DOI:https://doi-002.org/6812/17721756056489

Abdullah Alzlfawi                                                           

Department of Civil and Environmental Engineering, College of Engineering, Majmaah

University, Al Majmaah 11952, Saudi Arabia; a.alzlfawi@mu.edu.sa

Abstract

The problem of estimating the settlement of shallow foundations on cohesionless soils is very complex and not yet entirely understood. Over the years, many methods have been developed to predict the settlement of shallow foundations on cohesionless soils. However, methods for such predictions that have the required degree of accuracy and consistency have not yet been developed. Accurate prediction of settlement is essential since settlement, rather than bearing capacity, generally controls the design process of shallow foundations. In this research Long Short-Term Memory Network (LSTM) is used in an attempt to obtain more accurate settlement prediction. A total of 189 in situ test data were gathered from the literature to build the LSTM model. The following factors are regarded as inputs: footing width (B), footing pressure (q), footing geometry (L/B), number of standard penetration test blows count (N), and embedment ratio (DF/B). The output parameter is settlement (Sm) The performance of LSTM model was evaluated using metrics such as coefficient of determination (R²), root mean square error (RMSE), and mean average error (MAE) to assess the prediction accuracy. The results demonstrate that the LSTM model exhibits high predictive accuracy, R²=0.95, RMSE=5.588, MAE =2.457, and r = 0.976 on the training dataset, R²=0.91, RMSE=8.459, MAE =5.669, and r = 0.955 on the testing dataset, R²=0.774, RMSE=13.398, MAE =6.773, and r = 0.889 on the validation dataset. These outcomes indicate that the LSTM model is capable of predicting foundation settlement with reasonable accuracy when compared to other methods reported in the literature.

Keywords: Shallow foundation, Settlement, Cohessionless soil, Long Short-Term Memory Network.

1.  Introduction

The settlement of shallow foundations is usually divided into three components: (a) immediate or distortion settlement, (b) consolidation settlement and (c) secondary compression settlement. Immediate settlement occurs with load application during, or immediately after, the erection of a structure. It is primarily a consequence of soil-grain distortion and reorientation. Consolidation settlement, on the other hand, is time-dependent and generally takes months to years to occur and is due to the dissipation of pore water pressure over time. Secondary compression settlement occurs as a result of soil creep, which is viscous flow under loading with no changes in effective stress. The total settlement of a foundation is the sum of the above three components. For cohesionless soils, only the immediate settlement is of concern, whereas consolidation and secondary compression settlements are the primary factors associated with cohesive soils.

The prediction of settlement of shallow foundations on cohesionless soils is very complex and not yet entirely understood. This can be attributed to the fact that settlement is governed by many factors that are uncertain and difficult to quantify. Among these factors are the distribution of applied stress [1], the stress- strain properties of the soil, soil compressibility and the difficulty in obtaining undisturbed samples of cohesionless soils for laboratory testing.

The challenge of prediction of shallow foundations on cohessionless soil is exceedingly complicated and remains unsolved since settlement is regulated by several unpredictable and unquantifiable variables [2]. Some of these variables include the distribution of applied stress, soil stress and strain parameters, soil compressibility, and the difficulty of collecting undisturbed samples of cohesionless soil. Therefore, because of its correlation with various variable variations, settlement behavior is an extremely difficult engineering challenge. Due to the difficulties of obtaining undisturbed samples for cohesionless soil, several settlement prediction methods have focused on the correlation between in situ studies, such as the standard penetration test (SPT) [3], cone penetration test (CPT) [4], dilatometer test [5], and plate load test [6]. Most of the existing solutions solve the problem by making a number of assumptions about the factors that influence settlement. These approaches are therefore unable to produce a reliable and accurate settlement forecast.

The geotechnical literature contains many methods, both theoretical and experimental, to predict settlement of shallow foundations on cohesionless soils. Due to the difficulties of obtaining undisturbed samples for cohesionless soil, several settlement prediction methods have focused on

the correlation between in situ studies, such as the standard penetration test (SPT) [3], cone penetration test (CPT) [4], dilatometer test [5], and plate load test [6]. Most of the existing solutions solve the problem by making a number of assumptions about the factors that influence settlement. These approaches are therefore unable to produce a reliable and accurate settlement forecast. Consequently, consistent and accurate prediction of settlement has yet to be achieved by the use of a variety of methods ranging from purely empirical to complex non-linear finite elements [7], Comparative studies of the available methods e.g. [8]; [9]; [10]; [11] indicate inconsistent prediction of the magnitude of settlements. As a result, alternative methods are needed, which can overcome the limitations of the existing methods and provide more accurate settlement prediction. In geotechnical engineering, predicting settlement in shallow foundations on cohesion less soil is crucial. Traditional methods often lack accuracy. Geotechnical engineering’s challenges with complex soil and rock behavior have found a solution in Artificial Intelligence (AI), particularly in modeling shallow foundations. AI’s adaptability, learning capacity, non-linearity handling, and data-driven approach enhance predictive accuracy, but it also faces limitations like data requirements and interpretability issues. This review highlights AI’s promise in addressing geotechnical complexities and the importance of understanding its strengths and weaknesses compared to traditional methods [12]. Predicting settlement in shallow foundations on uncertain cohesionless soils is a challenge for traditional methods. Recent advances in machine learning, specifically ensemble models like Bagging and XGBoost, offer promise by effectively addressing soil uncertainty. These models outperform traditional methods and other machine learning models, with evaluation criteria including R-squared, RMSE, and MAE. However, data quality and potential overfitting should be considered in their application, and further research is needed for practical engineering validation [13].

