Innovative piled raft foundations design using artificial neural network

Abstract

Studying the piled raft behavior has been the subject of many types of research in the field of geotechnical engineering. Several studies have been conducted to understand the behavior of these types of foundations, which are often used for uniform loading on the raft and piles with the same length, while generally the transition load from the upper structure to the foundation is non-uniform and the choice of uniform length for piles in the above model will not be optimally economic and practical. The most common method in identifying the behavior of piled rafts is the use of theoretical relationships and software analyses. More precise identification of this type of foundation behavior can be very difficult due to several influential parameters and interaction of set behavior, and it will be done by doing time-consuming computer analyses or costly full-scale physical modeling. In the meantime, the technique of artificial neural networks can be used to achieve this goal with minimum time consumption, in which data from physical and numerical modeling can be used for network learning. One of the advantages of this method is the speed and simplicity of using it. In this paper, a model is presented based on multi-layer perceptron artificial neural network. In this model pile diameter, pile length, and pile spacing is considered as an input parameter that can be used to estimate maximum settlement, maximum differential settlement, and maximum raft moment. By this model, we can create an extensive domain of results for optimum system selection in the desired piled raft foundation. Results of neural network indicate its proper ability in identifying the piled raft behavior. The presented procedure provides an interesting solution and economically enhancing the design of the piled raft foundation system. This innovative design method reduces the time spent on software analyses.

Keywords

innovative design / piled raft foundation / neural network / optimization

Introduction

In recent decades, numerous attempts have been made to identify piled raft behavior. The result of these efforts is to provide different approaches to investigating the piled raft behavior for their practical use. One of the disadvantages of most studies is using the uniformity of load taken from upper structure to raft, uniformity of pile length, uniformity of soil layering, etc., which is not compatible with actual conditions and restrict the applicability of these studies for practical reasons. On the other hand, considering the changes all of these parameters is time-consuming and needs more sophisticated studies. Although it is necessary to test the actual size piled raft foundations to understand real soil-pile-raft behavior, to do so is an expensive, virtually impossible and difficult process. For this reason, in this paper, the behavior of sample piled raft under non-uniform loading has been investigated by using numerical modeling and artificial neural network technique.

ANNs have been applied to many geotechnical engineering problems, such as Ellis et al. [¹], Goh [²], Lee and Lee [³], Rahman et al. [⁴], Shahin et al. [⁵,⁶], Sivakugan et al. [⁷], Teh et al. [⁸].

The process of learning in artificial networks is accomplished with a data set input to the network. This data transmits the knowledge or law contained in the data input to network structure. In this way, the network can establish linear or nonlinear communication between input data and target values. Correctness and data integrity play a determinative role in correct training of network. In this research, due to the lack of laboratory and field results, the data required for the learning and training of artificial neural network were generated by using software analyzes. Software’s that are capable of modeling piled raft are limited. However, use of this software’s requires awareness of their performance. Numerical methods is one of the most common methods for checking the behavior of piled raft. In the present study, the behavior of piled raft is studied by using the modeling of artificial neural networks method. Studies in this field are limited to calculating the bearing capacity of piles, calculating the settlement of piles, and estimating the load-settlement behavior of piles. In the context of estimating the bearing capacity of piles and the behavior of load-settlement of pile foundations, we can mention the studies of Shahin [⁹] and Ismail et al.[¹⁰], respectively.

In line with the proposed method, for studying the behavior of piled raft we can refer to studies conducted by Kuo et al. [¹¹]. They have proposed a model by using numerical modeling and artificial neural networks that it can estimate the bearing capacity of strip footing on multi-layered cohesive soil. These researchers used numerical modeling results for the learning and training of artificial neural networks.

Research method

General

Research process in this paper consists of two steps. In the first step, computerized modeling of piled raft has been conducted. For this purpose, ELPLA program has been used and all analyses presented in this paper were carried out with the program ELPLA. This program has been used to achieve settlement, differential settlement, and moment values in the raft [¹²]. Correctness of above software has been examined in previous studies [¹³–¹⁵]. In the second step, results of modeling are introduced as inputs to the neural network in order to educate the network. Neural network establishes a logical linear or nonlinear connection between input data and target by using the transfer functions that is determined by the user. Network efficiency and reliability are also measured by controlling the network error and values ​​of correlation coefficients between target value and network output. Finally, an optimal network with error values ​​and acceptable correlation coefficients will be used to continue the research [¹⁶].

