Minding the geotechnical data gap: appraisal of the variability of key soil parameters for slope stability modelling in Saint Lucia
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Abstract
Identification of failure thresholds and critical uncertainties associated with slope stability often requires the specification of geotechnical parameter values for input into a physicallybased model. The variation of these parameters (including mechanical soil properties such as effective friction angle and cohesion) can have a significant impact on the computed factor of safety. These uncertainties arise from natural variations in soils, measurement techniques, and lack of reliable information. Researchers may use statistical analysis coupled with numerical simulation to determine possible ranges of slope factors of safety and the relative influence of geotechnical and other parameters, such as topsoil depth and rainfall. This study investigates the variation of geotechnical parameters observed on the island of Saint Lucia in the Eastern Caribbean. A database of particle size distributions, insitu moisture contents, Atterberg and direct shear box test results is compiled from 91 samples of tropical soils in Saint Lucia. A study of various probability distributions shows that the Weibull distribution may be favoured for the effective friction angle of the Saint Lucian soils considered based on the Akaike information criterion, employed as an estimator of the relative quality of statistical models dealing with the tradeoff between goodnessoffit and simplicity of the model.
Keywords
Tropical soils Friction angle Probability distributions Weibull distribution Landslides Saint LuciaNotation
 c'
cohesion intercept, kPa
 CF
clay fraction
 k
number of parameters in a model
 L
likelihood
 n
number of data points
 PI
plasticity index, %
 p
pvalue; probability of rejecting the null hypothesis and thus concluding that no correlation exists between two parameters
 r
correlation coefficient
 R^{2}
coefficient of determination
 SF
siltclay fraction, % (taken here as percent passing the 0.075mm sieve)
 w_{nat}
natural water content, %
 w_{L}
liquid limit, %
 w_{P}
plastic limit, %
 x
a variable
 β
Weibull shape factor
 δ
Weibull scale factor
 μ
statistical mean
 σ'
effective normal stress, kPa
 τ
shear stress, kPa
 ϕ'
effective friction angle, degrees
 ϕ'_{crit}
effective critical state friction angle, degrees
 ϕ'_{peak}
effective peak friction angle, degrees
Introduction
Landslides and geotechnical data
Landslides triggered by rainfall and seismic events affect people, the built environment and economies worldwide. The susceptibility of slopes to landslides is due to a combination of preparatory factors including slope angle, geology, soil properties, groundwater conditions and vegetation cover. Human actions such as the construction of buildings and roads or changes to natural vegetation can affect these preparatory factors and decrease the stability of a slope. Rapid rates of urbanisation and land use change (both planned and informal) in landslideprone developing countries mean that they are disproportionately affected by landslide hazards and their consequences (Petley, 2009). In such locations, landslides frequently occur due to a combination of localised factors such as slopecutting, surcharge loading, altered surface water drainage patterns, and leakage from water services, water tanks and latrines – as reported in the city of São José dos Campos, Brazil, by Mendes et al. (2018), for example.
Implementation of landslide hazard assessments at the required resolution to inform landslide exposure, vulnerability and risk assessments, and risk management are often hindered by the limited availability of data in such regions. Acquisition of soil geotechnical information poses a particular challenge due to the expense of soil sampling in relevant locations and laboratory testing, the inherent heterogeneity of soils, the disturbance of insitu soil structure and moisture content that occurs with sample extraction, and the resulting uncertainties associated with parameter values and sparse data. Furthermore, any such data from previous studies and projects tend to be inaccessible or undocumented. Thus, engineers and slope stability modellers encounter a geotechnical data gap when attempting to use physicsbased models to investigate highly localised urban landslide processes (and potential mitigation measures) and when parameterising spatiallydistributed landslide hazard models in Geographical Information Systems (GIS) at city or regional scales (e.g., Mutekanga et al. 2010; RingroseVoase et al. 2017; Du et al. 2018).
Effective friction angle
More sophisticated models representing dynamic hydrological processes of rainfall infiltration, subsurface flow, pore water pressure and slope stability response have shown that in certain cases the choice of friction angle design values can affect computed factors of safety to the same extent as variations in rainfall for deeply weathered residual soil slopes in the humid tropics (e.g., Holcombe et al. 2016, Beesley et al. 2017 and Shepheard et al., 2018a, 2018b). Physicallybased models can also be applied using reliability or stochastic approaches, in which input parameters are described using probability distributions rather than discrete values. Sensitivity analysis of model inputs and outputs may then be performed to identify dominant slope stability mechanisms for different classes of slope, system behavioural thresholds and ultimately data acquisition priorities.