Artificial neural networks (ANN) have been used to solve a number of geotechnical engineering challenges in recent years, with some degree of success.[14] provide a summary of ANN applications in geotechnical engineering. ANN are numerical modeling approaches used to represent the functioning of the human brain and nervous system.

The intention of this study is to apply an alternative approach to obtain more accurate settlement prediction. The approach has been successfully applied to many problems including those of a geotechnical engineering nature and is known as Machine Learning. Machine learning (ML) is the scientific study of algorithms and statistical models that computer systems use to perform a

specific task without being explicitly programmed. ML is used to teach machines how to handle the data more efficiently. Sometimes after viewing the data, we cannot interpret the extract information from the data. In that case, we apply machine learning.

In this research LSTM is used in an attempt to obtain more accurate settlement prediction. A total of 189 in situ test data were gathered from the literature to build the LSTM model. The following factors are regarded as inputs: footing width (B), footing pressure (q), footing geometry (L/B), number of standard penetration test (SPT) blows number (N), and embedment ratio (Df/B). The output parameter is measured settlement. The performance of these models will be evaluated using metrics such as correlation coefficient (R²), root mean square error (RMSE), and mean average error (MAE) to assess the prediction accuracy. In this paper, LSTM algorithm is used to predict the settlement of shallow foundations on cohesionless soils. The objectives of the paper are:

1. To investigate the feasibility of the LSTM technique for predicting the settlement of shallow foundations on cohesionless soils and to provide executable models for routine use in practice; and
2. To compare the performance of the LSTM model with some of the most commonly used methods developed in literature.

2.  Data Catalog

The database consist of 189 individual cases, 125 cases were reported by [15], 22 cases by [16], 5

cases by [17], 30 cases by [11] , 4 cases by [18], 1 case by [19] and 2 cases by [20]. Total of 189 in situ test data were gathered from the literature to build the LSTM model. The following factors are regarded as inputs: footing width (B), footing pressure (q), footing geometry (L/B), number of standard penetration test blows count (N), and embedment ratio (DF/B). The output parameter is settlement (Sm). Figure 1 depicts the correlations between several parameters in the dataset. All of the input and output variables under study were correlated using the Pearson’s correlation coefficient (r). Each cell in the plot has a correlation coefficient, which represents the strength of relationship between two factors. The “r” between the various parameters in Figure 1 is evaluated as follows:

r(m, m¢) = cov(m, m¢)

smsm¢

(1)

where cov = covariance, 𝜎_𝑚 = the standard deviation of m while 𝜎_𝑚′ = the standard deviation of

m’. The coefficients range from -1 to 1, indicating the strength and direction of the correlation. As

shown in Figure 1, some correlations between features are moderately correlated (i.e., r between

0.40 and 0.69) than others. For example, pairwise features N–q and Df/B–B are moderately

correlated (i.e., r =0.41 and r =0.43) On the hand, correlation coefficients less than 0.40 are

weekly correlated (e.g., q–B, N–B, L/B–q, Sm–B, Sm–q).

Figure 1. Pearson’s correlation matrix of the dataset.

3.  LSTM Modeling

LSTM networks are a type of recurrent neural network (RNN) architecture capable of detecting long-term dependencies and patterns in sequential data. They were created to overcome the vanishing gradient issue that afflicted traditional RNNs, restricting their capacity to accurately

capture long-term relationships in sequences. The LSTM has been utilized in various sectors for data prediction and proven excellent performance on a wide range of problems [21-25]. Hochreiter and Schmidhuber [26, 27] designed LSTM to address the problem posed by classical RNNs [28] and ML methods. The central component of an LSTM model is a memory cell known as a ‘cell state’ that maintains its state across time. The horizontal line across the top of Figure 2 represents the cell state. It can be likened to a conveyor belt through which information flows unaltered. The LSTM is implemented in Python with the Keras library.

Figure 1. Architecture of LSTM Model.

