Prediction of Pile Settlement Using Artificial Neural Networks Based on Cone Penetration Test Data

F. Pooya Nejad¹; Mark B. Jaksa²

1 Dept. of Civil Engineering, Ferdowsi University of Mashhad, Mashhad, Iran. 2 School of Civil, Environmental and Mining Engineering, University of Adelaide, Australia. Abstract

In recent years artificial neural networks (ANNs) have been applied to many geotechnical engineering problems with some degree of success. With respect to the design of pile foundations, accurate prediction of pile settlement is necessary to ensure appropriate structural and serviceability performance. In this paper, an ANN model is developed for predicting pile settlement based on the results of cone penetration test (CPT) data. Approximately, 300 data sets, obtained from the published literature, are used to develop the ANN model. In addition, the paper discusses the choice of input and internal network parameters which were examined to obtain the optimum model. Finally, the paper compares the predictions obtained by the ANN with those given by a number of traditional methods. It is demonstrated that the ANN model outperforms the traditional methods and provides accurate pile settlement predictions. keywords: Pile load test, Pile foundation, Settlement, Neural networks Introduction

Piles are part of the sub-structure which is intended to transfer the structural loads through a soft or otherwise unsuitable stratum onto a deeper and firmer stratum. In order to ensure the safety of foundations, foundation engineers predict and determine the pile settlement cautiously. The problem with estimating the settlement of piles is very complex and not yet entirely understood. This can be attributed to the uncertainty associated with the factors that affect the magnitude of this settlement. Among these factors are the distribution of applied stress, stress-strain history of the soil, soil compressibility, and difficulty in obtaining undisturbed samples of soil (Shahin et al. 2002). The geotechnical literature has included many methods, both theoretical and experimental, to predict the settlement of piles. Most of the available methods simplify the problem by incorporating several assumptions associated with the factors that affect the settlement of piles. Consequently, most of the existing methods fail to achieve consistent success in relation to accurate settlement prediction (Poulos 1999).

In recent times, artificial neural networks (ANNs) have been applied to many geotechnical engineering problems and have demonstrated some degree of success. ANNs are a form of artificial intelligence, which, by means of their architecture, attempt to simulate the biological structure of the human brain and nervous system.

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Although the concept of artificial neurons was first introduced in 1943, research into applications of ANNs has blossomed since the introduction of the back propagation training algorithm for feed forward ANNs in 1986 (Rumelhart et al. 1986). ANNs may thus be considered a relatively new tool in the field of prediction and forecasting. In this paper, ANNs are used to predict the settlement of piles base on cone penetration test (CPT) data. The purpose of the paper is to develop an ANN model for accurately predicting the settlement of singles axially loaded piles. Neural network model

The development of ANN models includes the determination of model inputs and outputs, division and pre-processing of the available data, the determination of appropriate network architecture, stopping criteria, and model validation (Shahin et al. 2002). The personal computer-based software NEUFRAME version 4.0 (Neurosciences Corp. 2000) is used to simulate ANN operation in this work. The data used to calibrate and validate the neural network model were obtained from the literature of pile load tests that include field measurements of pile settlements as well as the corresponding information regarding the piles and soil. The database contains a total of 292 cases from 26 individual pile load tests that include 2 steel piles, 21 concrete piles, and 3 composite piles. Model inputs and outputs

In order to obtain accurate settlement prediction, a thorough understanding of the factors affecting settlement is needed (Shahin et al. 2002). Most traditional methods include pile geometry, pile material properties, applied load, and soil properties. There are some additional factors, such as the pile installation type, load test method, and end of pile (closed or open). Since settlement depends on the soil compressibility and the CPT is one of the most commonly used tests in practice for measuring the in situ compressibility of soils, consequently for the purposes of this study, CPT along the embedded length of the pile is used as a measure of soil compressibility. To account more accurately for the variability of the soil properties along the pile shaft, the embedded length of the pile is divided into five segments of equal thickness, with each being an average of qc and fs over that segment. The average qc and fs (qcave , fsave) for each subdivision, j, is calculated as below:

∑∑=

i

icicave Z

Zqq

j (1)

∑∑=

i

isisave Z

Zff

j (2)

Where, Zi is the soil layer thickness in that segment with qci and fsi over that layer.