Geotechnical correlations and classification systems
Where extensive laboratory testing is not available or affordable, it is common practice to use comparisons with other soil index properties, such as the plasticity index (PI) as a proxy for friction angle (e.g., Kenney, 1959; Brooker and Ireland, 1965, Ladd et al. 1977 and Sorensen and Okkels, 2013). Such relationships allow geotechnical engineers to draw additional information from the routine soil tests carried out as part of civil engineering design and construction of foundations and transport infrastructure.
Another source of proxies for soil mechanical properties can be agricultural soil maps and databases developed at national and worldwide scales. Agricultural soil data often include soil indices such as particle size distribution and soil bulk density and aspects of soil chemistry relating to clay particles, though not always the PI. Current engineering and agricultural databases of soil properties are most representative of North America, Europe and other regions with resources for soil testing. The most landslideprone areas, typically encompassing developing countries in subtropical and tropical climatic zones, are less well represented. On the other hand, more recently, studies based in developing countries are becoming available (e.g., Roopnarine et al. 2012, Havaee et al. 2015). Roopnarine et al. (2012) reported the results of a study of Trinidadian soils and used soil physical properties to predict friction angle, reporting that the sand and clay fractions were the key predictors of residual and peak friction angle. Havaee et al. (2015) obtained significant positive correlation between friction angle and gravel content for Central Iran, and they also observed improvement in prediction models of soil shear strength derived using basic soil properties and normalized difference vegetation index.
Study aims
 (i)
Based on preliminary work by Shepheard et al. (2018b) and Vardanega et al. (2018), to investigate whether significant soil property correlations can be derived to link soil friction angle to basic soil parameters for the Saint Lucia database (hereafter referred to as the 'SL database');
 (ii)
To distinguish different classes of Saint Lucia’s soils using both a soil type classification framework and the wellknown Casagrande approach (Casagrande 1947);
 (iii)
To fit probability distribution curves to the soil properties, the functions that best fit the available data.
The overall aim is to provide local engineers and landslide researchers with information to make a priori estimates of key geotechnical parameters based on available local data instead of (or in addition to) more generic probability distributions derived from regional or global datasets.
Materials and methods
The Saint Lucia soil data were made available by the Government of Saint Lucia materials testing laboratory in 2016 as part of collaboration on the landslide hazard assessment component of a World Bank funded public infrastructure asset risk management project (‘Vision 2030’). The database contains the results of a variety of historical laboratory tests carried out on soil samples from across the island. These data represent a subset of the laboratory’s historic soil test records, which are currently archived in largely analogue format. Tests typically included the determination of field moisture content, particle size distribution and Atterberg limits as well as direct shear tests on partiallydisturbed samples. The direct shear apparatus (DSA) in Saint Lucia has previously been satisfactorily benchmarked against a modified DSA at the University of Bristol by repeating the tests reported in Lings and Dietz (2004), using loosely and densely compacted samples of Leighton Buzzard sand. The DSA testing procedure for Saint Lucia was also reviewed as part of the Vision 2030 project and found to have been consistently applied by the laboratory technicians. The Saint Lucia procedure is to extract samples from the field and place them into the direct shear box, without sieving or remoulding in the classical sense, although some degree of disturbance is inevitable during extraction and transportation.
Results and discussion
Geotechnical correlations
In soil engineering and geotechnics it is common to estimate engineering parameters that are complex or hard to measure by using a simpler property, or combination of properties (e.g., Kulhaway and Mayne, 1990; Ching and Phoon, 2014a, 2014b; Havaee et al. 2015; Zolfaghari, et al. 2016; Ahmed (2018), Bayat et al. (2018); Jie et al. (2018); Pham et al. (2018) and Schjønning and Lamandé, 2018). Preliminary statistical analysis of this database has been reported in Shepheard et al. (2018b) and Vardanega et al. (2018).
Equation 3 was found to have an R^{2} = 0.36 for n = 52 with p < 0.001.
