Advanced Interpretation Of Field Tests

Geotechnical Site Characterization, Robertson and Mayne (eds) © 1998 Balkema, Rotterdam, ISBN 90 5410 939 4

Advanced interpretation of field tests G.T. Houlsby Department of Engineering Science, Oxford University, U.K.

ABSTRACT: A selective review is made of some of the advanced techniques that are available for the interpretation of in situ tests. Soil classification from CPT tests has in the past been based principally on use of charts, and the use of Neural Network classification systems offers a powerful and general alternative. An important feature of the interpretation of cone or pressuremeter tests is that the strength, stiffness and horizontal stress combine to give a particular test result. Advanced interpretation methods must take into account this interaction, so that factors used to derive one parameter may depend on the value of another. In the analysis of pressuremeter tests two developments are highlighted: the analysis of the unloading phase of the tests, and the realisation that the finite length of the pressuremeter has a substantial effect on strength measurements. Interpretation of the cone pressuremeter requires use of some advanced techniques (and in particular requires use of large strain analysis), but this is repaid by the benefit that it combines many of the advantages of both the CPT and the pressuremeter. 1 INTRODUCTION

on computational techniques, • new methods which have not yet gained current acceptance in practice, yet potentially offer improvements over conventional approaches.

The purpose of this paper is to conduct a rather general review of the circumstances in which advanced interpretation of field tests is justified, and of some of the techniques that can then be used. Many of those involved in research on field testing are already using or developing advanced interpretation methods. Practising engineers are often, however, more sceptical about the merits of some of the more advanced methods. This paper is therefore primarily aimed at practising engineers, with the intent of encouraging them to adopt new methods when they are appropriate. What constitutes “advanced” interpretation of field tests? This question has no simple answer, and can only be interpreted within the context of the currently accepted state-of-the-art. What is at present regarded as an advanced technique may in the future be regarded as commonplace. For the purpose of this paper “advanced” methods will be taken as any that fall into one or more of the following categories: • methods which involve corrections to current approaches, based on improved understanding of the mechanics of the test. • methods which are intrinsically complex (by present standards), e.g. those which rely heavily

1.1 Field testing or laboratory testing? A discussion of the advanced interpretation of field tests must first address the long-standing debate on the relative merits and applications of laboratory and field testing. The interpretation of tests must also be set in the context of the design methods that will be used in connection with the test results. The way in which in situ test results have been used has depended very much on the history of the development of geotechnical engineering in different countries. For instance, in the United Kingdom since about the mid-1950’s, geotechnical engineers have relied heavily on the triaxial test as the primary means of measuring the strength and deformation properties of soils. In, for example, slope stability analysis, the method described by Bishop (1955) would usually be used. The choice of a safety factor would be based on the combination of use of triaxial testing and Bishop’s method. If either of these were to be changed, then new experience on appropriate safety factors would need to be obtained. 99

The above position meant that, as in situ testing has become established in the U.K., much effort has been put into use of field tests to measure the same engineering parameters as are measured by the triaxial test. During this process it has been recognised that, for instance, the mode of shearing affects the undrained shear strength, so that experience has been obtained in converting measurements made with field tests back to equivalent values from triaxial tests. The development of field testing in the U.K. can be contrasted with, say, the history of the pressuremeter test in France. At the time that the Ménard pressuremeter was developed, the use of laboratory testing as the primary tool for measuring soil properties was less well established in France. As a result, design methods were developed in which the results of the pressuremeter tests were used directly in, for instance, foundation design. Although correlations were later established between the parameters measured by the Ménard pressuremeter and more fundamental engineering parameters, it is not necessary to know the latter to use the pressuremeter “design rules”. The “direct method” of use of in situ test results (exemplified by the French application of the pressuremeter) and the “indirect method” (exemplified by the approach commoner in the U.K.) are illustrated in Figure 1. The direct approach has advantages, principally in that it is straightforward to apply, since it tends to rely on a series of rather well-defined procedures. Provided that these have been well thought out, the method can be quick and economical. It has, however, a number of disadvantages in that: • it relies heavily on the collection of large numbers of case records for calibration, • it does not provide the engineer with a sense of the importance of particular features of the soil Direct Approach In Situ Test Results

behaviour on the design, • it is not readily generalised to new soils, new types of construction or new tests. As a result of these constraints, the direct approach does not lend itself to rapid change, and so there are few developments of “advanced” interpretation in this area. The examples given below will therefore be within the context of the indirect approach. When in situ tests are employed using the direct approach, then the relative merits of in situ and laboratory tests for a particular engineering application may need to be discussed. However, when using the indirect method, such a debate is perhaps less important, since a combination of laboratory and in situ tests can be used. In the second phase of the design (B in Figure 1) the engineer will need to select the most important parameters needed. The decision then becomes one of a choice of the most appropriate method to measure these parameters. The issues in choosing a method will usually include: • the relative simplicity and accuracy of laboratory and field methods, • problems of sample disturbance, • how well the field test may reproduce the design conditions, • possible benefits of measuring a quantity by more than one means, • cost. 1.2 Chemical and environmental testing Many sophisticated new testing methods are being introduced in the area of environmental testing. A prime example is the use of laser-fluorescence techniques to identify hydrocarbon contamination at polluted sites (Lambson and Jacobs, 1995). The development of such tests has involved a major investment both in equipment, and in the interpretation techniques for the tests. The author has no direct experience of use of in situ tests for environmental purposes, so these applications are not covered here. They are, however, addressed elsewhere at the ISC’98 conference. The author acknowledges that many of the “advanced” techniques currently under development are in the geo-environmental area.