Hypotheses and limitations

The neural network used in this research is multi-layer perceptron and it is created by using the MATLAB program. The network has an input layer, an output layer, and a number of intermediate (hidden) layers. The number of hidden layers in a neural network is a function of problem complexity. By increasing the number of independent variables in an issue, it can be guided by increasing the number of hidden layer nodes to make the network more closely linked to the parameters. In researches done so far in the field of geotechnical engineering using neural networks, observed networks with a hidden layer and with a suitable transfer function can find a suitable connection between the data. Establishing the relationship between neural network inputs with target values is done ​​through the transfer functions assigned by the user. Choosing the proper function will play an important role in training an ideal network. Input variables (diameter, length, and distance of piles) and expected results (settlement, differential settlement, moment) in computer modeling provide input data and target values for neural networks, respectively. Production of an efficient neural network is strongly influenced by the accuracy, breadth, and uniformity of the data used in network training. Hence, numerical modeling attempts to produce a complete range of input data for this purpose. After passing through the training of neural network, the validity of network is measured by using data not used in the training phase. At this step, the results of computer modeling are compared with the results of the neural network.

Transfer function used here is the sigmoid tangent function and learning algorithm from Levenberg-Marquette type. The input and output data tuples were scaled between -1.0 and +1.0 before training. The criteria used in this study for evaluation of the model performance are given in Table 1. In the table, S, S_ANN, \overline{S}, {\overline{S}}_{\mathrm{A}\mathrm{N}\mathrm{N}} are the measured and predicted values, measured and predicted mean values, respectively, and n is the number of samples [¹⁷].

Neural network model

One of the distinct characteristics of the ANN is its ability to learn from experience and examples and to generalize them. Typically there are two steps in neural methods: training and recalling. Training of an ANN usually requires a large training pattern set. However, after training, it can be used directly to substitute complex system dynamics [¹⁸].

Application of artificial neural networks in geotechnical engineering is presented in details by Shahin [⁶]. The multilayered perceptron (MLP) is one of the most popular ANN architectures. An MLP is very efficient for function approximation in high dimensional spaces and is composed of neurons and layers connected to each other via weights [¹⁹]. Structure of all multilayer perceptron neural networks includes a number of processor elements or nodes that are usually arranged in a number of layers. These layers include an input layer, an output layer, and one or more hidden (middle) layers. Each of the nodes in each layer is fully or partially connected to the nodes in other layers by means of weighted values. Data distribution in the MLP network begins at the input layer.

After performing the first set of calculations, network output is compared with the actual results and the amount of errors generated is calculated. By using this error and utilizing a learning rule, the network can achieves the desired level of learning for stopping. Therefore, network is able to set values for weights so that the lowest possible error value is created. This process is known as learning and network training.

Geometry of the problem and a neural network model architecture are presented in Figs. 1(a) and 1(b), respectively.

Application of neural network model for an optimal design sample

In our research, we considered 60 input values for each output separately, and we have selected the appropriate input data. Sixty inputs for settlement, 60 inputs for differential settlement, and 60 inputs for maximum moment. Total data set size is 180. In analyzes of example design optimization, various types of parameter are considered (the diameter of piles, the height of piles, load type and pile spacing). Three ANN models were considered: settlement network model, differential settlement network model, and maximum moment network model. In example design, five input values and one output were considered for each design parameter. In example design, L₃ parameter equal to L₂ and this parameter were neglected from the input parameters. Thickness changes of the raft and raft dimensions are not considered due to the uniqueness of any practical project. Raft dimensions are selected according to the occupancy level of upper structure and its thickness to provide to punch resistance failure. In the present example, raft dimension is 26 m × 26 m and its thickness is 1 m. This method suggested for each case study and in each case, soil and piled raft parameters are constant and considered in software modeling. Soil and piled raft material parameters used in the analysis are summarized in Table 2. Load type, load level, and considered geometry for an optimal design sample shown in Fig. 2 [²⁰].

According to the purpose of this study, a neural network has been used to investigate precisely the behavior of piled raft foundations and optimal design. Neural network training is done using numerical modeling results. A perceptron neural network with a hidden layer estimates a continuous function that it can calculate the maximum settlement, the differential settlement and the raft moment. However, the optimal number of nodes in the hidden layer should be determined by trial and error.

One of the most important parameters affecting the results of a neural network is the number of optimum nodes in the hidden layer. To determine the number of optimum nodes in the hidden layer, a number of neural networks with the number of variable nodes in the hidden layers should be trained by using the available data to determine the error value and correlation-coefficient (RMSE) of these networks and are compared with each other. A network with the number of optimum nodes in the hidden layer is a network that can establish a reasonable correlation between the network output values ​​and the target values ​​with the minimum possible error value. In this study, networks with 20, 20, 15 nodes for the hidden layer have the least amount of error and maximum performance in the maximum settlement, the differential settlement, and the maximum moment network model, respectively.