Equation 4 was found to have an R^{2} = 0.56 for n = 47 with p < 0.001. Vardanega et al. (2018) found that when ϕ'_{peak} was regressed against liquidity index for the SL database a R^{2} of 0.43 was obtained.
Classification of soils from Saint Lucia
Classification of soils based on formation and weathering
The natural structure of soil, and thus its geotechnical behaviour, is dependent on its parent material and the climate, topography, biological factors (microorganisms, plants and animals) and time. The formation process for many finegrained soils can be categorised simply as either ‘residual’ or ‘sedimentary’. Sedimentary soils are formed from minerals and organic materials that have been eroded (or produced by a volcanic eruption), transported and deposited by air, water or ice, and become consolidated (Wesley, 1990). Over time, sedimentary soil horizons may develop, and bonds can form between particles so that the material eventually behaves more like intact rock. For engineers, the stress history of sedimentary soils is recognised to be an important factor in determining their geotechnical behaviour. Conversely, taking the definition of The Geological Society Professional Handbook on Tropical Residual Soils (Fookes, 1997a, p10), residual soil profiles are formed from the in situ physical and chemical weathering of rock, leaching and accumulation of insoluble minerals and movement of fine particles, animal activity, plant root growth, and incorporation of organic materials, typically leading to cohesive soils and in some cases the cementation of the soil (e.g. laterites); essentially the reverse of the sedimentary soil formation process (Wesley, 1990). Large areas of the earth are mantled by residual soils, and deep profiles can form in humid tropical regions, such as the Caribbean, where readily available moisture and high temperatures lead to aggressive weathering. Both the mineralogy and structure of the parent material and the degree of weathering decomposition strongly influence the geotechnical behaviour of residual soils (cf. Wesley, 2009).
The 1966 soil survey of Saint Lucia (Regional Research Laboratory, 1966) primarily focuses on soils regarding their agricultural usage. It names 53 soil types based on parent material, geomorphological or topographical context, estimated particle size distribution, mineralogy, chemistry, nutrient availability, drainage, erodibility and depth. These soils are grouped into six classes according to the prevailing soil science taxonomy of the time (see legend of Fig. 1b). Although soil science terms such as ‘latosols’ are not often used by engineers (Wesley, 2009), they do encapsulate information on the soil formation process, parent material and structure. Thus, the soil series and classes defined in global and national soil maps, such as those compiled by FAOUNESCO and reported by Hartemink et al. (2013), for example, can provide a starting point for investigating potential soil strength properties (e.g., Bonilla and Johnson, 2012). When the 1966 Saint Lucia soil survey information was combined with field observations, soil sample descriptions and depths, and local geotechnical engineering knowledge of the soils, it was possible to identify three distinct soil classes for this study: A) residual soils B) agglomerate soils and C) ashderived soils, the second two classes having been formed through the weathering of sedimentary materials that were originally deposited by volcanic activity.
As well as identifying which of the three classes each soil sample in the SL database belonged to, a further distinction was made based on the degree of weathering of the residual soils (A) and the soil matrix from the agglomerate material (B). For residual soils the weathered state of rock is often defined in terms of gradations from rock to soil, numbered from the fresh parent rock, Grade I, to completely weathered residual soil, Grade VI (GCO Geotechnical Control Office, 1982; Fookes, 1997a, 1997b; Toll, 2012). In this paper, the term ‘residual soil’ is used to describe soil samples in the Saint Lucia dataset that are likely to fall within both weathering Grade V (completely decomposed rock) and weathering Grade VI (soil) classes; due to the weathering grade classification being based largely upon visual inspection of samples (GCO Geotechnical Control Office, 1982), and the fact that the Saint Lucia soil sample descriptions did not explicitly record the weathering grade. This is also in keeping with Fookes (1997a, p12) who recognised that using the term ‘soil’ for weathering Grade VI only is “… somewhat restrictive for engineering purposes as much material normally described as ‘soil’ occurs below this Grade in the weathered profile”.