Indirect Approach In Situ Test Results

or

Laboratory Test Results

A Engineering Properties,e.g. G, s u etc. B Engineering Design

Engineering Design

Figure 1: Direct and indirect interpretation of in situ tests.

methods

1.3 Geophysical testing of

100

Another area where rapid advances are being made is that of geophysical testing. In particular the development of tomography and other imaging

techniques certainly involves “advanced” interpretation of the data. Geophysical tests are treated elsewhere in ISC’98 and are not therefore addressed here.

3 SOIL CLASSIFICATION Soil classification is here taken as the qualitative description of the soil (e.g. sand/silt/clay), together with qualifying comments (loose/dense, normally consolidated/overconsolidated, soft/stiff etc.), but not involving quantitative measurement of parameters. The two primary in situ devices for soil classification are the CPT (and especially the piezocone) and the Marchetti dilatometer. One advantage of the CPT is that it gives a continuous profile, and the dilatometer too gives quite a detailed profile (with data usually at 100mm intervals). The interpretation as far as soil classification and stratigraphy is concerned is almost entirely empirical, and has principally been expressed in the form of charts. Those published by Robertson et al. (1986) for the interpretation of the piezocone are a typical example. This approach is undoubtedly valuable, principally because it allows practitioners to gain a quick estimate of the sorts of soil present, without the need for any sophisticated calculation. It does, however, have drawbacks. CPT classification charts were originally presented in terms of two variables, usually cone resistance qt and friction ratio f r (see e.g. Douglas and Olsen, 1981). In this case the classification can be represented in a simple way on a two-dimensional chart. There is inevitably some overlap of the zones, but this can be reduced by normalising the parameters in a suitable way. Wroth, q − σvo (1984, 1988) suggested use of Qt = t and σ′vo fs Fr = , both of which can easily be q t − σ vo determined provided that estimates of in situ vertical stress and pore water pressure can be made. Robertson (1990) adopted this normalised form. Houlsby and Hitchman (1988) showed that the cone resistance is more closely related to the horizontal stress than the vertical stress, so that the q − σho use of modified factors such as Qh = t σ′ho would result in charts with less overlap of different regions. The problem is that, to use such a chart, an estimate of K o must be made. Since this is often not possible with any accuracy, authors have preferred the normalisation with respect to vertical stress. This practice is, however, misleading, since the dependence on K o is effectively hidden in the inaccuracies in the chart rather than being explicitly

1.4 Examples The examples given below all involve the use of advanced techniques to determine the physical characteristics of soils. They are drawn principally from the use of the cone penetrometer (CPT) and the pressuremeter, since these are probably the commonest in situ devices for measuring the mechanical properties of soil. The two tests are complementary, in that the principal application of the CPT is as a profiling tool, with a supplementary use for estimating soil property values, while the pressuremeter is less appropriate for profiling, but is used primarily for property measurement. The examples are drawn principally from the Author’s own experience, but there are many others who are also working on the development of advanced interpretation methods.

2 PREREQUISITES There are certain prerequisites that have to be satisfied for any interpretation of in situ tests, and these are of course even more important if the interpretation is to be of a sophisticated nature. In the following it will be assumed that the following minimal criteria will be satisfied as a matter of good practice: • All tests will be carried out using equipment that is in good working order, properly maintained and calibrated, and suitable for testing the particular soil encountered. • Test procedures will adhere to accepted standards (where these are published), including proper record-keeping of all relevant data. • All necessary corrections will be applied to raw data so that the results properly represent the soil response (examples of corrections are those for the membrane stiffness in a pressuremeter test, or of the correction from q c to qt in the CPT). • Data should be presented in an appropriate way, where possible making use of properly defined dimensionless groups. For example, use of (qt − σvo ) s u is acceptable, but use of q t σvo is not, since, in an undrained CPT test σ vo simply results in an additive term on qt .

