Enhanced data interpretation: combining in-situ test ...

For Volume 2: Geotechnical and Geophysical Site Characterisation 5 – Lehane, Acosta-Martínez & Kelly (Eds)

© 2016 Australian Geomechanics Society, ISBN 978-0-9946261-2-7 Enhanced data interpretation: combining in-situSydney, testAustralia, data by Bayesian updating Enhanced data interpretation: combining in-situ test data by Bayesian Enhanced data interpretation: combining in-situ test data by Bayesian Enhanced data interpretation: combining in-situ test data by Bayesian updating updating updating J. Huang

ARC Centre of Excellence for Geotechnical J. Australia J. Huang Huang J. Huang ARC Centre ARC Centre of of Excellence Excellence for for Geotechnical Geotechnical R. Kelly ARC Centre of Excellence for Geotechnical Australia Australia SMEC, Brisbane, Queensland, Australia Australia

Science & Engineering, University of Newcastle, Science Science & & Engineering, Engineering, University University of of Newcastle, Newcastle, Science & Engineering, University of Newcastle,

R. Kelly R. Kelly S.W. Sloan R. Kelly SMEC, Brisbane, SMEC, Brisbane, Queensland, Queensland, Australia Australia

ARC Centre of Excellence for Australia Geotechnical Science & Engineering, University of Newcastle, Australia SMEC, Brisbane, Queensland,

S.W. S.W. Sloan Sloan S.W. Sloan of ARC ARC Centre Centre of Excellence Excellence for for Geotechnical Geotechnical Science Science & & Engineering, Engineering, University University of of Newcastle, Newcastle, Australia Australia