Class A: Tropical residual soils are the classical ‘tropical residual soils’. They are reddishbrown, clayey soils with deep weathering profiles, and are particularly associated with the latosolic soils and andesitic polysols of the 1966 Regional Research Laboratory soil survey. Colluvium derived from these soils is also included as Grade VI material, based on field observations. Two subsets are defined, where ‘A1’ (n = 17) describes the upper layer of weathering Grades V and VI (soil), and ‘A’ (n = 23) is the underlying layer of weathered Grade IV material in which some of the relict rock structure and cementation is still present (which, in turn is underlain by Grades III, II and the Grade I parent material). Subset ‘A1’ contains only data which are known to pertain to the topsoil layer based on knowledge of the original samples. Subset ‘A’ contains all other ‘A’ data, excluding ‘A1’.

Class B: Agglomerate soils derived from poorly sorted pyroclastic deposits. This soil is recognisable by the presence of boulders and gravels with a weakly cemented (and sometimes clayey) weathered soil matrix. Two subsets are defined, where ‘B1’ describes the most weathered layer in which the soil matrix is fully weathered and few large particles remain (large particles are manually removed from samples before direct shear testing), and ‘B’ the underlying less weathered layer. Because the soil matrix of Soil ‘B’ tested in the DSA is thought to be similar to that of Soil ‘A’, Soil ‘A’ is included in the statistical analysis of angle of friction: Subset ‘B1’ contains all data for Soil ‘A’, ‘A1’ and ‘B’ (n = 47). Subset ‘B’ contains all data for Soil ‘A’ (excluding A1) and Soil ‘B’ (n = 30).

Class C: Volcanic ash soils derived from pumice or tuff. This class contains only data points described recognised as a distinctive grey ash (or tuff) soil, sometimes highly cemented, but otherwise friable (n = 14). It is typically associated with the southern geological series (Fig. 1). Wright et al. 1984 give further commentary on the soils of Saint Lucia and is part of the so called ‘Belfond Pumice’.
Of the 91 samples collected, 47 can be classed as residual soils (‘A1’, ‘A’, ‘B1’ and ‘B’), according to these geological maps and soil descriptions (see column 2, Table 4).^{1}
Classification of soils based on soil index parameters
Statistical Models
Probability density functions can be used to describe the variability of soil parameters and account for parametric uncertainty in reliabilitybased design, the development of decisionsupport tools, and stochastic physicsbased modelling. When data for a particular site or region are limited, a geotechnical database and derived probability distributions, can provide useful information. Vardanega and Bolton (2016) suggest that reliabilitybased design analysis is best used for assessing the performance of geostructures, as opposed to failure analysis. For instance, analysis of various predictors of undrained shear strength using a database and probability density function has been recently reported (Ching and Phoon, 2014a, 2014b). Pham et al. (2016) and Pham et al. (2017) have used decision support trees for landslide susceptibility assessments in Vietnam and India. Chen et al. (2018a, 2018b) used datamining approaches to develop landslide susceptibility maps for the Shangnan County and Shangzhou district in China. Numerical models can be coupled with probability distributions when studying the effects of different sources of uncertainty on computed slope factors of safety, and the sensitivity of the system to different model inputs (e.g., Singh et al., 2014; Pianosi et al., 2016; Almeida et al., 2017). Recent work by Almeida et al. (2017) used Classification and Regression Tree (CART) Analysis (Breiman et al. 1984) in conjunction with the CHASM model (see Anderson and Howes, 1985; Wilkinson et al., 2002) to evaluate thresholds for slope failure due to parameter variation. Almeida et al. (2017) assigned uniform, normal and lognormal distributions to the parameter inputs for CHASM simulations in order to investigate the effects of various parameters on the failure of a modelled slope in Saint Lucia.^{2}
Lumb (1966) suggested the normal distribution gives a good fit for the w_{L} and w_{P} (and thus also PI), and the strength parameters ϕ' and c' for some Hong Kong soils. A review by Scott et al. (2003) noted that while the normal distribution may be the “least biased” model, many soil parameters cannot have negative values – therefore the lognormal distribution may be more appropriate. Similarly, Lumb (1970) used the beta distribution to adapt the normal distribution to skewed data. However, to fit a beta distribution the data must be transformed into the range [0,1], thus increasing the number of computational steps required.