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apparent to the engineer. The charts therefore work well for soils with typical K o values, and not so well for other soils. It would be better to use normalisation with respect to horizontal stress, and provide engineers with guidance on the estimation of Ko . The major problem with the use of charts for classification arises when they are extended from two variables to three or more. Robertson (1990) presents charts involving Qt against Fr and Qt against Bq . The charts represent projections of

Qt

Fr

Bq

Hidden Layer

Type 1

Type 2

Type 3

classification zones in the three-dimensional Qt , Fr , Bq space onto two-dimensional planes. The

Figure 2: Neural network soil classification system

problem lies not with the choice of variables, but the limitations inherent in presenting three-dimensional information in two-dimensional form. If the zones to be represented have anything other than the simplest of shapes, this approach rapidly becomes unsatisfactory. A variety of additional sensors (further pore pressure measurements, acoustic sensors etc.) have been added to the CPT, and if these are to be exploited for classification, the problem becomes one of combining data from four, five or even more sensors. Such a task is daunting, and it is unlikely that simple two-dimensional charts will offer a solution. It is possible that ingenious correlations could be devised (either empirically or with some theoretical input), but this process becomes increasingly difficult the more variables are involved. An alternative approach, in which the Author has been involved, is the use of techniques developed in the IT area to assist in classification. Specifically, neural networks have been used to classify soils. The procedure is as follows, and is illustrated in Figure 2. A number of input quantities are chosen for the Neural Network, in the case illustrated these are the normalised cone resistance, friction ratio and pore pressure measurement. The values of the “hidden layer” units are each a weighted sum of the values of the input units, and the values of the output units are in turn weighted sums of the values of the hidden layer units. Most importantly, nonlinearities are introduced in both these summation processes (usually in the form of a function that effectively saturates at a particular value). The values of the output units can represent either numerical values of quantities such as density, horizontal stress or undrained strength, or particular values can be assigned to mean for instance “clay” or “silt” or “sand”. Neural Networks are therefore suitable both for determining numerical values of engineering

parameters, or for classification of soils into categories. When used to determine numerical values the method fulfils a similar role to multiple regression analysis, but has the advantage that the form of the function fitted to the data does not have to be chosen in advance. The Neural Network is first “trained” on a large set of data for which both the input and output values are known (in the same way that classification charts are based on databases of tests from known sites). During this phase the weighting factors are found by an optimisation process which minimises the errors in the prediction of the output variables. Once the network has been “trained”, i.e. the weighting factors are known, it is then tested by applying it to a second set of data for which both input and output are known. The accuracy of the predictions of the output quantities is measured, and provided that this is acceptable, the trained network is then of use for application to data where the output is unknown. Houlsby and Ruck (1998) give an example of the use of such a system for the identification of both soil type (in this case distinguishing between three types of sand) and engineering properties of sands. Both conventional CPT data, and the data from an acoustic sensor were used. The method proved to be particularly effective for identifying soil type, but was less effective as far as quantitative estimation of soil properties is concerned. The Neural Network approach clearly has certain disadvantages when compared to the use of charts: • it requires use of computer software rather than a sheet of paper, • the classification process is not as obvious to the engineer, since it is hidden within the weighting factors of the network, rather than being transparently obvious as lines drawn on a chart.

(

)

102

q t = N k t s u + σ vo

The first of the drawbacks is rapidly becoming less important. The second can be offset by the fact that, in a properly designed system, an indication of the confidence with which a network is able to make a classification is available as well as the classification itself. (This is equivalent to the answer to the question “How close is the point to the boundary between two classifications?”). What are the direct advantages of the new approach? The most important are: • The method can be extended simply to any number of inputs, and so gets away entirely from the limitations of two-dimensional charts, • The classification process can be carried out in a rigorous mathematical way, and is not biased by subjective judgement. (Some may of course regard this as a disadvantage, since it leaves little room for engineering judgement). The use of modern IT techniques certainly has a role to play in the identification of soil types from in situ data, especially where several measured variables may affect the classification. Engineers’ quite justifiable suspicion that such methods represent “black boxes” over which they have little control should be allayed by clear presentation of the principles on which any method is based.

(1)

A significant advance was the recognition that the total cone resistance qt (which is corrected for the pore pressure acting in the groove behind the cone tip) should be used, not simply the measured cone resistance q c . This practice has now, fortunately, become almost universal, but it means that some early databases that use q c are no longer of value. “Advanced” interpretation of the cone here relates entirely to the determination of the factor N k t . The main variables that affect N k t are: • the soil stiffness, • the horizontal stresses in the ground. This reveals immediately one of the key features of in situ tests: that the engineering parameters for the soil cannot be measured separately, but that strength, stiffness and horizontal stresses all combine to affect the results of the tests. Despite the apparent simplicity of the cone test, it is not straightforward to analyse. Houlsby and Teh (1988) analysed the CPT test in clay using a combination of the strain path method and finite element methods, and arrived at the following empirical expression which fitted their calculated N k t values:

4 MEASUREMENT OF THE ENGINEERING PROPERTIES OF SOILS

 1 G σ − σvo  + 2.2 + 1.8 ho N k t = N s 1 + 2s u  2000 s u 

A key feature of developments in the understanding of the interpretation of in situ tests has been the realisation that the results of the tests are affected by a multiplicity of factors. The strength, stiffness and in situ stresses interact to produce a particular measurement in a test. There are exceptions, such as the vane test, which provides a direct measurement of the undrained strength, and it is accepted that the vane strength is relatively unaffected by other factors such as the soil stiffness. The general rule is, however, that the results obtained represent the combined effect of several factors. The following discussion is therefore organised in terms of different tests, rather than in terms of different measured quantities.

