Probabilistic Soil Strata Delineation Using DPT Data and Bayesian Changepoint Detection

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.

Full text

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

2
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
6
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
15
tends to be computationally intensive.
16
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
18
(SPT). Like CPT, DPT uses a cylindrical steel cone penetrometer. However, DPT drives the
19
cone into the ground using a hammer, and the measured result is the number of blows  for a
20
given penetration (e.g. 100mm). The primary advantage of DPT over CPT is lower costs, faster
21
speed of operation and applicability in terrains with poor accessibility. However, there are limited
22
methods to interpret DPT results for soil strata delineation.
23
This paper aims to develop a method that enables fast soil strata delineation using DPT data.
24
The proposed method uses Bayesian changepoint detection (BCPD) methods to detect abrupt
25
changes in the soil data trends indicative of transitions between different soil strata. Unlike most
26
Bayesian approaches, the proposed method is computationally efficient. Two BCPD methods
27
are explored: (i) ‘online’, where each data point is processed as it becomes available and
28
inferences are made without knowledge of future measurements (e.g. Fearnhead and Liu, 2007;
29

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)
32
predominantly fine-grained soils (e.g. clay, silt), (ii) predominantly sand, and (iii) predominantly
33
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
35
proposed method bears some similarities to that of Zhang and Tumay (1999), who applied fuzzy
36
analysis to CPT data to identify three soil categories, although the methodology and nature of
37
the data are different. The performance of the proposed BCPD methods are evaluated using a
38
real-world case study.
39
40
Methodology
41
Changepoints are abrupt changes in data, which typically represent transitions between states,
42
as shown in Fig. 1. Given a sequence of data, these changepoints split the data into a set of
43
non-overlapping partitions, where it is assumed that the data within a partition are generated by
44
the same model. While many changepoint detection methods are available (Reeves et al. 2007;
45
Aminikhanghahi and Cook 2017; Truong et al. 2020), this paper focuses on Bayesian
46
changepoint detection (BCPD) methods.
47
Online Bayesian changepoint detection
48
The first method investigated in this paper is an online BCPD method (Adams and Mackay
49
2007), denoted ‘BCPD-ON’. In the following exposition, the notation  refers to the set of data
50
󰇝󰇞. BCPD-ON estimates the probability of a changepoint at a given depth based
51
only on data processed up to that depth. It does so by computing the probability distribution of a
52
random variable called the ‘run length’ , which represents the length of the current data
53
partition. Each new data point either (a) comes from the same distribution, in which case the
54
parameter estimates of the current distribution is updated using Bayes’ theorem and 
55
increases by one, or (b) it belongs to a new distribution which means a changepoint occurs and
56
the new distribution will reset back to the prior distribution and  resets to zero. When the most
57

3
probable value of  is zero, it is likely that there is a changepoint at depth , the probability of
58
which is equivalent to the posterior probability of  :
59
󰇛󰇜 󰇛 󰇜
(1)
The posterior distribution of the run length i.e. 󰇛󰇜 can be calculated as:
60
󰇛󰇜󰇛󰇜
󰇛󰇜
(2)
where 󰇛󰇜󰇛󰇜
. The joint distribution 󰇛󰇜 can be calculated using the
61
following recursive relationship:
62
󰇛󰇜  󰇛󰇜󰇛󰇜

 󰇛󰇜󰇛
󰇜󰇛󰇜

(3)
where 
 is the set of data associated with the run length . 󰇛󰇜 is a recursive term,
63
which represents the previous iteration of Eq. 3 at depth   . 󰇛󰇜 is the conditional
64
distribution of the run length. Finally, 󰇛
󰇜 is the posterior predictive distribution and it
65
can be calculated analytically by assuming that the data point  comes from some probability
66
distribution (e.g. Gaussian) and by adopting conjugate priors. More details about these
67
calculations can be found in Adams and Mackay (2007).
68
Offline Bayesian changepoint detection
69
The second method investigated in this paper is an offline BCPD method (Fearnhead 2005,
70
2006) denoted ‘BCPD-OFF’, which was previously employed by Houlsby and Houlsby (2013) for
71
clay layer delineation using undrained shear strength data. BCPD-OFF is based on a recursive
72
algorithm that computes the posterior probability distribution exactly over the location of
73
changepoints. This is significantly more efficient than previous Markov Chain Monte Carlo
74
(MCMC) approaches for computing the posterior (e.g. Punskaya et al. 2002).
75
In this case, the data within each partition are modelled by some probability distribution, with
76
distribution parameters independent of those determined for other partitions. Let represent
77

4
the th changepoint. The posterior distribution of  is . The probability of a
78
changepoint occurring at depth  can be calculated as:
79
󰇛󰇜   


(4)
where all possible scenarios of 1 to  changepoints thus far are considered. This approach
80
differs from that of Houlsby and Houlsby (2013), which first identifies the maximum a posteriori
81
(MAP) number of changepoints and then the conditional MAP locations of the changepoints.
82
This modification makes the outputs of BCPD-OFF and BCPD-ON identical, thereby allowing
83
direct comparisons.
84
 in Eq. 4 is obtained by marginalising out the previous changepoints:
85
   