A typical LSTM unit consists of a cell, an input gate, an output gate, and a forget gate. The cell holds values for arbitrary time intervals, and the three gates regulate the flow of information into and out of the cell. Forget gates determine what information to discard from a previous state based on a comparison of the previous state and the current input, resulting in a value between 0 and 1. A number of one suggests that information should be maintained, whereas a value of zero indicates that information should be deleted. Input gates, like forget gates, determine which new information to store in the current state. Output gates control the information that is output from the current state by assigning a value between 0 and 1, while taking past and current states into account. This selective output of important information enables LSTM networks to sustain resilient long-term dependencies, allowing for accurate predictions across multiple time steps. Equations (2)–(7) depict the processes that occur in an LSTM cell.

𝑓_𝑡 = 𝜎_𝑔(𝑊_𝑓𝑥_𝑡 + 𝑈_𝑓ℎ_𝑡−1 + 𝑏_𝑓)                                                                                                       (2)

𝑖_𝑡 = 𝜎_𝑔(𝑊_𝑖𝑥_𝑡 + 𝑈_𝑖ℎ_𝑡−1 + 𝑏_𝑖)                                                                                                         (3)

𝑜_𝑡 = 𝜎_𝑔(𝑊_𝑜𝑥_𝑡 + 𝑈_𝑜ℎ_𝑡−1 + 𝑏_𝑜)                                                                                                      (4)

𝑐^′_𝑡 = 𝜎_𝑔(𝑊_𝑐𝑥_𝑡 + 𝑈_𝑐ℎ_𝑡−1 + 𝑏_𝑐)                                                                                                     (5)

𝑐_𝑡 = 𝑓_𝑡 ⊙ 𝑐_𝑡−1 + 𝑖_𝑡 ⊙ 𝑐_𝑡−1                                                                                                             (6)

ℎ_𝑡 = 𝑜_𝑡 ⊙ 𝜎_ℎ(𝑐_𝑡)                                                                                                                                 (7)

Where 𝑓_𝑡 is the forget gate, 𝑖_𝑡 is the input gate, 𝑜_𝑡 is the output gate, σ is the sigmoid activation function, ℎ_𝑡 is the hidden state, 𝑐_𝑡 and 𝑐^′_𝑡 is the cell state, ⊙ represents element-wise multiplication, 𝑏_𝑓, 𝑏_𝑖, 𝑏_𝑜, and 𝑏_𝑐 are bias vectors. 𝑊_𝑓, 𝑊_𝑖, and 𝑊_𝑖 weight for the forget gate, input gate and output gate respectively.

3.3 Performance Measures

The evaluation stage involves the computation of diverse assessment metrics, encompassing Coefficient of determination (R²), Root Mean Squared Error (RMSE), and Mean Absolute Error (MAE), These metrics serve to gauge the efficacy of the model’s performance, shedding light on the extent to which the model’s predictions correlate with the actual target values. The formulations used to calculate these performance metrics are expressed in Equations (9) – (11).

∑^𝑛  (𝑑 − 𝑦 )²

R2 = 1 −         i=1       𝑖             𝑖            

(9)

∑^𝑛  (𝑑 − 𝑑          )²

𝑖=1       𝑖             𝑚𝑒𝑎𝑛

1        𝑛                               2

(10)

𝑁

𝑅𝑀𝑆𝐸 = √ ∑          (𝑑_𝑖 − 𝑦_𝑖)

𝑖=1

1        𝑛

𝑁

𝑀𝐴𝐸 = ∑          |(𝑦_𝑖 − 𝑑_𝑖)|

𝑖=1

(11)

where di is the ith observed value, yi is the ith predicted value, and dmean is the mean value of the observed values.

4.  Results and Discussion

The proposed models that predict the scour depth is developed using orange software. The predictor variables were provided via an input set defined by x = [B, q, L/B, N, Df/B)], while the target variable (y) is settlement (Sm). Every modelling stage requires the selection of the suitable size of training and testing datasets. The proposed models were tuned through trial and error to get an optimal hyperparameters values owing to accurate prediction of settlement (Sm). This study optimizes some essential model parameters and clarifies the definitions of these hyperparameters. The tuning parameters for the models were selected and then changed during the trials until the best metrics presented in Table 1 were obtained. The proposed LSTM model consists of two LSTM layers with 100 units each, both using the (ReLU) activation function. Between the LSTM layers, there’s a dropout layer with a dropout rate of 0.2 to prevent overfitting. After the second LSTM layer, there are two fully connected (Dense) layers with 50 and 1 units respectively, both using the (ReLU) activation function except for the last layer, which doesn’t have an activation function specified, implying a linear activation.

The model is compiled using the Adam optimizer with a custom learning rate of 0.0038 and mean absolute error as the loss function. Early stopping is implemented with a patience of 100 epochs, aiming to restore the best weights when validation loss stops decreasing. The model is trained for 800 epochs with a batch size of 16. The obtained results may vary given the stochastic nature of the LSTM model therefore, we have run it several times.

