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Probabilistic soil strata delineation using DPT data and Bayesian changepoint detection

Stephen K. Suryasentana1, Ph.D.

Myles Lawler2, Ph.D.

Brian B. Sheil3, Ph.D.

Barry M. Lehane4, Ph.D.

Affiliations

1 Lecturer, Department of Civil and Environmental Engineering, University of Strathclyde, 75

Montrose St, Glasgow G1 1XJ, UK.

2 Independent Geotechnical Consultant, Ireland.

3 RAEng Research Fellow, Department of Engineering Science, University of Oxford, Parks

Road, Oxford OX1 3PJ, UK.

4 Winthrop Professor, Department of Civil, Environmental and Mining Engineering, University of

Western Australia, 35 Stirling Hwy, Crawley WA 6009, Australia.

Full contact details of corresponding author

Stephen K. Suryasentana

stephen.suryasentana@strath.ac.uk

Main text word count: 2517

Figures: 5

Tables: 1

Mar 26, 2022

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Abstract

Soil strata delineation is a fundamental step for any geotechnical engineering design. The

dynamic penetration test (DPT) is a fast, low cost in-situ test that is commonly used to locate

boundaries between strata of differing density and driving resistance. However, DPT data are

often noisy and typically require time-consuming, manual interpretation. This paper investigates

a probabilistic method that enables delineation of dissimilar soil strata (where each stratum is

deemed to belong to different soil groups based on their particle size distribution) by processing

DPT data with Bayesian changepoint detection methods. The accuracy of the proposed method

is evaluated using DPT data from a real-world case study, which highlights the potential of the

proposed method. This study provides a methodology for faster DPT-based soil strata

delineation, which paves the way for more cost-effective geotechnical designs.

Keywords

bayesian analysis, site investigation, soil classification

3

List of notation

N DPT no. of blows

‘Run length’ random variable

Set of data

Parameters of inverse gamma distribution

Changepoint probability threshold

Introduction

1

Soil strata delineation is a fundamental step for any geotechnical engineering design.

2

Delineation divides the soil volume into separate layers of geological material deemed to belong

3

to the same group. This process typically requires a time-consuming, manual interpretation of a

4

combination of borehole data and associated in-situ and laboratory test results (Parry et al.

5

2014). It is highly desirable to develop a rapid approach that can delineate the soil strata

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automatically.

7

The cone penetration test (CPT) (Lunne et al. 1997) is an in-situ ground investigation method

8

that is widely used for soil delineation by applying soil behaviour type (SBT) classification rules

9

(e.g. Robertson 1990; Jefferies and Davies 1993; Schneider et al. 2008) to the measured CPT

10

data. Other delineation approaches include fuzzy analysis (Zhang and Tumay 1999), clustering

11

analysis (Hegazy and Mayne 2002; Depina et al. 2016), signal processing analysis (Ching et al.

12

2015) and statistical/Bayesian analysis (Wickremesinghe and Campanella 1991; Phoon et al.

13

2003; Wang et al. 2013, 2019, 2020; Li et al. 2016; Cao et al. 2019). Bayesian analysis has the

14

advantages of being robust to noisy data and allowing quantification of uncertainty, although it

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tends to be computationally intensive.

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The dynamic probing/penetration test (DPT) is a fast and low cost in-situ ground investigation

17

method (BS 2005), which bears some similarities to both CPT and the standard penetration test

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(SPT). Like CPT, DPT uses a cylindrical steel cone penetrometer. However, DPT drives the

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cone into the ground using a hammer, and the measured result is the number of blows for a

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given penetration (e.g. 100mm). The primary advantage of DPT over CPT is lower costs, faster

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speed of operation and applicability in terrains with poor accessibility. However, there are limited

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methods to interpret DPT results for soil strata delineation.

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This paper aims to develop a method that enables fast soil strata delineation using DPT data.

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The proposed method uses Bayesian changepoint detection (BCPD) methods to detect abrupt

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changes in the soil data trends indicative of transitions between different soil strata. Unlike most

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Bayesian approaches, the proposed method is computationally efficient. Two BCPD methods

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are explored: (i) ‘online’, where each data point is processed as it becomes available and

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inferences are made without knowledge of future measurements (e.g. Fearnhead and Liu, 2007;

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2

Adams and MacKay, 2007); and (ii) ‘offline’, where the entire DPT dataset is required before

30

making inference (e.g. Barry and Hartigan, 1993; Stephens, 1994; Fearnhead, 2005, 2006).