(5)
As the probability of a changepoint is assumed to be dependent only on the previous
86
changepoint, the integrand in Eq. 5 can be calculated as:
87
  󰇛󰇜󰇛󰇜
(6)
Each of the terms on the right hand side of Eq. 6 can be calculated exactly and efficiently using
88
the recursive algorithm described in Fearnhead (2005, 2006).
89
90
Case study
91
The proposed BCPD methods are evaluated using a case-study involving multi-layered alluvial
92
deposits, consisting of sands, silts, clays, and gravels. This case study is based on the
93
Deutsche Bahn AG (German Rail) ‘DB46/2’ project, which is an expansion line from Emmerich
94
to Oberhausen in Germany. A complex three-dimensional (3D) ground model for this project
95
has been documented in Prinz (2019). This paper considers 26 DPT tests from the case study:
96
20 (approximately 77% of the dataset) are randomly selected for calibration of the priors and
97
hyperparameters for BCPD-OFF and BCPD-ON; the remaining 6 DPT locations (labelled ‘T1’ to
98
‘T6’) are used for testing to evaluate the performance of the calibrated methods. A plan map of
99
the DPT calibration and test locations is shown in Fig. 2.
100

5
Expert predictions are also made for each DPT location, where the soil strata are identified
101
among the three soil categories defined in the introduction. These expert predictions were
102
extracted from the 3D ground model that was developed separately for the case study (Prinz
103
2019). This ground model was based on careful, manual interpretation of both the DPT data and
104
the borehole data in an integrated manner, ensuring no conflicts between the interpretation of
105
the soil layering boundaries based on both types of data (e.g. the soil stratification interpreted
106
from the DPT data should be consistent with that observed from a neighbouring borehole). Fig.
107
3 shows a typical DPT profile from one of the DPT locations and its corresponding expert
108
prediction of the soil strata. The proposed BCPD methods will be applied to DPT data only.
109
110
Calibration
111
For both BCPD-OFF and BCPD-ON, the data in each partition are assumed to be normally
112
distributed with unknown mean  and variance . Therefore, the DPT data were preprocessed
113
using a Freeman-Tukey transformation (Freeman and Tukey 1950):  
114
where  represents the raw DPT blowcount data. This transformation is typically used to make
115
discrete count data better approximate a normal distribution (Mosteller and Youtz 2006; Lin and
116
Xu 2020). To test for normality of the transformed data, the Shapiro-Wilk test (Shapiro and Wilk
117
1965) was applied to the transformed data in each soil layer at DPT locations where
118
neighbouring borehole data is available to determine the approximate locations of the soil layer
119
boundaries. The p-values obtained are greater than 0.05 and thus the null hypothesis that the
120
transformed data is normally distributed is not rejected. Following Houlsby and Houlsby (2013),
121
the variance  is assumed to follow an inverse gamma distribution and the distribution
122
parameters  = 1.8 and  = 0.38 are obtained by curve-fitting the cumulative distribution of the
123
variance for the DPT calibration dataset, as shown in Fig. 4.
124
Outputs of interest for both BCPD-ON and BCPD-OFF are the probabilities of a changepoint
125
occurrence at each depth (i.e. using Eq. 1 and Eq. 4, respectively). When the changepoint
126
probability exceeds a predefined threshold , the soil is considered to have changed category
127
at this depth. The optimal value of  is dependent on the method adopted (BCPD-ON or
128
BCPD-OFF) and is calibrated as a hyperparameter. For each method, a grid search is
129

6
implemented within the set of trial  󰇝󰇞 to identify the
130
value of  that achieve the best match with the expert predictions for the soil stratification at
131
each DPT calibration location. To quantify the match with expert predictions, the accuracy
132
measure, F1 score, is adopted,
133
F1 score = 2(Precision * Sensitivity)/(Precision + Sensitivity)
(7)
where Precision = True Positive/(True Positive + False Positive) and Sensitivity = True
134
Positive/(True Positive + False Negative). True Positive (TP) is the number of times an expert
135
prediction for soil layer boundary has been correctly identified, while False Positive (FP) is the
136
number of times an expert prediction for soil layer boundary has been incorrectly identified.
137
False Negative (FN) is the number of times an expert prediction for soil layer boundary has not
138
been identified. A higher F1 value indicates a better match with the expert predictions. As the
139
predicted boundaries based on the DPT data are not expected to exactly match the expert
140
predictions, this paper considers a soil layer boundary to be correctly identified if the DPT-
141
predicted boundary is within a distance of 1m from the expert prediction for a boundary. The
142
grid search exercise gives the optimal values of  = 0.45 and 0.4 for BCPD-OFF and BCPD-
143
ON respectively.
144
145
Results
146
Fig. 5 shows the soil strata predictions determined using BCPD-OFF and BCPD-ON for the 6
147
DPT test locations. The BCPD changepoint probability predictions are shown in the figure as
148
grey lines and a soil strata boundary is identified when these predictions exceed .
149
From this figure, it can be observed that both BCPD-OFF and BCPD-ON perform well for most
150
locations, where the predicted soil strata boundaries are similar to the expert predictions. The
151
exception to this is Location T3, where the expert prediction for the soil strata is very complex,
152
and both BCPD methods only detect some of the soil strata boundaries. Nevertheless, the
153
overall performance is encouraging as the BCPD predictions agree well with the expert
154
predictions, despite using information only from the local DPT data. Some of the soil strata
155