Table 1. Hyperparameter optimization results.

Model    Hyperparameter optimization value

LSTM  Lstm layer 1 =100(Relu), Layer 2 =100(Relu), Dropout rate =0.2, Dense layer =50 and 1, Optimizer Adam Learning rate =0.0038, Loss function =MAE, No of epochs

=800, Batch size =16

The LSTM model was developed using a total of 106 data points for training, with 45 data points employed during the model testing phase and 38 data points used for validation to assess model performance. The scatter plots (see Figures 3-5) of predicted versus actual values for the training, testing, and validation datasets exhibit good alignment along the diagonal, indicating high predictive accuracy with R²=0.95, RMSE=5.588, MAE =2.457, and r = 0.976 in training dataset, R²=0.91, RMSE=8.459, MAE =5.669, and r = 0.955 in testing dataset, R²=0.774, RMSE=13.398,

MAE =6.773, and r = 0.889 in validation dataset. The similarity in distribution and clustering patterns across the three plots suggests that the model generalizes well which confirm the robustness and reliability of the developed LSTM model in representing the underlying relationships in the data.

Figure 3. Scatter plots of predicted Sm as opposed to actual Sm of LSTM model in the training stage.

Figure 4. Scatter plots of predicted Sm as opposed to actual Sm of LSTM model in the testing stage.

Figure 5. Scatter plots of predicted Sm as opposed to actual Sm of LSTM model in the validation stage.

The predicted values closely coincide with the actual values, as evidenced by the strong alignment as shown in Figures 6-8. This high degree of correlation indicates that the LSTM model is capable of accurately capturing the underlying patterns in the data. The minimal deviation between predicted and observed values in Figures 6-8 suggests strong predictive performance and reliability. Such close correspondence further implies that the model has not only learned the training data well but is also capable of making accurate predictions on unseen data, affirming its robustness and generalizability.

Figure 6. Line graph showing the comparison between predicted and actual values of Sm using the LSTM model in the training stage phase.

Figure 7. Line graph showing the comparison between predicted and actual values of Sm using the LSTM model in the testing stage phase.

Figure 8. Line graph showing the comparison between predicted and actual values of Sm using the LSTM model in the validation stage phase.

5.  Comparison with Traditional and Soft Computing Methods for Settlement Prediction

The results of the current research were also validated against literature reports on the implementation of traditional methods and soft computing models over the validation modeling phase. Table 2 represents the comparative performance traditional methods for settlement prediction of shallow foundations on cohesionless soils are presented in literature, for instance, the Meyerhof [29], Schultze and Sherif [30], and Schmertmann et al. [31] Many traditional methods for settlement prediction of shallow foundations on cohesionless soils are presented in literature. Among these, three are chosen for the purpose of assessing the relative performance of the LSTM model. These methods are chosen as they are commonly used, represent the chronological development of settlement prediction, and the database used in this work contains most parameters required to calculate settlement by these methods. The parameters needed for each method are summarized in Table 2, which also includes the performance of the traditional methods and the ANN model for the validation set. According to the results, LSTM model achieved the maximum r (0.889), followed by Schmertmann et al. [31] (0.798). The proposed LSTM model (r= 0.889, RMSE = 13.398 and MAE =6.733) was demonstrated as being a robust modelthat can be implemented in the future for shallow foundationdesign applications. Among the methods evaluated, LSTM consistently achieved the highest correlation coefficient, lowest RMSE and MAE error metrics, with a rank of 3, indicating the best overall performance. Ranks were assigned such that higher metric values resulted in lower (better) ranks.

Table 2. Comparison of rank analysis with traditional methods for settlement prediction.

Method	r	RMSE	MAE	r	RMSE	MAE	Rank
Meyerhof [29]	0.440	25.72	16.59	4	4	4	16
Schultze and Sherif [30]	0.729	23.55	11.81	3	2	2	7
Schmertmann et al. [31]	0.798	23.67	15.69	2	3	3	8
LSTM (this study)	0.889	13.398	6.733	1	1	1	3

Furthermore, the developed LSTM model are compared with other available models in Table 3 including the ANN model developed by Shahin, M. A., et al. [32] and also with Evolutionary Polynomial Regression (EPR), Genetic Programming (GP) and Gene Expression Programming

(GEP) models proposed by Shahnazari, H., et al. [33]. The result supports the conclusion that the LSTM model generalizes well.

Table 3. Comparison with soft computing methods for settlement prediction.