(2)

where N s is the spherical cavity expansion pressure  G  4  1 + ln    , and the above expression is a  3  su   simplification of Houlsby and Teh’s expression in which an intermediate value of cone roughness has been assumed. The advantage of an expression such as the above is that it explicitly recognises the role of the horizontal stress and the stiffness in affecting the cone resistance. The engineer can assess the impact of different assumptions about (for instance) the horizontal stress on the calculated undrained strength. Equation (2) was derived theoretically, and because of the shortcomings of the analysis (which, for instance, did not take into account pre-failure changes of stiffness, or the possibility of any sensitivity) it probably will not agree with field data at a given site. Locally established correlations would usually provide superior estimates of N k t ,

5 THE CONE PENETROMETER 5.1 The CPT in clay The undrained strength of a clay is derived from the CPT results from a formula of the well-known form:

103

B

but equation (2) could nevertheless be used to estimate the sorts of variation of N k t that might be expected at locations with different horizontal stress and stiffness values. Although the measurement of the strength with the CPT is affected by the stiffness and horizontal stress, the CPT provides no independent measurement that can provide values of these quantities: they must be estimated by other means. This means that, as far as measuring soil properties is concerned, the CPT is best used in conjunction with other devices.

q (kPa) 50 A

D

G

100

150

C 50

p' (kPa)

E -50 F

5.2 The CPT in sand

Figure 3: Stress states used in calibration chamber tests

Interpretation of the CPT in sand is a more challenging task than interpretation in clay. Analysis of the cone penetration process is much more difficult in a frictional, dilating material than it is in undrained clay. Some analyses have been made, but even the most successful of these (see for example Durgunoglu and Mitchell, 1975, and Last, 1982) must only be regarded as approximate. As a result, the interpretation of cone data in sands is based more on empirical evidence. The difficulty of obtaining site data where the properties of sands can be well established by independent means has in turn led to the development of calibration chamber testing. Most of the “advanced” interpretation of the CPT in sand is based on results from calibration chamber tests. Note that this is in contrast with clays, for which calibration chamber tests are time-taking and expensive, and calibration of analytical procedures at well-documented test sites is a more favourable option. Large calibration chambers for sand are widely available. Lunne et al (1997) provide a useful compendium of work completed at NGI, ENEL CRIS, ISMES and Southampton University. Much other work has been carried out at Oxford University and at Monash University. The main disadvantage of calibration chamber tests is that even if the chamber is very large, there is still some measurable influence of the boundaries in dense sands (Schnaid and Houlsby, 1991). Appropriate corrections can, however, be made, so that correlations established in chambers can be used with some confidence in the field. Another problem is that there is evidence that the properties of naturally aged sands differ significantly from those of sand prepared in the laboratory. Nevertheless, data from well-planned series of calibration chamber tests can be used to establish correlations for field interpretation. The correlations

are principally empirical, although some include some physical insight to the problem. It is difficult to control the stiffness of a sand separately from the values of other variables. This means that, although the influence of the stiffness on the measured cone resistance is recognised, the precise effect cannot be quantified in calibration chamber tests. The principal quantities which can be controlled are: • sand type, • horizontal and vertical stresses, • density, • stress history (typically expressed as overconsolidation ratio). In most of the work collected by Lunne et al (1997) the lateral strain was kept as zero during sample preparation, and so the horizontal stress is largely controlled by the value of the overconsolidation ratio. Furthermore a very high proportion of the tests are at an OCR of 1.0. This aspect of the tests mean that they do not provide a means of separating out the influence of OCR and of horizontal stress. In the field the OCR and K o values are of course also correlated for many deposits in which the K o value has arisen as a result of a simple deposition and erosion process. The tests from Italy/NGI/ Southampton will be relevant to these sites, and represent an impressive database of considerable value. They will not, however, be so relevant to sites with more unusual stress histories, which have resulted in an unusual combination of OCR and horizontal stress. Using the results for such sites would therefore be misleading. With this problem in mind, the focus of calibration chamber work at Oxford University has been on tests in which the stresses are controlled independently of the overconsolidation ratio. 104

1000.0

Hokksund NC (qt - σho)/σ'h

Hokksund OC Ticino NC Ticino OC

100.0

LBS Yellow LBS White Dogs Bay Equation 3

10.0 0.0

20.0

40.0

60.0

80.0

100.0

Relative Density Figure 4: Correlation between cone resistance and horizontal stress from calibration chamber tests The tests are carried out in sands that have been stressed to one of seven standard stress values, as shown on Figure 3. By comparing different combinations of tests the influence of horizontal stress, vertical stress and overconsolidation ratio can be examined separately. Early work by Houlsby and Hitchman examining the behaviour of the Marchetti dilatometer in sand (see Smith, 1993) led to the conclusion that the influence of the horizontal stress was much more important than the influence of overconsolidation. The conjecture is therefore that the differences observed in the data reported by Lunne et al (1997) for tests at different OCR values, are in fact principally due to the differences in horizontal stress, and not in the OCR itself. A correlation which has been found to fit a large body of calibration chamber data reasonably well is:  q − σ ho   = 1.51 + 1.23DR log 10  t  σ′ho 