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Hence the factors that are presented to the ANN as model input variables are: type of test (maintained load or constant rate penetration), type of pile (concrete, steel, and composite ), type of installation (bored or driven), end of pile (closed or open), axial rigidity of pile (EA), cross sectional area of end of pile (Atip), perimeter of pile in contact with soil (O), length of pile (L), length of embedded pile (Lembed), the averaged CPT results along the embedded length of the pile (qc1, fs1, qc2, fs2, qc3, fs3, qc4, fs4, qc5, fs5) along the embedded length of pile, CPT result in end of pile (qctip), and applied load (P). Settlement (sm) is the single output variable. It should be noted that when type of test is constant rate penetration the measured settlement of pile will be immediate settlement, but in the case of maintained load test the measured settlement of pile will be combination of immediate and consolidation settlement.

Data division and pre-processing

It is common practice to divide the available data into two subsets; a training set, to construct the neural network model, and independent validation set to estimate model performance in the deployed environment (Twomey and Smith 1997). A modification of the above data division method is cross-validation (Stone 1974) in which the data are be divided into three sets; training, testing and validation. The training set is used to adjust the connection weights, whereas the testing set is used to check the performance of the model at various stages of training and to determine when to stop training to avoid over-fitting. Consequently, the database is divided into three sets: training, testing and validation. In total, 90% of the data (261 cases) are used for training and 10 % (31 cases) are used for validation. The training data are further divided into 90% (236 cases) for the training set and 10% (25 cases) for the testing set. Since it is essential that the data used for training, testing, and validation represent the same population (Master 1993), the statistical properties (e.g. mean and standard deviation) of the data subsets need to be similar (Shahin et al. 2002). Also ANNs are unable to extrapolate beyond the range of their training data. Consequently, in order to develop the best possible model, all patterns that are contained in the data need to be included in the training set. Similarly, since the test set is used to determine when to stop training, it needs to be representative of the training set and should therefore also contain all of the patterns that are present in the available data (Shahin et al. 2002). In this study, in order to achieve this, several random combinations of the training, testing and validation sets are trialled until three statistically consistent data sets are obtained. The statistical parameters considered include the mean, standard deviation, minimum, maximum and range (Table 1). On the whole the statistics are in good agreement and all three data sets may be considered to represent the same population. Once the available data have been divided into their subsets, it is important to pre-process the data by scaling them in a suitable form before they are applied to the ANN., The output variables need to be scaled to be commensurate with the limits of the transfer functions used in output layers (Shahin 2003). Scaling the input variables is not necessary, so in this study the

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output variables are scaled between 0.0 to 1.0, as the sigmoid transfer function is used in the output layer.

Table 1. Artificial Neural Network Input and Output Statistics

Model Variables and

data sets

Statistical parameters

Mean Std. Dev Maximum Minimum Range

Axial Rigidity of pile, EA (MN) Training set 17359.74 12376.44 33106.34 2110.29 30996.05 Testing set 14623.56 11708.80 33106.34 2110.29 30996.05 Validation set 17149.56 11743.84 33106.34 2110.29 30996.05 Cross sectional Area of pile tip, Atip (cm2) Training set 4750.01 2553.45 7854.00 325.72 7528.28 Testing set 3820.66 2742.19 7854.00 325.72 7528.28 Validation set 4536.21 2711.80 7854.00 325.72 7528.28 Perimeter of pile, O (cm) Training set 445.26 312.47 957.56 100.00 857.56 Testing set 385.93 320.17 957.56 100.00 857.56 Validation set 438.04 318.55 957.56 100.00 857.56 Length of pile, L(m) Training set 24.58 15.11 56.39 6.00 50.39 Testing set 25.27 17.28 56.39 6.00 50.39 Validation set 26.89 16.80 56.39 6.00 50.39 Embedded Length of pile, Lembed (m) Training set 18.14 10.83 45.00 6.00 39.00 Testing set 18.67 12.64 45.00 6.00 39.00 Validation set 20.48 13.10 45.00 6.00 39.00 qc1 (MPa) Training set 3.56 2.66 9.33 0.00 9.33 Testing set 3.85 2.19 9.33 0.00 9.33 Validation set 3.40 2.58 9.33 0.00 9.33 fs1 (kPa) Training set 50.42 46.90 184.88 0.00 184.88 Testing set 55.40 52.70 184.88 0.00 184.88 Validation set 53.51 54.37 184.88 0.00 184.88 qc2 (MPa) Training set 5.13 3.49 12.92 0.05 12.87 Testing set 4.61 3.10 12.92 0.05 12.87 Validation set 4.61 3.35 12.92 0.05 12.87 fs2 (kPa)