Reference	Model	R²	RMSE	MAE
Shahin, M. A., et al. [32]	ANN	0.851	10.25	7.14
Shahnazari, H., et al. [33]	EPR	0.871	9.53	6.88
Shahnazari, H., et al. [33]	GP	0.878	9.27	6.03
Shahnazari, H., et al. [33]	GEP	0.799	11.89	7.73
This study	LSTM	0.91	8.459	5.669

5. Conclusions

This study developed LSTM for predicting the settlement of shallow foundation on cohesion less soil, the application of these developed algorithms has rarely been employed for the prediction of settlement of shallow foundation. In order to execute the LSTM algorithm, the four significant input parameters footing width (B), footing pressure (q), footing geometry (L/B), number of standard penetration test (SPT) blows number (N), and embedment ratio (DF/B) are used as input parameter and the corresponding settlement (Sm) is employed as output parameter. Furthermore, the LSTM model was developed using a total of 189 data points, of which 106 were used for training, 45 for testing, and 38 for validation to assess the model’s performance. The developed models were executed in python programing language. In this study, the LSTM outperformed the traditional and soft computing methods with R²=0.95, RMSE=5.588, MAE =2.457, and r = 0.976 in training dataset, R²=0.91, RMSE=8.459, MAE =5.669, and r = 0.955 in testing dataset, R²=0.774, RMSE=13.398, MAE =6.773, and r = 0.889 in validation dataset. Therefore, the LSTM exhibits high accuracy in the training and testing phases, respectively. In this study, the developed LSTM algorithm proved to be the best-fit algorithm for predicting the settlement of shallow foundation on cohesionless soil. Future work can be expanded employing different datasets to verify the accuracy of the proposed algorithms.

Notation

AI artificial intelligence;

ANN artificial neural network;

B footing width;

Df footing embedment depth;

EPR evolutionary polynomial regression GP genetic programming;

GEP gene expression programming;

L footing length;

LSTM long short term memory

MAE mean absolute error;

N average standard penetration test blows count/300 mm to depth of influence of foundation;

Ncorrected corrected standard penetration test blow count;

q footing net applied pressure; RMSE root mean square error; RNN recurrent neural network; R² determination coefficient;

r correlation coefficient; and

Sm settlement

Authors Contribution: All authors made significant contributions in the research work.

Data Availability: “Data is provided within the manuscript”.

Acknowledgments: The author extends the appreciation to the Deanship of Postgraduate Studies and Scientific Research at Majmaah University for funding this research work.

Appendix A

S. No.	B (m)	q (kPa)	N	L/B	Df/B	Sm (mm)
1	60	385	47	1	0.09	40
2	0.8	78	15	1	0	7
3	2.1	697	50	1	0.71	2.3
4	14	18.32	15	1.61	0.18	4.2
5	2.5	284	60	3.8	1.2	1
6	2.8	142	4	5	0.36	97
7	1.2	250	25	10.6	0.25	10
8	0.9	300	20	1	3.44	6.7
9	25	70	6	1	0.04	121
10	1.2	150	45	1	0.5	0.6
11	4.5	195	35	1.3	0.67	3.9
12	5.5	93	35	2.9	0.52	6.5
13	4.3	161	20	1.6	0.49	5
14	4.5	91	12	6.8	0.6	11
15	15	81	35	4.9	0.2	5.4
16	4.9	188	20	1.59	0.47	15
17	4	145	20	1.6	0.5	7.4
18	2.5	158	21	5.24	0	11.7
19	1.5	77	13	1	0.8	2.1
20	6	190	7	1	0	74
21	1	284	45	1	0.5	4.7
22	3.3	304	40	1.7	0.9	11.6
23	12.2	130	17	1	0.09	22
24	5.2	127.8	58	3.7	0	17
25	3.8	90	12	3.2	0.39	15.5
26	6.7	113	21	1.59	0.51	5
27	27.4	154	17	1	0	100
28	25	75	6	1	0.11	87

S. No.	B (m)	q (kPa)	N	L/B	Df/B	Sm (mm)
29	1.2	199	7	1	0.17	13
30	4.3	102	20	1.6	0.49	7.1
31	21.7	148	30	1	0.14	19.8
32	5.2	95.8	42	5.3	0.44	9.9
33	1	220	34	1	0	3.6
34	2.5	245	16	1	0	11
35	4.9	118.7	22	1.1	0.3	6.4
36	4	512	37	1.8	1.3	12.8
37	1.5	77	13	1	0.8	1.3
38	36.6	193	28	1	0	18
39	14.5	74	6	4.4	0.07	75
40	30.2	386	18	1	0.09	91.6
41	6.4	71.8	18	1.45	0.23	6.6
42	4.1	125	20	1	1.2	17.8
43	3	140	38	4.8	0.95	3
44	4	225	20	1.6	0.5	9.1
45	6.4	150	20	1.6	0.5	14.5
46	4.3	139	20	1.6	0.49	7.1
47	16.2	154	16	1.6	0.29	15
48	4.9	123	20	1.6	0.47	6.6
49	1.2	300	50	1	0.42	4.5
50	4.9	107	20	1.6	0.47	3.6
51	22.5	221	20	2.9	0.44	21
52	2.5	576	18	1	0.3	25
53	3.7	135	20	1	1.4	10.1
54	22.4	64	6	3.8	0.04	70
55	4.9	182	20	1.6	0.47	13.8
56	4.3	134	20	1	1.2	15.4
57	3	500	18	1	0.29	25
58	5.1	114.9	42	4.6	0.35	5.8