different soils and conditions. Even more scatter can of course be expected for field tests. Correlations such as equation 3 (and the many others that have been published in the literature on interpretation of in situ tests) should be used with caution, and as approximate indicators only of soil properties. 6 THE SELF-BORING PRESSUREMETER 6.1 Approaches to interpretation of the pressuremeter test The pressure-expansion curve from self-boring pressuremeter test can be derived using simplified theories for either clay (Gibson and Anderson, 1961) or sand (Hughes, Wroth, and Windle, 1977). In each case the shape of the curve explicitly depends on the strength parameters (undrained strength for clay, angles of friction and dilation for sand) the shear modulus and the in situ horizontal stress. The commonest way of interpreting experimental data is to plot it in ways that single parameters can be extracted from the experimental curves. Different practitioners use slightly different methods, but a common approach would be: 1. obtain the horizontal stress from an estimate of the “lift-off” pressure at which straining of the soil begins. 2. obtain the undrained strength by measuring the

(3)

where DR is the Relative Density (as a ratio). It is assumed that Relative Density can be readily converted to an indication of the friction angle by, for instance, the correlation published by Bolton 1986). The correlation is shown in Figure 4, where it can be seen that even well-controlled calibration chamber tests lead to quite a considerable scatter for 105

slope of a replotted pressure-expansion curve as ψ against ln (ε ) (Gibson and Anderson, 1961). There is an analogous procedure for sands, which requires also an estimate of the angle of friction at constant volume (Hughes, Wroth and Windle, 1977). 3. estimate the shear modulus from the slopes of unload-reload loops. Whilst the above approach is well established, it has some drawbacks. The estimation of in situ horizontal stress from lift off pressures is, for instance, notoriously dependent on (a) any tendency to overdrill or under-drill the hole and (b) the engineer’s judgement. An obvious alternative is to construct the theoretical curve for a pressuremeter test, and then tune the parameters used to define the curve so that the best fit is obtained. The curve can be obtained either from a simple formula, or perhaps from a numerical analysis. Shuttle and Jefferies (1995) term this process “Iterative Forward Modelling”, and have used it with some success to fit pressuremeter test results. As theories for analysing pressuremeter tests become more sophisticated this approach becomes increasingly attractive. The danger is that, if the model used involves a large number of parameters, then equally good fits to the data (in practical terms) may be achieved by different combinations of parameter values. Some additional “intelligence” needs to provided during the fitting process so that unlikely values of parameters are avoided.

final results are relatively straightforward. Given the expense of conducting a pressuremeter tests, it should be routine practice always to obtain data from the unloading curve as this can provide useful additional data for interpretation. 6.3 Effect of length to diameter ratio The pressuremeter is usually analysed on the assumption of plane strain conditions in the axial direction. this is equivalent to the assumption that the pressuremeter is infinitely long. This assumption is clearly questionable, since a typical self-boring pressuremeter has a length-to-diameter ratio of only about 6. The common assumption that the simplification of infinite length introduces only a small error is probably rooted in some early work in which elastic analyses of the pressuremeter were carried out. It is true that the stiffness measured by a short pressuremeter is only marginally higher than for an infinitely long pressuremeter (the difference is about 1.5% for L / D = 6 ). The same is not true, however, once plastic deformation begins. Yeung and Carter (1990) reported a study using finite element analysis in which the effects of pressuremeter length were taken into account. This study was extended by Houlsby and Carter (1994). Further work has been carried out on the effects of finite length by Yu (1990), Yao (1996) and Shuttle and Jefferies (1995). The principal conclusions from the above studies are that in clay the measured strength from the pressuremeter test needs to be reduced by a factor which depends on (a) the stiffness of the clay and (b) the strain range over which the strength is measured (if the slope of the Gibson and Anderson (1961) plot is used). In sand the picture is slightly more complex, since the simplifications inherent in the Hughes, Wroth and Windle (1977) analysis tend to counteract the effects of the finite length. Yu (1990) gives details of corrections which can be applied, and these again depend on the soil stiffness.

6.2 Unloading curves An important development in the understanding of pressuremeter tests was the realisation that useful information could be extracted from the unloading curve as well as the loading curve. An analysis of the unloading sections of pressuremeter curves in sand was published by Houlsby, Clarke and Wroth (1986), and an equivalent analysis for tests in clay by Jefferies (1988). The importance of these analyses is that the unloading curves are insensitive to any imperfections in the drilling process, which affect the shape of the loading curve but not the unloading. The analyses are certainly “advanced” in that they involve quite complex mathematics. A careful track has to be kept of the stress history of elements of soil around the pressuremeter as they are (a) loaded elastically, (b) loaded plastically, (c) unloaded elastically and finally (d) unloaded plastically. In spite of the complexity of the analyses, the

6.4 Stiffness measurement with the pressuremeter test The single most important issue in the measurement of the stiffness of soils that has become recognised in recent years in the strong dependence of stiffness of the amplitude of the strain. The characteristic “Sshaped” curve in the plot of G / p ′ against ln( ∆γ) is by now well known to geotechnical engineers. It should be recognised that the existence of this curve is itself proof that soil is not “elastic” except at