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Training set 71.17 61.21 275.50 1.83 273.67 Testing set 61.25 60.58 275.50 1.83 273.67 Validation set 73.32 70.47 275.50 1.83 273.67 qc3 (MPa) Training set 6.20 6.66 31.54 0.30 31.24 Testing set 7.69 6.53 31.54 0.30 31.24 Validation set 7.16 7.53 31.54 0.30 31.24 fs3 (kPa) Training set 78.30 76.17 353.00 1.62 351.40 Testing set 79.11 68.70 353.00 10.00 343.00 Validation set 86.09 85.44 353.00 1.62 351.40 qc4 (MPa) Training set 9.79 8.30 33.37 0.25 33.12 Testing set 10.80 9.24 33.37 0.25 33.12 Validation set 9.52 9.11 33.37 0.25 33.12 fs4 (kPa) Training set 114.28 104.75 423.00 4.42 418.58 Testing set 91.91 81.17 423.00 10.00 413.00 Validation set 109.88 112.32 423.00 4.42 418.58 qc5 (MPa) Training set 12.96 11.58 53.82 0.25 53.57 Testing set 13.56 11.81 53.82 0.25 53.57 Validation set 12.85 12.95 53.82 0.25 53.57 fs5 (kPa) Training set 168.01 176.68 559.00 10.00 549.00 Testing set 126.81 143.06 559.00 10.00 549.00 Validation set 143.86 157.14 559.00 10.00 549.00 qctip (MPa) Training set 16.08 15.28 70.29 0.25 70.04 Testing set 16.17 15.28 70.29 0.25 70.04 Validation set 16.17 17.12 70.29 0.25 70.04 Applied load, P (kN) Training set 3827.22 4632.15 30000.00 0.00 30000.00 Testing set 2240.84 3182.87 14000.00 0.00 14000.00 Validation set 3154.45 2910.53 10000.00 40.00 9960.00 Measured settlement, sm (mm) Training set 11.64 17.86 137.88 0.00 137.88 Testing set 3.76 3.76 12.85 0.00 12.85 Validation set 4.98 3.21 15.00 0.86 14.14

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Architecture of ANNs model

Determining the network architecture is one of the most important and difficult tasks in ANN model development (Maier and Dandy 2000). It requires the selection of the optimum number of hidden layers and the number of nodes in each of these. There is no unified theory for determination of an optimal ANN architecture (Shahin 2003). The number of nodes in the input and output layers are restricted by the number of model inputs and outputs. The No. input variables in this study are 21 and the output layer has only one node representing the measured value of settlement (sm). Although, it has been shown that a network with one hidden layer can approximate any continuos function (Hornik et al. 1989), in this research a single and multiple hidden layers are used. In order to determine the optimum network geometry, first ANNs with one hidden layer and then ANNs with two, three and four hidden layers are trained.

All models have been trained with a sigmoidal and a hyperbolic tangent (tanh) transfer function for the hidden layers. In the single hidden layer model, a sigmoidal transfer function is adopted for the hidden and output layers, and for the multi-hidden layers models, a tanh transfer function is used for the hidden layers and asigmoidal transfer function is adopted for the output layer. These were combinations of transfer functions were found to yield the most accurate predictions of pile settlement when compared to the measured values. Model optimization (Training)

Training or learning is the process of optimizing the connection weights. The aim is to find a global solution to what is typically a highly non-linear optimization problem (White 1989). The method most commonly used for finding the optimum weight combination of feed-forward neural networks is the back propagation algorithm (Rumelhart et al. 1986), which is based on first-order gradient descent. The advantage of this method is that it has the ability to escape local minima in the error surface and, thus, produces optimal or near optimal solutions (Shahin 2003). However it also has a slow convergence rate. Consequently, the back-propagation algorithm is used for optimizing the connection weights in this study. Details of the back propagation algorithm can be found in many publications (e.g. Fausett 1994). Also in this study the momentum term used is 0.8 and the learning rate used is 0.2.