S. No.	B (m)	q (kPa)	N	L/B	Df/B	Sm (mm)
59	4.9	97	20	1.6	0.47	4.3
60	4.3	150	20	1.6	0.49	6.8
61	1	294	40	1	0	5
62	22	79	21	1	0.23	10.5
63	5.2	134	22	1	0.96	14.7
64	25	75	6	1	0.09	87
65	33.5	156	19	1	0	90
66	1.2	215	18	1	2.2	8.6
67	6.6	168.1	39	2	0	15.5
68	4.3	145	20	1.6	0.49	11
69	5.2	153.2	44	3.7	0	8.9
70	4.9	161.4	49	2.8	0	7.1
71	22.4	75	6	3.8	0.04	92
72	5	181.9	24	1.7	0.5	11.9
73	3.4	129	20	1	1.5	11.5
74	11	120	24	3	0.45	19.6
75	20	85	5	1	0.15	116
76	2.6	147	10	8.5	0.77	12
77	4	507.5	32	1.8	1.3	11.9
78	4.5	304	40	1.5	0.67	18.3
79	1.2	268	8	1	0.75	12.7
80	3.7	215	20	1.59	0.49	15
81	13.1	47.6	25	1.8	0.23	3.6
82	33	191	34	1	0.16	43.8
83	8.5	102.5	24	1	0	16.3
84	1.5	150	35	1	0.4	2.1
85	1	247.5	16	1	0	9.9
86	4.9	112	20	1.7	0.31	7.4
87	3.7	215	20	1.59	0.49	6.4
88	4.9	113	20	1.59	0.47	8.9

S. No.	B (m)	q (kPa)	N	L/B	Df/B	Sm (mm)
89	16	209	14	2.7	0.46	18.6
90	22	82	21	3.4	0.22	7.7
91	1.2	215	26	1	2.2	1.5
92	10	240	60	1	0.15	7
93	1.4	230	25	1	2.1	3.9
94	4.3	134	20	1.6	0.49	10.2
95	4.9	102	20	1.59	0.47	6.9
96	3.3	52	8	4.2	0.54	35
97	6	214.5	42	2.7	0.6	4.1
98	2.1	584	50	1.1	1.4	4.6
99	1.4	300	50	1	2.6	1.5
100	4.4	93	10	5.5	0.57	8
101	1.6	250	25	7.9	0.25	9.3
102	4.9	199	20	1.6	0.47	11.7
103	23.6	167	35	1.14	0.13	15.4
104	1.5	666	18	1	0.51	25
105	3.3	52	8	4.2	0.54	20
106	2.5	284	60	3.8	1.2	3
107	19	80	15	1	0	52
108	22.9	165	30	1.4	0.13	20.4
109	5.5	139	20	1.6	0.47	9.4
110	3	231	20	1.6	0.5	8.1
111	3.7	290	20	1.59	0.49	11.2
112	3.4	247	20	1.6	0.5	12.2
113	12.2	181	53	1	0.25	9.6
114	7	177	22	1.6	0.5	8.3
115	5.6	112	22	4.3	0.27	15.5
116	13	193	18	2.4	0.16	22
117	3.3	98.6	7	4.4	0.61	37.1
118	1.2	320	25	1	0	2.8

S. No.	B (m)	q (kPa)	N	L/B	Df/B	Sm (mm)
119	25	63	6	1	0.08	84
120	13	193.8	18	1.7	0.16	18.8
121	4.6	112	24	5	0.43	11.2
122	6.1	155.6	38	5	0.25	16.8
123	4.6	85.7	39	4.5	0.59	21.1
124	1	564	45	1	0.5	4.4
125	5.8	72.8	17	4.1	0.43	11.9
126	4.6	113	20	1.6	0.5	5.1
127	3.7	252	20	1.6	0.49	16.5
128	6.1	144.1	23	5	1.1	11.7
129	3.7	139	20	1.6	0.49	7.4
130	7	131.2	42	5.1	0.33	11.9
131	6	158	42	2.7	0.47	7.9
132	3.7	279	20	1.6	0.49	8.6
133	16	70	12	1.3	0.09	90
134	6	162	30	2.7	0.6	11
135	0.9	113	6	1	1	6.4
136	3.4	81.4	34	6.7	0	10.7
137	4	97	20	1.6	0.5	6.1
138	2.4	190	22	1.6	1.9	8.5
139	17.6	218	20	4.8	0.61	26
140	4.3	177	20	1.6	0.49	8.1
141	3	500	18	1	0.25	25
142	1.5	150	50	1	0.4	1
143	55	233.6	60	1.8	0.18	25
144	5.3	121	17	9.9	0.49	12
145	1	196	25	1	3	6
146	42.7	166	21	1	0	80
147	20	85	5	1	0.15	81
148	0.9	300	30	1	1.3	4