ARC Centre ofCombining Excellencedata for sets Geotechnical Sciencesite & characterization Engineering, University of Newcastle, Australia ABSTRACT: obtained during studies has the potential to enhance data An example is provided where seismic data is combined with preconsolidation pressures ghan,interpretation. NSW, Australia ABSTRACT: Combining data sets obtained during during site characterization characterization studies has has the the potential potential toand enhance obtained from Combining laboratory data tests.sets Semi-empirical relationships between preconsolidation pressureto shear ABSTRACT: obtained site studies enhance ABSTRACT: Combining data sets obtained during site characterization studies has the potential to enhance data interpretation. An example is provided where seismic data is combined with preconsolidation pressures ghan, NSW, Australia wave velocity can be used to estimate the preconsolidation pressure. Conventionally, the uncertainties in the data An example is provided where seismic combined with preconsolidation pressures Faculty of Engineering and data BuiltisEnvironment ghan,interpretation. NSW, Australia data interpretation. An example is provided where seismic data is combined with preconsolidation pressures obtained from laboratory tests. Semi-empirical relationships between preconsolidation pressure and shear ghan, NSW, Australia relationships are ignored. The Bayesian updating approach is used to take these uncertainties into account. obtained from laboratoryThe tests. Semi-empirical relationships between preconsolidation University of Newcastle, Callaghan, NSW 2308, Australia pressure and shear obtained from laboratory tests. Semi-empirical relationships between preconsolidation pressure and shear wave velocity can be used to the Conventionally, the in the Faculty Engineering Built Environment Both analysis and kriging interpolation are used forand thepressure. laboratory tests on the preconsolidation pressure wave trend velocity can be used to estimate estimate theof preconsolidation pressure. Conventionally, the uncertainties uncertainties in the Faculty ofpreconsolidation Engineering and Built Environment wave velocity can be used to estimate the preconsolidation pressure. Conventionally, the uncertainties in the relationships are ignored. The Bayesian updating approach is used to take these uncertainties into account. Faculty of Engineering and Built Environment The University ofupdating Newcastle, Callaghan, NSW 2308, Australia to derive the are priorignored. distributions. The posterior preconsolidation pressures arethese then uncertainties obtained by incorporating relationships The Bayesian approach is used to 2308, take into account. The University of Newcastle, Callaghan, NSW Australia relationships are ignored. The Bayesian approach used to 2308, take these uncertainties Both and kriging interpolation are for the laboratory tests on the preconsolidation pressure The University Newcastle, Callaghan, NSW Australia shear wave analysis velocity measurements from of a updating seismic dilatometer test. The analyses demonstrate thatinto theaccount. seismic Both trend trend analysis and kriging interpolation are used used for the is laboratory tests on the preconsolidation pressure Both trend analysis and kriging interpolation are used for the laboratory tests on the preconsolidation pressure to derive the prior distributions. The posterior preconsolidation pressures are then obtained by incorporating dilatometer candistributions. be enhancedThe by the laboratory data set. This approacharecan be obtained extended by to enhance twoto derive thedata prior posterior preconsolidation pressures then incorporating to derive the prior distributions. The posterior preconsolidation pressures are then obtained by incorporating shear wave velocity measurements from a seismic dilatometer test. The analyses demonstrate that the seismic dimensional geophysical surveys by conditioning on a small number of accurate laboratory or in-situ test shear wave velocity measurements from a seismic dilatometer test. The analyses demonstrate that the seismic shear wave velocity measurements from a seismic dilatometer test. The analyses demonstrate that the seismic dilatometer data can be enhanced by the laboratory data set. This approach can be extended to enhance twomeasurements. dilatometer data can be enhanced by the laboratory data set. This approach can be extended to enhance twodilatometer can be enhanced laboratory on dataaa set. approach can be extended enhance dimensional geophysical surveys by conditioning small number of laboratory in-situ test dimensionaldata geophysical surveys by by the conditioning on smallThis number of accurate accurate laboratoryto or or in-situtwotest dimensional geophysical surveys by conditioning on a small number of accurate laboratory or in-situ test measurements. measurements. measurements. 1 INTRODUCTION raphy/material properties between test locations (e.g., Foti 2013). raphy/material properties test locations 1 INTRODUCTION A typical site investigation program for a linear inBayesian updating is a between probabilistic raphy/material properties between test numerical locations 1 INTRODUCTION raphy/material properties between test 1 INTRODUCTION (e.g., Foti 2013). frastructure project could include multiple types of method can be used to combine data. locations The ad(e.g., Fotithat 2013). (e.g., Fotiof2013). A site program for inBayesian updating is sitetypical characterization techniques including geophysvantage Bayesian is that smallnumerical data sets A typical site investigation investigation program for aa linear linear inBayesian updatingupdating is aa probabilistic probabilistic numerical A investigation program for linear updating is a combine probabilistic frastructure project could multiple types of method used to data. The adics,typical in-situsite testing, borehole drilling andalaboratory canBayesian be that used.can In be paper we demonstrate frastructure project could include include multiple types inof method that can bethis used to combine data.numerical Thehow adfrastructure project could include multiple types of method that can be used to combine data. The adsite characterization techniques including geophysvantage of Bayesian updating is that small data sets testing. Currently these data are including often usedgeophysin isolaBayesianofupdating by is combining site characterization techniques vantage Bayesianworks updating that smalldata datafrom sets site characterization techniques including geophysvantage of Bayesian updating is that small data sets ics, in-situ testing, borehole drilling and laboratory can be used. In paper we how tion in-situ from each other.borehole For example, surin-situ velocity measurements and laborics, testing, drillinggeophysical and laboratory can beshear used.wave In this this paper we demonstrate demonstrate how ics, testing, borehole drilling can be used. In this paper we demonstrate how testing. Currently these data site are oftenand usedlaboratory inbut isolaBayesian updating works by combining data from veysin-situ could be usedthese to assess stratigraphy not atory tests with depth at a single location (one ditesting. Currently data are often used in isolaBayesian updating works by combining data from testing. Currently these data are often