7
boundary detections are noteworthy (e.g. see Fig. 5d), as they are not obvious from manual
156
inspection of the noisy DPT data alone.
157
Comparing the two BCPD methods, it is evident that BCPD-OFF is the more sensitive of the
158
two, as it can detect more soil strata boundaries (e.g. at locations T3 and T4), despite having a
159
higher  than BCPD-ON. However, this increased sensitivity comes with the drawback of
160
producing more false positives (see Figs. 5b, c). To quantify the accuracy of both methods, their
161
F1 scores are calculated based on Eq. 7, as detailed in Table 1. BCPD-ON has a slightly higher
162
F1 score than BCPD-OFF, indicating that BCPD-ON has a slightly better balance of precision
163
and sensitivity. In terms of computational efficiency, BCPD-ON has the advantage of being
164
much faster than BCPD-OFF (on average, BCPD-ON takes approximately 0.03 seconds to
165
process each DPT location, while BCPD-OFF takes approximately 5 seconds).
166
A key highlight is that both BCPD-OFF and BCPD-ON could detect soil strata boundaries
167
quickly and automatically without manual intervention. This makes them helpful to industry
168
practitioners for extracting additional insights from the DPT data to complement their current
169
workflow for identifying soil strata. A useful application of the approach could be, for example, to
170
assist the design of large-scale foundation projects such as solar farms. Engineers could be
171
faced with up to 1000 DPT locations in one project, and this approach provides a consistent,
172
automated and rapid way to interpret the soil stratigraphy.
173
When applying these BCPD methods to a new site, a calibration process should be carried out
174
to obtain site-specific values for both the priors and the  hyperparameter; this should provide
175
improved soil layer boundary detection results. Site-specific calibration should not be an issue
176
as DPT tests are typically carried out in conjunction with borehole tests. However, if calibration
177
data is not available at the new site, the calibrated parameters in this paper may be used for
178
preliminary analysis, using the BCPD methods to highlight potential locations of soil layer
179
boundaries through the ‘spikes’ in the changepoint probability. However, caution is advised as a
180
non-site specific calibration of  and the priors will affect the precision of the soil layer
181
boundary detections. To investigate the sensitivity of the calibration to the number of DPT tests,
182
the calibration results (i.e. the calibrated values for ) were determined using random
183
selections of 3, 4, 5, 6, 7, 8, 9, 10, 15, 20 DPT tests. The analysis indicates that when 5 or more
184

8
DPT tests are used for calibration, the calibrated  values are the same and the calibrated
185
values of  change by less than 4% from the values used in the current study. However,
186
caution should be advised against taking this as a general rule as these results may be specific
187
to the dataset used in the current study. Furthermore, in this study, each DPT test location is
188
near a calibration location. The effect of the distance between the calibration and test locations
189
on the predictive accuracy of the BCPD methods has not been evaluated in this study. Further
190
research is required with a comprehensive study, involving a larger database of DPT data from
191
a wider range of sites, to provide more definitive answers to the above questions and to obtain
192
values of the priors and hyperparameter more suited to general use across different sites.
193
194
Conclusion
195
This paper proposes a fast, automatic Bayesian approach for soil strata delineation using DPT
196
data. The proposed approach is based on the concept of offline and online Bayesian
197
changepoint detection, which allows both retrospective and real-time soil strata delineation. Its
198
reliability and utility have been evaluated using DPT data from a real-world case study. The
199
proposed approach is very fast to run and provides additional insights from the DPT data for a
200
more robust soil strata identification solution.
201
202
Acknowledgements
203
The authors would like to acknowledge Deutsche Bahn AG and Aloys Kisse, Dr.-Ing. for the use
204
of the test data for research purposes. Oriol Ciurana, OSI is gratefully acknowledged in the
205
development of the 3D ground model referred to herein. The third author is funded by the Royal
206
Academy of Engineering under the Research Fellowship scheme.
207
208
Competing interests statement
209
Competing interests: The authors declare there are no competing interests.
210
211
Funding statement
212
Funding: The authors declare no specific funding for this work.
213
214

9
Data availability statement
215
Some or all data, models, or code that support the findings of this study are available from the
216
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
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3
2
0.80
0.857
0.827
BCPD-ON
10
0
4
1.00
0.714
0.833
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303
304
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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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Fig. 2 Locations of DPT dataset used for calibration and testing of the BCPD methods.
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317

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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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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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