S. No.	B (m)	q (kPa)	N	L/B	Df/B	Sm (mm)
149	20	145	7	1	0	120
150	3.5	25	12	1	0.43	3
151	2.1	584	50	1.1	1.1	4.4
152	24.4	120	27	1	0	14.3
153	1.2	215	29	1	2.2	2.5
154	9	115	11	8	0.5	25
155	4.6	111.1	43	3.5	0	23.9
156	3.6	304	40	1.8	0.83	13.3
157	25	76	6	1	0.08	85
158	3.7	225	20	1.6	0.49	7.4
159	13	193	18	2.1	0.16	23.5
160	14.5	253.5	26	1	0.24	18
161	41.2	104	36	1	0.24	10
162	6	162	30	2.7	0.47	10.5
163	34	270	30	1.7	0.23	22
164	3.3	99	4	4.4	0.3	37
165	25	86	6	1	0.1	120
166	1.8	575	50	1.6	0.83	2.7
167	15	148	20	1.3	0	40
168	1	339	45	1	0.5	6
169	15.2	33	20	1	0.02	2.8
170	15	136	55	1.7	0.4	16.2
171	2.6	293	37	4.1	0.38	10.9
172	6.4	100.5	18	1	0.23	7.1
173	4.6	166	20	1.6	0.5	8.1
174	1.2	150	28	1	0.5	1.3
175	6.1	161	20	1.6	0.49	10.2
176	3	230.8	50	3.3	1	21.1
177	1.1	78	13	1	1.09	2
178	1.8	230	25	1	1.7	3.4

S. No.	B (m)	q (kPa)	N	L/B	Df/B	Sm (mm)
179	0.9	133	5	1	0.33	7.6
180	5.1	116.8	19	3.1	0.24	19.3
181	0.9	300	20	1	1.33	2.7
182	2.25	400	8	1.1	1.02	43
183	2.6	196.3	9	8.1	0.77	33
184	2.1	347	50	1.9	1.4	1.8
185	14.5	74	6	4.4	0.07	74
186	25.5	175	21	1	0.1	25
187	1	284	25	2.2	3	10.5
188	17.2	34	17	2.5	0.27	3.6
189	18.3	41	20	1	0.02	4.8

Note: S. No. 1–106 used for training, 107–151 for testing, and 152–189 for validation.

References

• U. Holzlohner, “Settlements of shallow foundations on sand,” Soils and foundations, vol. 24, no. 4, pp. 58-70, 1984.
• Z. Zhang, F.-R. Rao, and G.-B. Ye, “Design method for calculating settlement of stiffened deep mixed column-supported embankment over soft clay,” Acta Geotechnica, vol. 15, pp. 795-814, 2020.
• A. Standard, “Standard test method for standard penetration test (SPT) and split-barrel sampling of soils,” 2008.
• P. K. Robertson and K. Cabal, “Guide to cone penetration testing for geotechnical engineering,” Signal Hill, CA: Gregg Drilling & Testing, 2015.
• P. Mayne, “In-situ test calibrations for evaluating soil parameters,” Characterization & engineering properties of natural soils, vol. 3, pp. 1601-1652, 2007.
• N. C. Consoli, F. Schnaid, and J. Milititsky, “Interpretation of plate load tests on residual soil site,” Journal of Geotechnical and Geoenvironmental Engineering, vol. 124, no. 9, pp. 857-867, 1998.
• L. T. Chen, H. Poulos, and N. Loganathan, “Pile responses caused by tunneling,” Journal of Geotechnical and Geoenvironmental Engineering, vol. 125, no. 3, pp. 207-215, 1999.

• E. Jorden, “Settlement in sand-methods of calculating and factors affecting,” Ground Engineering, vol. 10, no. 1, 1977.
• J. K. Jeyapalan and R. Boehm, “Procedures for predicting settlements in sands,” in

Settlement of Shallow Foundations on Cohesionless Soils: Design and Performance, 1986,

pp. 1-22: ASCE.