used in isolaBayesian updating works by combining data from tion from each other. For example, geophysical surin-situ shear wave velocity measurements and laborused to assess material parameters. When data are mension). theory can measurements be extended toand two and tion from each other. For example, geophysical surin-situ shearThe wave velocity labortion from other. For example, geophysical in-situ shear wave velocity laborveys could be used assess site but not atory with depth at single location (one dicombined, they canto different resolutions. A three tests dimensions. Theaa measurements example weand present veys couldeach be used tohave assess site stratigraphy stratigraphy butsurnot atory tests with depth at single location (one diveys could be used to assess site stratigraphy but not atory tests with depth at a single location (one diused to assess material parameters. When data are mension). The theory can be extended to two and profiletoofassess boreholes and parameters. in-situ tests can be overlain combines preconsolidation obtained used material When data are mension). The theory can pressures be extended to twofrom and used to assess material parameters. When data are mension). The theory can be extended to two and combined, they can have different resolutions. A three dimensions. The example we present on geophysics to help interpret stratigraphic constantdimensions. rate of strain (CRS) with combined, they data can have different resolutions. A three The consolidation example wetests present combined, they have different A three dimensions. Theobtained examplefrom wea seismic present profile of and in-situ tests can be combines preconsolidation pressures obtained from boundaries fromcan ‘blurry’ geophysics data. In-situ shear wave velocity data profile of boreholes boreholes and in-situ tests resolutions. can be overlain overlain combines preconsolidation pressures obtained from profile boreholes in-situ tests canstratigraphic be overlain combines preconsolidation obtained on data to interpret constant rate of consolidation tests with testsgeophysics canofbe performed different locations to boredilatometer test. on geophysics data and toathelp help interpret stratigraphic constant rate of strain strain (CRS) (CRS)pressures consolidation tests from with on geophysics data to help interpret stratigraphic constant rate of strain (CRS) consolidation tests with boundaries from ‘blurry’ geophysics data. In-situ shear wave velocity data obtained from a seismic holes and compared with the laboratory test data obboundaries from ‘blurry’ geophysics data. In-situ shear wave velocity data obtained from a seismic boundaries from ‘blurry’ geophysics data. In-situ shear wave velocity data obtained from a seismic tests can be performed at different locations to boredilatometer test. tained from soil samples to develop material patests can be performed at different locations to boredilatometer test. tests can performed at the different locations to boredilatometer test.UPDATING holes and compared with laboratory test obrameters. The soil between the in-situ tests and the 2 BAYESIAN holes andbe compared with the laboratory test data data obholes and compared with the laboratory test data obtained from soil samples to develop material paborehole locations is assumed have uniform tained from soil samples to to develop materialproppatained material rameters. The soil between in-situ and the 2 BAYESIAN UPDATING erties. from updating is a stochastic method that is well rameters. Thesoil soilsamples betweentothe thedevelop in-situ tests tests and pathe 2Bayesian BAYESIAN UPDATING rameters. The soil between the in-situ tests and the 2 BAYESIAN UPDATING borehole locations is assumed to have uniform propProbabilistic numerical methods be used to suited to geotechnical processes, particularly when borehole locations is assumed to havecan uniform propborehole locations is assumed to have uniform properties. Bayesian updating is a stochastic is combine many of these different data sets to extract limited information is availablemethod (e.g., that Kelly and erties. Bayesian updating is a stochastic method that is well well erties. Bayesian updating is a stochastic method that is well Probabilistic numerical methods can be used to suited to geotechnical processes, particularly when additional information from data that are routinely Huang to2015). Bayes’ processes, formula can be written as Probabilistic numerical methods can be used to suited geotechnical particularly when Probabilistic methods can beto used to suited geotechnicalis combine many of these data sets extract limited available (e.g., and collected. The numerical methods have the follows:toinformation combine many ofnumerical these different different data sets topotential extract limited information is processes, available particularly (e.g., Kelly Kellywhen and combine many of these of different to extract limited information is formula availablecan (e.g., Kelly and additional information from data that are routinely Huang 2015). Bayes’ be as to increase resolution stratigraphic assessments additional information from datadata thatsets are routinely Huang 2015). Bayes’ formula can be written written as P  θ | y  2015). P  y | θ Bayes’ P θ (1) additional information from data that are routinely Huang formula can be written as collected. The numerical methods have the potential follows: using geophysics combined with other convert collected. The numerical methods havedata, the potential follows: collected. The numerical methods have the potential follows: to increase resolution of stratigraphic assessments geophysics to material properties, improve the to increase data resolution of stratigraphic assessments of P || y θθ prior probability distribution(1) P  θ θwhere y   P PPy yθ||θ θ isP P the to increase stratigraphic assessments (1) using geophysics combined with resolution ofresolution in-situ testsofcombined withdata, highconvert quality using geophysics combined with other other data, convert P  θmaterial | y   P  yparameters, | θ P θ (1) P y | θ the is the probability of   using geophysics with data, convert geophysics data material properties, improve the laboratory measurements and to other interpolate stratiggeophysics data to tocombined material properties, improve the prior of where y  conditional on distribution the material measurements P  θ θ  is isthe the prior probability probability distribution of where P geophysics data to material properties, improve the resolution of in-situ tests combined with high quality P  θparameters, is the prior probability distribution where resolution of in-situ tests combined with high quality  P y | θ the material is the probability of   θ P θ | y and is the posterior parameters     y θ the material parameters, is the probability of resolution in-situ tests combined with high stratigquality laboratory measurements and P  y | θ  ison the material parameters, probability of laboratory of measurements and to to interpolate interpolate stratigmaterial measurements  yy  conditional conditional onthe the the material measurements laboratory measurements and to interpolate stratigyand conditional on the material measurements   θ P θ | y is the posterior parameters      θ  and P  θ | y  is the posterior 1437 parameters parameters  θ  and P  θ | y  is the posterior