106

G0 G1 a

r1

Figure 6, Pressuremeter in soil with stiffness varying with radius from the pressuremeter vary strongly with the radius. In an undrained test the strains are inversely proportional to the square of the radius (from the centreline of the pressuremeter). This means that for a typical SBPM test, with a pressuremeter diameter of 80mm, the strains in the soil about 85mm from the surface of the pressuremeter are only 1/10 of the value at the pressuremeter surface. Figure 5 shows the results of some laboratory measurements of stiffness of clays, and shows that a tenfold change in the strain can have an enormous effect on the stiffness, especially in the range of strain from about 0.01% to 1%, which is typical of the strains used in pressuremeter testing. Unless proper account is taken of the variation of strain, then it is impossible to put measurements of stiffness in context with other results. Two approaches are considered here. In the first approach we simply try to identify a representative strain for a pressuremeter test, in terms of the strain applied at the pressuremeter surface. There will be no unique solution, but the following analysis helps to resolve whether the measured stiffness is dominated by the material close to the pressuremeter or distant from it. Consider the problem shown in Figure 6, which represents a highly idealised test. A pressuremeter of radius a is surrounded by elastic soil with stiffness G1 out to radius r1 , and outside that the soil has modulus G0 . It is straightforward to show that the measured shear modulus (for an undrained test in which ν = 0.5 ) will be given by:

Figure 5, Typical variation of shear modulus with strain (data for Todi Clay, after Georgiannou et al., 1991) extremely low strain amplitudes (less than say ∆γ = 10 −5 ). The use of the terminology of an “elastic modulus” G is therefore strictly incorrect, but has become common in practice. In a triaxial test the shear strain amplitude is easy to calculate, using the usual simplifying assumption that the soil deforms as a right cylinder. Even if barrelling of the specimen is taken into account it is found that the shear strain throughout most of the specimen corresponds quite closely to the nominal calculated value. The stress conditions are also well defined in the triaxial test, so that the mean stress will be known. Thus it is possible to plot the whole of the G / p ′ against ln( ∆γ) curve with considerable confidence about each data point (although the resolution of stiffness at small strain amplitudes requires rather sophisticated instrumentation). Consider now the measurement of the stiffness of a soil from unload-reload loops from a pressuremeter test. In principle this is an excellent method of measuring stiffness since it avoids all the problems of sample disturbance that usually reduce the measured stiffness in the laboratory. An estimate of the mean effective stress during the cycle must be made so that the G value can be reduced to a normalised value G / p ′ . The problem is twofold: • The radial stress at the pressuremeter surface is known, but the hoop and axial stresses are not measured, and can only be estimated, • All three stresses are varying with distance from the surface of the pressuremeter, so that (even if the full stress system could be estimated) a representative value of p′ has to be chosen from a range of possible values. Of more importance is the fact that the strains undergone by elements of soil at different distances

a2 Gm = G1 + (G0 − G1 ) r12

(4)

Taking the change of stiffness at the radius at which the shear strain will have dropped to only 1/10 of that at the pressuremeter surface, the factor a 2 r12 at this radius is also 1/10. The measured shear

107

modulus would therefore be Gm = 0.9G1 + 0.1G0 . This demonstrates that the measured modulus is very much dominated by the stiffness of the material close to the pressuremeter. The shear strain at the pressuremeter surface is therefore a reasonable estimate of an appropriate shear strain for interpretation of the modulus values. The second approach is to investigate the way that moduli defined in different ways can be transformed. In a laboratory test we can define a secant modulus Gs = τ γ , and a tangent modulus Gt = dτ dγ . Similarly in a pressuremeter test in which pressure ψ is plotted against cavity strain ε , one could define a secant modulus G ps = (ψ − σ ho ) 2 ε and a tangent modulus G pt = 1 dψ dε . The definitions of the moduli can 2

be used to show that: dGs dγ dG ps G pt = G ps + 2ε 2dε Gt = Gs + γ

(5)

dG ps 2dε

(7)

Thus the tangent modulus measured from the pressuremeter curve is equal to the secant modulus from a conventional laboratory test. Muir Wood (1990) pursues the implications of the above relationships when particular forms of variation of shear modulus with strain are assumed. Here we explore the more general relationships. It is common to plot modulus against logarithm of strain (as in Figure 5), and it is useful to see how the moduli are related in this plot. Define x = ln γ for a laboratory test and x = ln (2ε ) for a pressuremeter test (it is straightforward to show that the maximum shear strain in the soil in a pressuremeter test is 2ε ). It can then be shown that: Gt = Gs +

dGs dx

Gs = G pt = G ps +

dx

Gpt = Gs -dGps /dx

Gt

-dGs /dx

x = ln(γ) or x = ln(2ε)