After selecting the optimum neural network geometry, all input data are divided into two classes of training and validation with randomly division (70 to 30). Data used in the validation section should not be used in the network training section. This work is done to estimate the validity of the neural network and evaluate piled raft behavior based on data that is not used in the training section. Statistical characteristics of training section data and validation should be very close to each other in order to achieve the best result. Statistical properties of the data sets are shown in Table 3.

The performance evaluation criteria of the ANN model are presented in Table 4 and according to these results can say that the performance of the proposed model is very good with acceptable accuracy.

Discussion of results

The capability of the ANN model for optimization of the piled raft foundations is demonstrated using the following example. The optimization task was carried out using a communication between ELPLA and ANN model. The ELPLA results for learning, training, and creating the ANN model. Large domains of results are achieved from ANN model for considered parameters. The optimization procedure is illustrated graphically in Figs. 3, 4, and 5. All of these results are achieved from the purposed artificial neural network model. Optimization process illustrated by three steps. The first step is to recognize feasible domain (all nodes in chart which it provide maximum settlement limitation) of the maximum settlement with total pile length that it must provide maximum settlement limitation. The design constraints for this example design were considered with reference to the IS 1904 Code of practice for design and construction of foundations in soils. According to this code, maximum settlement and maximum differential settlement cannot exceed 7.5 and 2.5 cm, respectively. The first step is illustrated in Figs. 3(a) and 3(b) for 3D and 6D pile spacing, respectively. It can be concluded that for certain configurations, the total pile length can be reduced and has only negligible influence on maximum settlement of the piled raft foundation. This has been demonstrated by Russo and Viggiani [²¹] for the foundation of the multistory Stonebridge park building by reducing the number of piles.

The second step is providing differential settlement limitation. Figures 4(a) and 4(b) shows the feasible domain of the differential settlement with the total pile length for 3D and 6D pile spacing, respectively.

In the final step, draw the more limited domain achieved from past steps for maximum moment with the total pile length chart and each point on this chart which have the minimum moment and minimum total pile length is the optimum choice. In Figs. 5(a) and 5(b) can be seen this optimum domain in maximum moment with total pile length chart for 3D and 6D pile spacing, respectively.

Optimum pile configuration detected from Matlab code which is added to ANN model. After selecting the optimum pile configuration by network model, compare it with numerical modeling results. Results comparison and optimum pile configuration properties summarized in Table 5. This results shown acceptable accuracy of the ANN model.

In Table 6, a comparison was conducted between two design patterns for the uniform and non-uniform pile length. As you can see, design requirements can be achieved in the case of uniform pile length with the 2025 m total pile length. In the non-uniform pile length, these requirements can be achieved with the 1441 m. It is not claimed here that the pile configuration proposed by ANN model would be the best design alternative for this example design. However, it should be pointed out that considerable reduction in total pile length (from 2025 m for L₁ = L₂ = 25 to 1441 m for optimum design) by using of this method has been achieved.

Another type of results achieves from ANN model illustrated in Figs. 6, 7, and 8. Figure 6 shows the effect of center pile increment on maximum settlement. It can be seen that maximum settlement variant not tangible by increasing center pile length in 3D pile spacing for large corner pile length.

It can be seen in Fig. 7 that for small pile spacing, increment of center pile length always not gausses maximum differential settlement decreasing. This is due to the concentration of the larger load in the center of the raft. With the increase in the length of the corner piles, differential settlement increases for maximum moment illustrated in Fig. 8 can be seen that the center pile length increment usually de-crease the maximum raft moment. Seen that the center pile length increment usually decrease the maximum raft moment.

Summary and conclusions

This paper presents innovative optimization method that it can estimate the behavior of the piled raft foundation with acceptable accurately. The ability of this method can be leads to be imply less consumption of construction materials and attaining the required level of the piled raft foundation performance. Based on the results, conclusions and the following guidelines for optimum design are proposed.

1) The considered example for an optimized design process shows the significance of a detailed parametric study based on a set of initial design variables in the search for an optimized piled raft foundation design. The example suggests that the installation of piles under the greater load areas, together with non-uniform pile lengths, yield the minimum total pile length.

2) The increase of the pile length considerably reduces the maximum settlement but there is an upper limit for the pile length that beyond it obtained a very little additional benefit. For an economical design, it is recommended that the pile length should only be increased in the positions with large settlements.

3) It should be noted that the results of neural network have a strong compatibility with the values obtained from numerical modeling. By this model, we can create an extensive domain of results for optimum system selection in the desired piled raft foundation with minimum time consumption and proper accuracy.

Many studies have been carried out to calculate the optimal piled raft option, most of which have used pile group relationships to produce continuous results for the production and evaluation of the behavior of this type of foundations. The assumptions used in the pile group relationships reduce the practical applicability and accuracy of the application. In this innovative method, the production of results is carried out using intelligent methods that provide a continuous range of high-accuracy results.

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