wave velocity are related parameters. Eq. (5) is written in terms of effective vertical stress and OCR as an analogy to Equation 5.

distribution of the material parameters updated by measurements. The measurements  y  represent the geophysics data and can be written as:

 yi f  θ   

n

  G0  A  v  OCR m pa  pa 

(2)

A relationship between preconsolidation pressure and shear wave velocity was obtained by adopting the values n = 0.9, m = 0.35 and A = 170 estimated from Atkinson (2007)) and rewriting OCR in terms of preconsolidation pressure. Eq. (5) is the model function and we consider that its accuracy is uncertain. The model function is used to convert the geophysical data into a form that can be compared with more accurate laboratory test data. Preconsolidation pressures assessed from constant rate of compression tests and the ones interpreted from a seismic dilatometer test are compared in Fig. 1. The laboratory test data are considered the prior set of material parameters and the seismic dilatometer data are the measurements.

where  is the mean “error” or difference between measurement and model function (or calculation) f  θ  . If the measured error is assumed to be normally distributed, the likelihood function of measurement yi can be written as:

 y  f  θ     P( yi | θ)    i    

(5)

(3)

where   is the standard deviation of the measurement errors, and  is the probability density function of the standard normal distribution. The Markov Chain Monte Carlo sampling method (MCMC) has been used to sample the posterior distribution. This method involves stepping through a Markov Chain where, at each step, a test realization for θ is proposed according the proposed distribution, and is then either accepted or rejected using a random decision rule based on the realization’s predicted data misfit and the misfit of the previously accepted model. After a certain “burn-in” period, required for the procedure to stabilize and become independent of the initial starting realization, accepted samples drawn at regular intervals along the Markov Chain will represent independent realizations of the posterior distribution and will occur at a frequency corresponding to their posterior probability of occurrence. The basic idea goes back to Metropolis et al. (1953)).

0

3 EMPIRICAL RELATIONSHIP BETWEEN PRECONSOLIDATION PRESSURES AND SHEAR WAVE VELOCITY Atkinson (2007)) proposed Eq. (4) relating small strain shear stiffness to yield stress ratio. In this Equation, G0 is the small strain stiffness, pa is a normalising pressure taken to be 1kPa, A , n and m are constants, p  is the effective mean pressure and R0 is the yield stress ratio.

Figure. 1 Comparison between preconsolidation pressures assessed from constant rate of compression tests and interpreted from a seismic dilatometer test.

4 PRIOR INTERPRETATION OF PRECONSOLIDATION PRESSURES

n

 p  G0  A   R0m pa  pa 

(4)

The prior distribution is obtained from laboratory test data. A log-normal distribution has been assumed for the prior values.

The shear wave velocity should therefore be related to the yield stress ratio because G0 and shear 1438

A prior distribution of the measurements can be obtained by obtaining a linear trend through the data with depth and then assessing the standard deviation of the data from the trend. This is equivalent to assuming the preconsolidation pressure increases linearly with depth as y az  b 

(6)

where z is reduced level, a and b are constants. The laboratory test data is fitted to Eq. (6) by the least square method, and a  6.38kPa and b  39.90kPa . The standard deviation from the trendline is 6.39kPa and is assumed to be constant with depth.

Figure. 3 Kriging interpolation of preconsolidation pressures assessed from constant rate of compression tests.

5 PRECONSOLIDATION PRESSURE UPDATED BY SHEAR WAVE VELOCITY The mean and standard deviation of the error between the seismic dilatometer data and the model function are not known in advance. Shear wave velocities measured from seismic dilatometer tests are likely to be quite accurate, as is their conversion to small strain shear stiffnesses. However, the accuracy of the model function, Eq. (5), is quite uncertain. If we assume that there is no bias in the model function then the mean of the error can be set to zero. If we assume that the model function is highly uncertain then we can assign a large standard deviation to the error. In this case, the prior information will dominate the posterior solution, and in the extreme they will be equal. This is the same as assuming that the preconsolidation pressures measured in the laboratory apply everywhere in the domain. If we assume that the error has a small standard deviation then the solution will be more heavily influenced by the seismic dilatometer data and model function. For the purpose of this example we have assumed that the standard deviation of the error is relatively small to highlight how the posterior is influenced by the prior and likelihood functions. The posterior mean preconsolidation pressure is compared with the linear prior and model function from the seismic dilatometer in Fig. 4. The posterior prediction has updated the seismic dilatometer data

Figure. 2 Trend analysis of preconsolidation pressures assessed from constant rate of compression tests.