31

The proposed method divides the soil profile up into three dissimilar soil categories: (i)

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predominantly fine-grained soils (e.g. clay, silt), (ii) predominantly sand, and (iii) predominantly

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gravel. These soil categories have very different permeability, stiffness and strength properties

34

such that poor identification will have a negative impact on optimal geotechnical design. The

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proposed method bears some similarities to that of Zhang and Tumay (1999), who applied fuzzy

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analysis to CPT data to identify three soil categories, although the methodology and nature of

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the data are different. The performance of the proposed BCPD methods are evaluated using a

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real-world case study.

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Methodology

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Changepoints are abrupt changes in data, which typically represent transitions between states,

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as shown in Fig. 1. Given a sequence of data, these changepoints split the data into a set of

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non-overlapping partitions, where it is assumed that the data within a partition are generated by

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the same model. While many changepoint detection methods are available (Reeves et al. 2007;

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Aminikhanghahi and Cook 2017; Truong et al. 2020), this paper focuses on Bayesian

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changepoint detection (BCPD) methods.

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Online Bayesian changepoint detection

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The first method investigated in this paper is an online BCPD method (Adams and Mackay

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2007), denoted ‘BCPD-ON’. In the following exposition, the notation refers to the set of data

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. BCPD-ON estimates the probability of a changepoint at a given depth based

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only on data processed up to that depth. It does so by computing the probability distribution of a

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random variable called the ‘run length’ , which represents the length of the current data

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partition. Each new data point either (a) comes from the same distribution, in which case the

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parameter estimates of the current distribution is updated using Bayes’ theorem and

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increases by one, or (b) it belongs to a new distribution which means a changepoint occurs and

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the new distribution will reset back to the prior distribution and resets to zero. When the most

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3

probable value of is zero, it is likely that there is a changepoint at depth , the probability of

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which is equivalent to the posterior probability of :

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(1)

The posterior distribution of the run length i.e. can be calculated as:

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(2)

where

. The joint distribution can be calculated using the

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following recursive relationship:

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(3)

where

is the set of data associated with the run length . is a recursive term,

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which represents the previous iteration of Eq. 3 at depth . is the conditional

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distribution of the run length. Finally,

is the posterior predictive distribution and it

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can be calculated analytically by assuming that the data point comes from some probability

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distribution (e.g. Gaussian) and by adopting conjugate priors. More details about these

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calculations can be found in Adams and Mackay (2007).

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Offline Bayesian changepoint detection

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The second method investigated in this paper is an offline BCPD method (Fearnhead 2005,

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2006) denoted ‘BCPD-OFF’, which was previously employed by Houlsby and Houlsby (2013) for

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clay layer delineation using undrained shear strength data. BCPD-OFF is based on a recursive

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algorithm that computes the posterior probability distribution exactly over the location of

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changepoints. This is significantly more efficient than previous Markov Chain Monte Carlo

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(MCMC) approaches for computing the posterior (e.g. Punskaya et al. 2002).

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In this case, the data within each partition are modelled by some probability distribution, with

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distribution parameters independent of those determined for other partitions. Let represent

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4

the th changepoint. The posterior distribution of is . The probability of a

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changepoint occurring at depth can be calculated as:

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(4)

where all possible scenarios of 1 to changepoints thus far are considered. This approach

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differs from that of Houlsby and Houlsby (2013), which first identifies the maximum a posteriori

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(MAP) number of changepoints and then the conditional MAP locations of the changepoints.

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This modification makes the outputs of BCPD-OFF and BCPD-ON identical, thereby allowing

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direct comparisons.

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in Eq. 4 is obtained by marginalising out the previous changepoints:

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(5)

As the probability of a changepoint is assumed to be dependent only on the previous

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changepoint, the integrand in Eq. 5 can be calculated as:

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(6)

Each of the terms on the right hand side of Eq. 6 can be calculated exactly and efficiently using

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the recursive algorithm described in Fearnhead (2005, 2006).

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Case study

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The proposed BCPD methods are evaluated using a case-study involving multi-layered alluvial

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deposits, consisting of sands, silts, clays, and gravels. This case study is based on the

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Deutsche Bahn AG (German Rail) ‘DB46/2’ project, which is an expansion line from Emmerich

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to Oberhausen in Germany. A complex three-dimensional (3D) ground model for this project

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has been documented in Prinz (2019). This paper considers 26 DPT tests from the case study:

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20 (approximately 77% of the dataset) are randomly selected for calibration of the priors and

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hyperparameters for BCPD-OFF and BCPD-ON; the remaining 6 DPT locations (labelled ‘T1’ to

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‘T6’) are used for testing to evaluate the performance of the calibrated methods. A plan map of

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the DPT calibration and test locations is shown in Fig. 2.