• R. M. Barker, J. M. Duncan, K. B. Rojiani, P. S. Ooi, C. Tan, and S.-G. Kim, Manuals for the design of bridge foundations: Shallow foundations, driven piles, retaining walls and abutments, drilled shafts, estimating tolerable movements, and load factor design specifications and commentary (no. 343). 1991.
• H. Wahls, “Settlement analysis for shallow foundations on sand,” in Proceedings of the 3rd International Geotechnical Engineering Conference, 1997, pp. 7-28.
• M. A. Shahin, “A review of artificial intelligence applications in shallow foundations,”

International Journal of Geotechnical Engineering, vol. 9, no. 1, pp. 49-60, 2015.

• N. Jibanchand and K. R. Devi, “Application of ensemble learning in predicting shallow foundation settlement in cohesionless soil,” International Journal of Geotechnical Engineering, vol. 17, no. 3, pp. 234-245, 2023.
• M. A. Shahin, M. B. Jaksa, and H. R. Maier, “Artificial neural network applications in geotechnical engineering,” Australian geomechanics, vol. 36, no. 1, pp. 49-62, 2001.
• J. Burland, M. Burbidge, E. Wilson, and Terzaghi, “Settlement of foundations on sand and gravel,” Proceedings of the institution of Civil Engineers, vol. 78, no. 6, pp. 1325-1381, 1985.
• M. Burbidge, “A case study review of settlements on granular soil,” Diss. Imperial College, University of London, 1982.
• A. R. S. S. Bazaraa, Use of the standard penetration test for estimating settlements of shallow foundations on sand. University of Illinois at Urbana-Champaign, 1967.
• J.-L. Briaud and R. Gibbens, “Behavior of five large spread footings in sand,” Journal of geotechnical and geoenvironmental engineering, vol. 125, no. 9, pp. 787-796, 1999.
• M. Picornell and E. Del Monte, “Prediction of settlements of cohesive granular soils,” in

Measured Performance of Shallow Foundations, 1988, pp. 55-72: ASCE.

• M. Maugeri, F. Castelli, M. R. Massimino, and G. Verona, “Observed and computed settlements of two shallow foundations on sand,” Journal of Geotechnical and Geoenvironmental engineering, vol. 124, no. 7, pp. 595-605, 1998.
• L. Ren, J. Dong, X. Wang, Z. Meng, L. Zhao, and M. J. Deen, “A data-driven auto-CNN- LSTM prediction model for lithium-ion battery remaining useful life,” IEEE Transactions on Industrial Informatics, vol. 17, no. 5, pp. 3478-3487, 2020.
• F. A. Gers, J. Schmidhuber, and F. Cummins, “Learning to forget: Continual prediction with LSTM,” Neural computation, vol. 12, no. 10, pp. 2451-2471, 2000.
• K. Chen, Y. Zhou, and F. Dai, “A LSTM-based method for stock returns prediction: A case study of China stock market,” in 2015 IEEE international conference on big data (big data), 2015, pp. 2823-2824: IEEE.
• J. Wang, J. Li, X. Wang, J. Wang, and M. Huang, “Air quality prediction using CT-LSTM,”

Neural Computing and Applications, vol. 33, pp. 4779-4792, 2021.

• S. Alhirmizy and B. Qader, “Multivariate time series forecasting with LSTM for Madrid, Spain pollution,” in 2019 international conference on computing and information science and technology and their applications (ICCISTA), 2019, pp. 1-5: IEEE.
• J. Schmidhuber, F. Gers, and D. Eck, “Learning nonregular languages: A comparison of simple recurrent networks and LSTM,” Neural computation, vol. 14, no. 9, pp. 2039-2041, 2002.
• S. Hochreiter and J. Schmidhuber, “Long short-term memory,” Neural computation, vol. 9, no. 8, pp. 1735-1780, 1997.
• A. Sherstinsky, “Fundamentals of recurrent neural network (RNN) and long short-term memory (LSTM) network,” Physica D: Nonlinear Phenomena, vol. 404, p. 132306, 2020.
• G. G. J. J. o. t. S. M. Meyerhof and F. Division, “Shallow foundations,” vol. 91, no. 2, pp. 21-31, 1965.
• E. Schultze and G. Sherif, “Prediction of settlements from evaluated settlement observations for sand,” in Proceedings eighth international conference on soil mechanics and foundation engineering, 1973, vol. 1, no. 3, pp. 225-230.
• J. H. Schmertmann, J. P. Hartman, and P. R. J. J. o. t. G. E. D. Brown, “Improved strain influence factor diagrams,” vol. 104, no. 8, pp. 1131-1135, 1978.

• M. A. Shahin, H. R. Maier, and M. B. Jaksa, “Predicting settlement of shallow foundations using neural networks,” Journal of geotechnical and geoenvironmental engineering, vol. 128, no. 9, pp. 785-793, 2002.
• H. Shahnazari, M. A. Shahin, and M. Tutunchian, “Evolutionary-based approaches for settlement prediction of shallow foundations on cohesionless soils,” International journal of civil engineering, vol. 12, no. 1, pp. 55-64, 2014.