 2220 | 552 | ||

15 | 200 | 2 | 92.19 | 96.02 | 2638 | 549 | |||

16 | 70 | 500 | 100 | 100 | 2 | 70.11 | 83.73 | 8450 | 90 |

17 | 4 | 87.66 | 93.63 | 5976 | 110 | ||||

18 | 6 | 90.97 | 95.38 | 4400 | 112 |

Dataset | Performance Index | Kaolin Soil | BC Soil |
---|---|---|---|

Training | R | 0.93713 | 0.95661 |

RMSE | 18.271 | 17.151 | |

MAE | 19.6 | 30.0 | |

RSE | 0.1280 | 0.1078 | |

RRMSE | 0.0543 | 0.0564 | |

NSE | 0.8720 | 0.8922 | |

ρ | 0.0280 | 0.02882 | |

Testing | R | 0.90014 | 0.96243 |

RMSE | 21.987 | 22.995 | |

MAE | 30.5 | 54.7 | |

RSE | 0.1972 | 0.0841 | |

RRMSE | 0.0458 | 0.0441 | |

NSE | 0.8028 | 0.9159 | |

ρ | 0.0241 | 0.0225 |

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## Share and Cite

**MDPI and ACS Style**

Khan, K.; Ashfaq, M.; Iqbal, M.; Khan, M.A.; Amin, M.N.; Shalabi, F.I.; Faraz, M.I.; Jalal, F.E.
Multi Expression Programming Model for Strength Prediction of Fly-Ash-Treated Alkali-Contaminated Soils. *Materials* **2022**, *15*, 4025.
https://doi.org/10.3390/ma15114025

**AMA Style**

Khan K, Ashfaq M, Iqbal M, Khan MA, Amin MN, Shalabi FI, Faraz MI, Jalal FE.
Multi Expression Programming Model for Strength Prediction of Fly-Ash-Treated Alkali-Contaminated Soils. *Materials*. 2022; 15(11):4025.
https://doi.org/10.3390/ma15114025

**Chicago/Turabian Style**

Khan, Kaffayatullah, Mohammed Ashfaq, Mudassir Iqbal, Mohsin Ali Khan, Muhammad Nasir Amin, Faisal I. Shalabi, Muhammad Iftikhar Faraz, and Fazal E. Jalal.
2022. "Multi Expression Programming Model for Strength Prediction of Fly-Ash-Treated Alkali-Contaminated Soils" *Materials* 15, no. 11: 4025.
https://doi.org/10.3390/ma15114025