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5

Expert predictions are also made for each DPT location, where the soil strata are identified

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among the three soil categories defined in the introduction. These expert predictions were

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extracted from the 3D ground model that was developed separately for the case study (Prinz

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2019). This ground model was based on careful, manual interpretation of both the DPT data and

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the borehole data in an integrated manner, ensuring no conflicts between the interpretation of

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the soil layering boundaries based on both types of data (e.g. the soil stratification interpreted

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from the DPT data should be consistent with that observed from a neighbouring borehole). Fig.

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3 shows a typical DPT profile from one of the DPT locations and its corresponding expert

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prediction of the soil strata. The proposed BCPD methods will be applied to DPT data only.

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Calibration

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For both BCPD-OFF and BCPD-ON, the data in each partition are assumed to be normally

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distributed with unknown mean and variance . Therefore, the DPT data were preprocessed

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using a Freeman-Tukey transformation (Freeman and Tukey 1950):

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where represents the raw DPT blowcount data. This transformation is typically used to make

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discrete count data better approximate a normal distribution (Mosteller and Youtz 2006; Lin and

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Xu 2020). To test for normality of the transformed data, the Shapiro-Wilk test (Shapiro and Wilk

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1965) was applied to the transformed data in each soil layer at DPT locations where

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neighbouring borehole data is available to determine the approximate locations of the soil layer

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boundaries. The p-values obtained are greater than 0.05 and thus the null hypothesis that the

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transformed data is normally distributed is not rejected. Following Houlsby and Houlsby (2013),

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the variance is assumed to follow an inverse gamma distribution and the distribution

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parameters = 1.8 and = 0.38 are obtained by curve-fitting the cumulative distribution of the

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variance for the DPT calibration dataset, as shown in Fig. 4.

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Outputs of interest for both BCPD-ON and BCPD-OFF are the probabilities of a changepoint

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occurrence at each depth (i.e. using Eq. 1 and Eq. 4, respectively). When the changepoint

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probability exceeds a predefined threshold , the soil is considered to have changed category

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at this depth. The optimal value of is dependent on the method adopted (BCPD-ON or

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BCPD-OFF) and is calibrated as a hyperparameter. For each method, a grid search is

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6

implemented within the set of trial to identify the

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value of that achieve the best match with the expert predictions for the soil stratification at

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each DPT calibration location. To quantify the match with expert predictions, the accuracy

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measure, F1 score, is adopted,

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F1 score = 2(Precision * Sensitivity)/(Precision + Sensitivity)

(7)

where Precision = True Positive/(True Positive + False Positive) and Sensitivity = True

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Positive/(True Positive + False Negative). True Positive (TP) is the number of times an expert

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prediction for soil layer boundary has been correctly identified, while False Positive (FP) is the

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number of times an expert prediction for soil layer boundary has been incorrectly identified.

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False Negative (FN) is the number of times an expert prediction for soil layer boundary has not

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been identified. A higher F1 value indicates a better match with the expert predictions. As the

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predicted boundaries based on the DPT data are not expected to exactly match the expert

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predictions, this paper considers a soil layer boundary to be correctly identified if the DPT-

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predicted boundary is within a distance of 1m from the expert prediction for a boundary. The

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grid search exercise gives the optimal values of = 0.45 and 0.4 for BCPD-OFF and BCPD-

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ON respectively.

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Results

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Fig. 5 shows the soil strata predictions determined using BCPD-OFF and BCPD-ON for the 6

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DPT test locations. The BCPD changepoint probability predictions are shown in the figure as

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grey lines and a soil strata boundary is identified when these predictions exceed .

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From this figure, it can be observed that both BCPD-OFF and BCPD-ON perform well for most

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locations, where the predicted soil strata boundaries are similar to the expert predictions. The

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exception to this is Location T3, where the expert prediction for the soil strata is very complex,

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and both BCPD methods only detect some of the soil strata boundaries. Nevertheless, the

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overall performance is encouraging as the BCPD predictions agree well with the expert

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predictions, despite using information only from the local DPT data. Some of the soil strata

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7

boundary detections are noteworthy (e.g. see Fig. 5d), as they are not obvious from manual

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inspection of the noisy DPT data alone.

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Comparing the two BCPD methods, it is evident that BCPD-OFF is the more sensitive of the

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two, as it can detect more soil strata boundaries (e.g. at locations T3 and T4), despite having a

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higher than BCPD-ON. However, this increased sensitivity comes with the drawback of

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producing more false positives (see Figs. 5b, c). To quantify the accuracy of both methods, their

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F1 scores are calculated based on Eq. 7, as detailed in Table 1. BCPD-ON has a slightly higher

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F1 score than BCPD-OFF, indicating that BCPD-ON has a slightly better balance of precision

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and sensitivity. In terms of computational efficiency, BCPD-ON has the advantage of being

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much faster than BCPD-OFF (on average, BCPD-ON takes approximately 0.03 seconds to

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process each DPT location, while BCPD-OFF takes approximately 5 seconds).

