The Netherlands is situated in a delta formed by the Rhine, Maas and Schelde rivers with much of the country being flat and altered anthropogenically, evident from its canalised streams, polders and dikes protecting the coastline and inland regions. Most of the country is dominated by Quartenary deposits, with the western half of the country immediately underlain by a very soft Holocene layer and the east by a firm sandy Pleistocene layer (Maljers et al., 2015). In the context of engineering applications, the western Holocene layer is particularly troublesome due to its high compressibility, with structures generally requiring long piles extending down towards the Pleistocene layer below (Houkes, 2016).

The data originates primarily from road and rail projects executed by Fugro throughout the Netherlands between 2008 and 2018 (see Fig. 1). For each location, sampling boreholes were automatically paired with CPT locations less than 25 m away, with the closest CPT location chosen where applicable. Given the size of the dataset, an individual geological assessment of each site was deemed infeasible and hence, a Python algorithm was developed for the oedometer–CPT test pairing process (Duffy, 2019).

In total, 286 oedometer–CPT pairs were used for the analysis, with the Koppejan's general constant of compressibility at stresses greater than the preconsolidation pressure C, the CPT cone resistance qc and the friction sleeve resistance fs brought forward for further analysis.

At an elementary level, decision trees are akin to a flow chart in that each “node” represents a variable, each “branch” represents a decision and each “leaf” represents an outcome. It can be used effectively for classification and regression purposes, with an example of a simple decision tree shown in Fig. 3.

In the process of creating a decision tree, the algorithm partitions the dataset into subsets of variables of similar magnitudes, ascertaining the effectiveness of potential splits as it moves through the tree. In other words, the tree assesses the improvement in model score (or reduction in error) caused by creating the split. The algorithm converges when it can no longer gain further information through the creation of more splits or when it reaches a pre-specified limit imposed on the model, known as the model's “hyperparameters”. An example of a hyperparameter may include the number of levels in the tree or the minimum number of samples required in a leaf node.

Boosting methods are an extension of the basic decision tree algorithm whereby the algorithm uses a combination of trees, with each new tree learning from the mistakes of previous trees. In this way, the model constantly aims to remove or reduce any pattern that may be preeminent in the residuals or the error. This is a core principle of the gradient boosting algorithm (Friedman, 2001).

In order to produce a result that is reliable and not a product of overfitting, 80 % of the data was randomly designated as training data, with the remaining 20 % being designated as unseen testing data. This split was chosen in order to retain a sufficient amount of testing data so a more robust and reliable result could be produced.

The input parameters chosen were qc, the ratio between fs and qc (also known as the friction ratio Rf) and σ0′, with Rf chosen in lieu of fs so that the possibility of any interpretability issues associated with the collinearity between qc and fs was avoided. C′ was used as the output parameter.

The gradient boosting model used as part of this study was implemented using the MLPRegressor class of the scikit-learn toolbox version 0.20.3 (Pedregosa et al., 2011), with 5-fold cross-validation used for hyperparameter tuning.

The model produced an r2 score of 0.73 and 0.37 for the training and testing sets respectively, with 5-fold cross validation returning a mean score of 0.36 with standard deviation of 0.115. In the context of geotechnical engineering, this can be described as a “medium to strong correlation” as per the guidelines set out by Jakobsen (2014).

This model also returned feature importances of 0.34, 0.13 and 0.53 for qc, Rf and σ0′ respectively. These scores highlight the role each variable plays in the calculation of the C′, with qc and σ0′ being the more dominant features in determining the model output, perhaps largely due to the relative inaccuracy associated with friction sleeve measurements (Lunne et al., 1997).

Notwithstanding, Fig. 4 shows that both the training and testing curves fail to converge together at higher sample sizes. This is indicative of variance within the model, a problem that may be resolved by increasing the number of samples and thus allowing the learning curves to converge more closely, redolent of a well-fitted model.

Furthermore, as illustrated by Fig. 5, there is significant fluctuation in the r2 score as the random state of the model is changed. In other words, if different training and testing sets are taken and if the model learns slightly differently compared to its last execution, the model score changes significantly. Based on a collective assessment of one hundred different random states, the median and maximum r2 scores obtained were 0.33 and 0.68 respectively. It is surmised that this instability is indicative of the variability and noise within the dataset, consequently leading to the presence of many local minima as the algorithms undergo gradient descent along the objective function. As a result of this, the model may be particularly prone to converging within these local minima, resulting in the dispersion of results as the random state is changed.

Consequently, it is recommended that further high-quality samples are sourced for the continued development of such an algorithm in order to yield a more complete convergence of the learning curves and to investigate the effect of the change of random state on the r2 score. Further development is also required into the automated process of pairing the CPTs to the oedometer tests, with a manual assessment taken where appropriate.