Figure 7: Links between definitions of the shear modulus So that the relationships between the moduli are as shown on Figure 7 (note that the horizontal scale uses natural logarithms, not logarithms to base 10 as is commonly used). The different definitions of the modulus give rise to different curves on this plot. The values only coincide if the shear modulus is constant, in which case all the definitions reduce to the same value. This will only be the case at very

7 THE CONE-PRESSUREMETER The great advantage of the CPT is that it provides a detailed profile of properties with depth. The pressuremeter is better suited to accurate measurement of properties at spot locations. These complementary functions naturally led to the development of the cone-pressuremeter, which combines all the features of a CPT with some of those of a pressuremeter. The cone-pressuremeter simply consists of a pressuremeter mounted behind a standard 15cm2 cone. The main obstacle to the understanding of the cone-pressuremeter test is that the pressuremeter test

(8) dG ps

G ps

low strains (typically γ < 10 − 5 ). For a substantial range of intermediate strains, the shear modulus (whatever the definition) falls approximately linearly with ln ( γ) , so that each of the dG dx terms is approximately constant, and the (approximately) straight sections of the three curves shown in Figure 7 will be parallel and equally spaced. The importance of the above observations is that, while it must be recognised that the different definitions of the modulus give rise to different G − ln (γ ) relationships, these can be interrelated in a rational way. The results of pressuremeter tests can therefore be properly related to those of other tests.

(6)

Muir Wood (1990) showed that, for an undrained pressuremeter test, the Palmer (1972) “subtangent” analysis leads to the result: Gs = G pt = G ps + 2ε

G

(9)

108

is carried out not in undisturbed ground, but in soil which has been displaced by the cone. This means that an understanding of the cone penetration process is needed, so that the analysis of the pressuremeter phase of the test is started at the appropriate initial conditions. This exercise is not trivial, and has been one of the catalysts for the development of advanced interpretation methods.

parameter approach is proving to be a more promising avenue, and the more advanced analysis in which changes of the angle of friction with stress level and density are taken into account appears to be amply justified. At present the interpretation of the cone pressuremeter in sand is, like the interpretation of the CPT, largely empirically based. Schnaid (1990) and Nutt (1993) studied the cone pressuremeter in sand. They derived empirical correlations which allow the relative density and the horizontal stress to be estimated from the cone tip resistance qt and the limit pressure ψ L from the pressuremeter test. The basis of the correlations is that both the cone resistance and the limit pressure depend on two variables: the horizontal stress and the relative density. Approximate empirical expressions for relationships are (Nutt, 1993):

7.1 Clays The interpretation of the Cone Pressuremeter in clays needs to take into account the installation of the cone, and requires the use of large strain analysis. The analysis was made by Houlsby and Withers (1988), and concentrates principally on the interpretation of the unloading section of the test. This is in contrast with self-boring pressuremeter tests, where most information is obtained from the loading section. The analysis gives rise to a simple geometric construction to determine the undrained shear strength, the shear modulus and the in situ horizontal stress. Studies of this procedure (Houlsby and Withers, 1988, Houlsby and Nutt, 1990, Powell and Shields, 1995) indicate that (a) the strength measurements correspond quite closely to those measured by other means, (b) the stiffness values are broadly comparable to those measured from unloadreload loops (although uncertainty about the appropriate strain range makes interpretation difficult), but (c) the implied horizontal stresses bear little resemblance to site values. Even when the effects of length-to-diameter ratio are taken into account (Yao, 1996) there is little improvement in the estimation of horizontal stress. One conclusion has to be that a full understanding of the mechanical processes involved in the test has yet to be achieved.

ψ L − σ ho = A + BD R = 1.98 + 19.1DR σ′ho qt − σ ho = C + DDR = 3.39 + 10.4 DR ψ L − σ ho

(10) (11)

The above equations can be solved simultaneously to give a quadratic in the horizontal stress: D(ψ L − σ ho )((ψ L − σ ho ) − A(σ ho − uo )) = B(σ ho − uo )((qt − σ ho ) − C (ψ L − σ ho ))

(12)

which can be solved for σ ho . A simple back substitution then gives the value of DR . Figure 8 shows a comparison between the measured horizontal stress in calibration chamber tests, with the horizontal stress deduced from the cone pressuremeter results using the above method. This figure shows that a reasonable estimate of the horizontal stress can be made with the cone pressuremeter. This position should be contrasted with the interpretation of the CPT, where one of the obstacles to interpretation was the fact that the horizontal stress was unknown. Figure 9 shows the comparison of measured relative density with the estimate from the above procedure, and demonstrates that reasonable estimates of the relative density can also be obtained. Manassero (1991) used a procedure similar to the above (although differing in detail) to combine the results of the CPT and the conventional self-boring pressuremeter to obtain estimates of horizontal stress in the field, and reported some success.