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A key highlight is that both BCPD-OFF and BCPD-ON could detect soil strata boundaries

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quickly and automatically without manual intervention. This makes them helpful to industry

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practitioners for extracting additional insights from the DPT data to complement their current

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workflow for identifying soil strata. A useful application of the approach could be, for example, to

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assist the design of large-scale foundation projects such as solar farms. Engineers could be

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faced with up to 1000 DPT locations in one project, and this approach provides a consistent,

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automated and rapid way to interpret the soil stratigraphy.

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When applying these BCPD methods to a new site, a calibration process should be carried out

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to obtain site-specific values for both the priors and the hyperparameter; this should provide

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improved soil layer boundary detection results. Site-specific calibration should not be an issue

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as DPT tests are typically carried out in conjunction with borehole tests. However, if calibration

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data is not available at the new site, the calibrated parameters in this paper may be used for

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preliminary analysis, using the BCPD methods to highlight potential locations of soil layer

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boundaries through the ‘spikes’ in the changepoint probability. However, caution is advised as a

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non-site specific calibration of and the priors will affect the precision of the soil layer

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boundary detections. To investigate the sensitivity of the calibration to the number of DPT tests,

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the calibration results (i.e. the calibrated values for ) were determined using random

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selections of 3, 4, 5, 6, 7, 8, 9, 10, 15, 20 DPT tests. The analysis indicates that when 5 or more

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DPT tests are used for calibration, the calibrated values are the same and the calibrated

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values of change by less than 4% from the values used in the current study. However,

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caution should be advised against taking this as a general rule as these results may be specific

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to the dataset used in the current study. Furthermore, in this study, each DPT test location is

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near a calibration location. The effect of the distance between the calibration and test locations

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on the predictive accuracy of the BCPD methods has not been evaluated in this study. Further

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research is required with a comprehensive study, involving a larger database of DPT data from

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a wider range of sites, to provide more definitive answers to the above questions and to obtain

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values of the priors and hyperparameter more suited to general use across different sites.

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Conclusion

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This paper proposes a fast, automatic Bayesian approach for soil strata delineation using DPT

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data. The proposed approach is based on the concept of offline and online Bayesian

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changepoint detection, which allows both retrospective and real-time soil strata delineation. Its

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reliability and utility have been evaluated using DPT data from a real-world case study. The

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proposed approach is very fast to run and provides additional insights from the DPT data for a

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more robust soil strata identification solution.

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Acknowledgements

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The authors would like to acknowledge Deutsche Bahn AG and Aloys Kisse, Dr.-Ing. for the use

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of the test data for research purposes. Oriol Ciurana, OSI is gratefully acknowledged in the

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development of the 3D ground model referred to herein. The third author is funded by the Royal

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Academy of Engineering under the Research Fellowship scheme.

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Competing interests statement

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Competing interests: The authors declare there are no competing interests.

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Funding statement

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Funding: The authors declare no specific funding for this work.

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Data availability statement

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Some or all data, models, or code that support the findings of this study are available from the

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corresponding author upon reasonable request.

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Table 1 Accuracy calculations for the BCPD-OFF and BCPD-ON soil layer boundary predictions

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TP

FP

FN

Precision

Sensitivity

F1 score

BCPD-OFF

12

3

2

0.80

0.857

0.827

BCPD-ON

10

0

4

1.00

0.714

0.833

302

303

304

305

13

Figures

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Fig. 1 Illustration of a sequence of data with abrupt changes, where y is the measured quantity

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and x is the index. The dashed lines represent the locations of the changepoints.

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14

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Fig. 2 Locations of DPT dataset used for calibration and testing of the BCPD methods.

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15

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Fig. 3 Exemplar DPT profile showing the development of the DPT blowcount, , with depth.

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The expert prediction for the soil strata at this location is also shown, where the soil categories

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are shown in the legend.

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16

330

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Fig. 4 Cumulative distribution of the variance of the transformed data within each soil strata

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identified in the DPT calibration dataset, compared with the inverse gamma cumulative

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distribution with .

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(a)

(b)

(c)

(d)

(e)

(f)

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Fig. 5 Comparison of soil strata boundaries (shown as horizontal black lines) predicted by BCPD-OFF and BCPD-ON, with the expert predictions, at locations T1 to T6.

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