Stopping criteria

Stopping criteria are those used to decide when to stop the training process (Shahin et al. 2002). The cross-validation technique (Stone 1974) is used as the stopping criteria in this work as it is considered that sufficient data are available to create training, testing and validation sets. It is the most valuable tool to ensure over fitting does not occur (Smith, 1993).

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Model validation

Once the training phase of the model has been successfully accomplished, the performance of the trained model should be validated for the validation data sets that have not been used as part of the learning process. The purpose of the model validation phase is to ensure that the model has the ability to generalize within the limits set by the training data in a robust fashion, rather than simply having memorized the input-output relationships that are containing in the training data (Shahin et al. 2002). The coefficient of correlation, r, the root mean squared error, RMSE, and the mean absolute error, MAE, are the main criteria that are used to evaluate the prediction performance of ANN models. The coefficient of correlation is a measure that is used to determine the relative correlation between the predicted and measured data. The root mean square error, RMSE, is the most popular measure of error and it has the advantage that large errors receive much greater attention than small errors (Hecht-Nielsen, 1990). Results

The results of the optimum networks are summarized in Table 2. It is observed that Model 13-7-2 is the optimum of the three hidden layer models, with 13 nodes in the first, 7 in the second and 2 in the third hidden layer and Model 16-11-5-2 is the optimum of the four hidden layer models, with 16 nodes in the first, 11 in the second, 5 in the third and 2 in the fourth hidden layer. It can be seen that model 16-11-5-2 has the highest correlation coefficient, r (0.956) and has the lowest RMSE (1.06 mm) for validation set.

Table 2. Results of optimum networks. Optimum multiple

hidden layer models Correlation coefficient, r RMSE(mm)

13-7-2 Training 0.993 2.04 Testing 0.912 2.03 Validation 0.947 1.08 16-11-5-2

Training 0.991 2.86 Testing 0.919 2.12 Validation 0.956 1.06

The plots of the measured and predicted settlement for validation set for these

two models are shown in Figures 1-a, and 1-b.Comparisons between the results obtained from the optimal ANN model and three traditional methods commonly used to determine the settlement of piles are presented in the following section.

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(a) (b)

Fig. 1. Measured versus predicted settlements for ANN models with respect to the validation set: (a) Model 13-7-2 and (b) Model 16-11-5-2.

Traditional methods for settlement prediction

Many traditional methods for settlement prediction of piles are presented in literature. Among these, three are chosen for purpose of assessing the relative performance of the ANN model. These include the methods proposed by Vesic (1977), Poulos and Davis (1980), and Das (1995). These methods are chosen as they are commonly used and the database used in this work contains most parameters required to calculate settlement by these methods. Summary of these methods have been presented by Pooya Nejad et al (2009). Comparisons of the results obtained using the ANN and the three traditional methods for the validation set are presented in Figure 2. It can be seen that the ANN method performs better than the traditional methods.

Conclusions

A back-propagation neural network was used to demonstrate the feasibility of ANNs to predict the settlement of piles. A database containing 292 case records of actual field measurements for settlement of pile was used for model development and verification. The results indicate that back-propagation neural networks have the ability to predict the settlement of pile with an acceptable degree of accuracy (r=0.956, RMSE=1.06 mm) for predicted settlements ranging from 0.0 to 137.88 mm. The ANNs method has another advantage over the conventional methods in that once the model is trained, the model can be used as an accurate and quick tool for estimating the settlement of piles. In contrast with the conventional methods, the ANNs method does not need any manual work such as using tables or charts to calculate the settlement.

Results of this study indicate that ANNs have a number of significant benefits that make them a powerful and practical tool for settlement prediction of piles.

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Fig. 3. Measured versus predicted settlement for artificial neural network and traditional methods

Acknowledgements

The authors would like to thank Richard Herraman and Peter Lai from the Departments of Transportation in Adelaide and Florida, respectively for their assistance in providing access to some of their pile load test data.

Notation

The following symbols are used in this paper: Atip cross sectional area of end of pile; EA axial rigidity of pile; fc1,… fc5 average sleeve friction result along the first, second, third,

fourth, and fifth segments along the embedded length of the pile; L length of pile; Lembed embedded length of pile; O perimeter of pile; P applied load; qc1,…, qc5 average cone penetration test along the first, second, third,

fourth, and fifth segments along the embedded length of the pile; qctip average cone penetration test at the pile tip to the depth of influence;

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sm measured settlement; Zi the soil layer thickness.

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