7.2 Sands The analysis of the cone pressuremeter in sands is significantly more complex than the equivalent analysis in clay. This is principally because of the difficulties of large strain analysis in frictional, dilative materials. The study of this problem was, however, the catalyst for the solution obtained by Yu (1990) for the complete expansion and contraction of a cylindrical or spherical cavity in a cohesive/frictional material with dilation (see also Yu and Houlsby, 1991, 1995). The analysis suggests that again the unloading section of the test will yield most information, but comparisons between the analysis and test results are not entirely satisfactory. Work by Yu (1994) using models based on the state 109

•

•

Figure 8: Estimations of horizontal stress using cone pressuremeter

• •

• Figure 9: Esimates of relative density from cone pressuremeter tests

•

7.3 Length-to-diameter ratio •

In spite of the fact that cone pressuremeters typically have a length-to-diameter ratio of 10, the effects of finite length are still significant. Schnaid (1993) and Yao (1996) carried out tests on pressuremeters with L D ratios of 5, 10 and 20. Figure 10 shows three of Schnaid’s results, all under the same soil conditions. It can be seen that the limit pressure depends strongly on the L D ratio (in fact a limit pressure was not reached for the test with L D = 5 ). Any correlations established are only appropriate for a pressuremeter of one particular geometry. Yao (1996) also studied the effects of finite length on the analysis of the cone pressuremeter in clay, and found that it had a relatively minor effect on the deduced value of the undrained strength.

•

•

engineering, allowing some engineering properties of soils to be measured that either cannot be determined from laboratory tests, or are less well determined by laboratory tests. Whilst some field tests can be interpreted by simple methods, others require more advanced methods for proper interpretation. Although simplicity has many merits, advanced methods (where necessary) should not be avoided. Soil classification from in situ tests has in the past been based primarily on the use of charts. Whilst this method is useful when only two quantities are measured, it becomes cumbersome when three or more measurements are mad. Use of Neural Networks is a promising technique in which classification can be carried out using several input quantities. It has already been proven as a useful technique for distinguishing between different sands. Interpretation of the CPT in clay to determine undrained strength should take into account the value of the stiffness and the horizontal stress. Interpretation of the CPT in sand is based principally on the results of calibration chamber tests rather than analysis. Again the value of the horizontal stress should be taken into account. The unloading curve from a pressuremeter test provides useful information and is amenable to analysis. Pressuremeter test results should be corrected to take into account the finite length of the pressuremeter if overestimates of strength parameters are to be avoided. Stiffness measurements from the pressuremeter can be related to those of other tests, but appropriate transformations between different stiffness measurements must be used. The cone pressuremeter can be used to give good estimates of the undrained strength of a clay (based on a theoretical analysis) and for the density and horizontal stress of a sand (based on calibration chamber test results). The effects of length-to-diameter ratio are significant for the limit pressure measured with the cone pressuremeter.

9 ACKNOWLEDGEMENTS The content of this paper is based to a large extent on the work of many research students and assistants at Oxford University, in particular that of Teh Cee Ing, Fernando Schnaid, Hai-Sui Yu, Nigel Nutt, Brendan Ruck and Mitsuhiro Yao.

8 CONCLUSIONS • Field tests fulfil an essential role in geotechnical 110

(MPa) Figure 10: Results of cone-pressuremeter tests with different length-to-diameter ration (after Schnaid,1990) 10 NOTATION DR fr fs G p′ qc qt Qt Qh su γ ε

Bolton, M.D. 1986 The strength and dilatancy of sands, Géotechnique, Vol. 36, No. 1, 65-78 Douglas, B.J. and Olsen, R.S. 1981 Soil Classification using electric cone penetrometer, Cone penetration testing and experience, Proc ASCE National Convention, St. Louis, 209-227 Durgunoglu, H.T. and Mitchell, J.K. 1975 Static penetration resistance of soils, Proc. ASCE Speciality Conf. on In Situ Measurements of Soil Properties, Rayleigh, Vol. 1, 151-189 Georgiannou, V.N., Rampello, S. and Silvestri, F. 1991 Static and dynamic measurements of undrained stiffness on natural overconsolidated clays, Proc 10th ECSMFE, Florence, Vol. 1, 9196 Gibson, R.E and Anderson, W.F. 1961, In situ measurement of soil properties with the pressuremeter, Civ. Eng. Pub. Works Review, Vol. 56, 615-618 Houlsby, G.T. and Carter, J.P. 1993 The Effects of Pressuremeter Geometry on the Results of Tests in Clay, Géotechnique, Vol. 43, No. 4, 567-576 Houlsby, G.T., Clarke, B.G. and Wroth, C.P. 1986 Analysis of the Unloading of a Pressuremeter in Sand, Proc. 2nd Int. Symp. on the Pressuremeter and Its Marine Applications, Texas, May, 245-264 Houlsby, G.T. and Hitchman, R.C. 1988 Calibration tests of a cone penetrometer in sand, Géotechnique, Vol. 38, No. 1, 39-44

Relative Density friction ratio friction sleeve measurement shear modulus mean normal stress (σ1′ + σ′2 + σ′3 ) 3 uncorrected cone resistance total cone resistance (qt − σ vo ) σ′vo (qt − σ ho ) σ′ho

undrained strength shear strain pressuremeter strain (tensile hoop strain at the pressuremeter surface) ν Poisson’s ratio ψ pressuremeter pressure ψ L Cone pressuremeter limit pressure

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