Pile foundations are vital components of substructure design. They enable the transmission of structural loads through weak soils to stable bedrock or other competent strata. The primary objectives of pile foundation design are to minimize settlement and enhance compressive strength.
Settlement arises from an increase in effective stress, which leads to a reduction in the volume of the subsoil. This phenomenon comprises two main components: (i) elastic compression of the soil skeleton,
which occurs rapidly and is typically minimal, and (ii) consolidation, or volume change, resulting from water expulsion. This process occurs swiftly in coarse-grained soils while taking place at a slower rate in fine-grained soils.
Numerous experimental and theoretical approaches are available for determining settlements. Given the challenges associated with obtaining undisturbed samples, many settlement prediction methods have
concentrated on correlating data from in situ tests, such as the cone penetration test (CPT), standard penetration test (SPT), and dilatometer test. However, most existing methods for predicting pile settlement often rely on simplifying assumptions regarding the influencing factors, which can result in inconsistent and inaccurate predictions. Consequently, there is a pressing need for alternative methodologies that can yield more reliable and precise settlement predictions.
The introduction of artificial neural network (ANN) back-propagation in 1986 has brought significant advancements in predictive modelling within the field of geotechnical engineering. This article discusses a
noteworthy study conducted by F. Pooya Nejad et al. at the Department of Civil Engineering, Ferdowsi University of Mashhad, Iran, which focuses on the prediction of pile foundation settlement utilizing a Standard Penetration Test (SPT) database. The authors employed NEUFRAME software to develop their ANN model, demonstrating its effectiveness in this application.
The dataset employed in this study comprises 1013 samples derived from 76 individual load tests. It includes 12 specific input parameters, which are as follows: (i) the type of pile load test conducted (either maintained load or constant rate of penetration); (ii) the material of the pile (concrete, steel, composite, or plastic); (iii) the method of installation used (replacement or displacement); (iv) the type of pile tip (either closed or open); (v) the axial rigidity of the pile (vi) the cross-sectional area of the pile tip (Atip); (vii) the perimeter of the pile in contact with the soil (viii) the length of the pile (L); (ix) the embedded length of the pile (x) the averaged and corrected Standard Penetration Test (SPT) blow count per 300 mm along the embedded length of the pile (N1, N2, N3, N4, N5); (xi) the corrected SPT blow count per 300 mm at the tip of the pile (Ntip); and (xii) the applied load (P). The single output variable of interest in this analysis is pile settlement. NEUFRAME allocates an input node for each text parameter in an artificial neural network (ANN) model.
The input layer consists of 22 nodes, including:
– 2 for the type of test (ML, CRP)
– 4 for pile material (Concrete, Steel, Composite, Plastic)
– 2 for the method of installation (Replacement,Displacement)
– 2 for the pile tip (Closed, Open)
– 1 for each input variable (EA, Atip, O, L, Lembed, N1, N2,N3, N4, N5, Ntip)
– 1 for parameter P
The output layer contains a single node representing the measured value of settlement (sm). The dataset was divided into 85.6% for training and 14.4% for validation.
Two artificial neural network (ANN) models were developed: one consisting of a single hidden layer and the other incorporating multiple hidden layers. For the single hidden layer model, a sigmoidal transfer function was utilized for both the hidden and output layers. Conversely, the multi-hidden layer models employed a hyperbolic tangent (tanh) transfer function for the hidden layers, while the output layer utilized a sigmoidal transfer function. This combination of transfer functions resulted in the most accurate predictions of pile settlement when compared to the measured values.
The optimal hyperparameter values were determined through a systematic trial-and-error approach, yielding a momentum term of 0.6 and a learning rate of 0.4. The ANN architecture was further refined by experimenting with varying the number of nodes (ranging from 3 to 45) in the single hidden layer model. Additionally, multi-hidden layer networks were trained with two, three, and four hidden layers, each featuring different node configurations to enhance model performance.
The optimal model for two hidden layers is identified as Model 14-6, which comprises 14 nodes in the first hidden layer and 6 nodes in the second. For the three hidden layer configuration, Model 13-8-3 is
determined to be the most effective, featuring 13 nodes in the first layer, 8 in the second, and 3 in the third layer. The four hidden layer model demonstrates the best overall performance, characterized by a structure of 15-13-5-2 nodes. It is important to note that the performance of this four hidden layer model is significantly influenced by the parameters of the back-propagation algorithm.
Additionally, the findings indicate that the artificial neural network (ANN) model with a single hidden layer is less effective, as it produces inaccurate predictions of negative settlements in lower settlement
regions. Furthermore, this single hidden layer model shows low correlation coefficients and high root mean square errors when applied to the validation set.
To assess the input variables that have the greatest influence on settlement predictions, a sensitivity analysis has been conducted on the trained neural network. The findings indicate that the applied load ,
the embedded length of the pile, and the soil properties are the most critical factors affecting predicted settlement, regardless of the initial weights used during training. This study demonstrates that artificial neural networks (ANNs) provide more precise predictions of pile settlement compared to the traditional
methods evaluated.
Reference
Nejad, F. P., Jaksa, M. B., Kakhi, M., & McCabe, B. A. (2009). Prediction of pile settlement using artificial neural networks based on standard penetration test data. Computers and geotechnics, 36(7), 1125-1133.
Nicely written.