A prior distribution can also be obtained by kriging through the data set. Kriging provides a best estimate of a random field between known data. The basic idea is to estimate X ( z ) at any point using a weighted linear combination of the values of X at each observation point. In kriging, high weights are given to the points that are closer to the unknown points. Interested readers are referred to Fenton and Griffiths (2008)). The kriged preconsolidation pressures assessed from constant rate of compression tests are shown in Fig. 3. In the example presented in this paper the scale of fluctuation is only used in the vertical direction but it can, in principle, be used to model 2D and 3D spatial variations.

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such that its trend and magnitude more closely approximates the laboratory values. A similar comparison with the kriged prior is shown in Fig. 5. Kriging incorporating a scale of fluctuation provides a set of prior values that are conditioned on the laboratory data but vary between data points according to the scale of fluctuation. The posterior prediction is a better fit to the laboratory test data, possibly due to the standard deviation of the prior kriged data being smaller than that of the prior linear data. Use of a scale of fluctuation with the kriged prior also provides greater accuracy when interpolating between data points with depth compared with the linear prior.

Preconsolidation pressure (kPa) 0

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6 DISCUSSION

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The previous section demonstrated some of the principles adopted when combining data. This method of analysis can be extended into two dimensions where a geophysical data set could be conditioned on laboratory and in-situ test data obtained at different spatial locations, both horizontally and with depth. The combined data set creates a 2D geotechnical model, where material parameters can be assigned to geophysical grid points. This model would be an enhancement of conventional models, where material parameters are assigned uniformly to a particular stratigraphic layer. In principle, this model could then be transformed into a finite element mesh. Further, mean and standard deviation of the parameter values are also associated with the grid points, which allows creation of 2D probabilistic models. Creation of such models is a fundamental precursor for the routine use of probabilistic analysis in design practice. However, a number of technical challenges remain to be overcome. One significant challenge is to quantify model error. At the moment it is difficult to quantify the magnitude of model error. Therefore the analyst can choose how much error to adopt in an analysis to effectively tune the model towards uniform material properties based on laboratory test data at one extreme or geophysics data at the other extreme. Selection of model error is therefore based on engineering judgment and the skill of the analyst. A second challenge is to incorporate Bayesian updating of stratigraphic boundaries into the process (e.g., Houlsby and Houlsby 2013) before updating the material properties. In the examples presented in

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Figure. 4 Posterior mean preconsolidation pressures using trend analysis of constant rate of compression tests as prior distribution. Preconsolidation pressure (kPa) 0

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Figure. 5 Posterior mean preconsolidation pressures using kriging interpolation of constant rate of compression tests as prior distribution.

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Section 5, the laboratory and dilatometer data sets were obtained from different physical locations and there is a difference in the depth to the base of the soft clay. The level at the base of the soft clay is approximately RL-9.5m at the location of the dilatometer and about RL-12m at the location of the laboratory test data. The Bayesian process, as presented here, updates both data sets irrespective of their stratigraphy. 7 CONCLUSIONS This paper combines two different sets of geotechnical test data, namely results from laboratory constant rate compression tests and field seismic dilatometer tests. Empirical relationships between the preconsolidation pressure and shear wave velocity are firstly derived from the two sets of data. Unlike the traditional direct transformation, where the uncertainty associated with the transformation is ignored, the Bayesian updating approach is used to form a rigorous framework for combining the two sets of data. It is shown that the uncertainties of preconsolidation pressure can be significantly reduced by incorporating shear wave velocity measurements. Further work is required to extend the process into two dimensions, incorporate stratigraphic updating and to investigate the magnitude of model error. 8 ACKNOWLEDGEMENTS The authors wish to acknowledge the support of the Australian Research Council Centre of Excellence for Geotechnical Science and Engineering. 9 REFERENCES Atkinson J The Mechanics of Soils and Foundations, Second Edition, Taylor & Francis 2007. Fenton GA and Griffiths DV Risk Assessment in Geotechnical Engineering, Wiley 2008. Foti S (2013) Combined use of geophysical methods in site characterization. Geotechnical and Geophysical Site Characterization 4, Vols I and Ii: 43-61. Houlsby NMT and Houlsby GT (2013) Statistical fitting of undrained strength data. Geotechnique 63(14): 1253 –1263. Kelly R and Huang J (2015) Bayesian updating for onedimensional consolidation measurements. Canadian Geotechnical Journal 52(9): 1318-1330. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH and Teller E (1953) Equation of state calculations by fast computing machines. The Journal of Chemical Physics 21(6): 1087-1092.

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