Goodness of fit tests
AndersonDarling test statistics for the exponential, normal, lognormal and Weibull distributions fitted to the SL database, including unclassified data (strongest fits shown in bold type)
Exponential  Normal  Lognormal  Weibull  n  

ϕ' _{ peak}  13.37  0.93  1.03  0.61  85 
c'  5.43  1.78  1.26  0.47  86 
PI  7.06  1.00  0.68  0.49  61 
w _{ nat}  9.59  0.99  0.68  0.79  58 
Akaike information criterion values modified for small samples for the exponential, normal, lognormal, Weibull and Generalised Extreme Value distributions fitted to the SL database, including unclassified data (strongest fits shown in bold type)
Exponential  Normal  Lognormal  Weibull  Generalised Extreme Value  n  

ϕ' _{ peak}  714  639  643  635  636  85 
c'  715  712  697  690  694  86 
PI  519  497  484  485  483  61 
w _{ nat}  529  470  470  467  470  58 
AndersonDarling results of fitting the normal, lognormal, Weibull and exponential distributions to the ϕ'_{peak} and c' data from the SL database subdivided by soil class
Distribution  Saint Lucia soil type (number of data points)  

A1 (n = 17)  A (n = 23)  B1 (n = 47)  B (n = 30)  C (n = 14)  U (n = 24)  
ϕ' _{ peak}  c'  ϕ' _{ peak}  c'  ϕ' _{ peak}  c'  ϕ' _{ peak}  c'  ϕ' _{ peak}  c'  ϕ' _{ peak}  c'  
Normal  0.35  0.69  0.28  0.80  0.31  1.45  0.25  0.73  0.65  0.21  1.15  0.64 
Lognormal  1.33  0.49  0.56  0.64  1.72  0.55  0.74  0.78  0.42  0.94  0.34  0.42 
Weibull  0.36  0.50  0.27  0.42  0.44  0.41  0.25  0.38  0.60  0.60  0.77  0.28 
Exponential  4.16  1.96  3.03  1.99  8.04  2.29  4.54  2.42  2.65  1.28  3.14  2.46 
Conclusions
A database comprising information on 91 soil samples from Saint Lucia has been presented and classified according to soil type and formation. Simple regression analysis has been performed for some soil parameters, and it is seen that the strongest correlation for the friction angle is found with the natural water content. Additionally, a variety of probability distributions have been fitted to key parameters from the SL database. According to two ranking criteria (i.e. AndersonDarling and Akaike), the Weibull distribution is preferred for ϕ'_{peak} and c'.
These results are directly applicable for slope stability assessments in Saint Lucia. For local engineers, the database, soil property correlations and statistical distributions provide a basis for estimating soil properties in preliminary geotechnical analyses and for prioritising data acquisition (from basic soil sampling to potentially costly geotechnical investigations). For slope stability modellers the identification of appropriate parameter ranges and probability distributions can inform parametric studies at specific sites (e.g. Holcombe et al., 2016) or stochastic physicsbased modelling of slope stability or over wide areas (Almeida et al., 2017), thus accounting for the effect on slope factor of safety of uncertainties in geotechnical and other slope properties.
In broader terms, this paper demonstrates that even in locations where traditional, wellcurated geotechnical data are relatively scarce, it can be possible to compile useful databases of soil properties. Where statistically significant correlations and probability distributions fitted, this can provide a basis for geotechnical analysis and reliabilitybased design. In this paper, based on the available data, the Weibull distribution is shown to be more appropriate for certain geotechnical parameters in Saint Lucia. This contrasts with the usual assumption by engineers and environmental modellers that the lognormal distribution is often the best representation for soil parameters (Kulhawy, 2010, Hamm et al., 2006). It is suggested that while the selection of a lognormal distribution has a strong precedent and is the default choice for “operational reasons” (Rackwitz, 2000, p201), if sufficient local soil data can be compiled, it is worthwhile exploring the possibility that another distribution may give a better fit.
Footnotes
Notes
Acknowledgements
The authors acknowledge the support of ‘Landslide risk assessment of lifeline roads for public asset management and rainfallbased index insurance’ which formed part of EP/P510920/1 ‘EPSRC Global Challenges Research Fund Institutional Sponsorship Award 2016  University of Bristol. The first author acknowledges the support of a Vacation Bursary in 2016 from the Queen’s School of Engineering, University of Bristol. The authors thank the reviewers of the paper for their helpful and insightful comments which have helped improve the paper. The authors also thank Dr. Raffaele De Risi and Miss Mair Beesley for their helpful comments and suggestions.
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