In Situ Tests and the Pre-failure Deformation Behaviour of Soils

In Situ Tests and the Pre-failure Deformation Behaviour of Soils G.T. Houlsby Department of Engineering Science, Oxford University, U.K. ABSTRACT: The non-linear pre-failure behaviour of soils influences the results of some in situ tests, in particular the group of tests which cause expansion of a cavity in the soil (the CPT, pressuremeter and dilatometer). Other tests are relatively unaffected by soil non-linearity, either because the strains are small (as in geophysical tests) or large (as in the vane test). Whilst several tests are affected by non-linearity, that does not necessarily mean that they are suitable for measuring non-linear properties. Of the tests considered, only the pressuremeter offers a realistic possibility of exploring non-linear behaviour in any detail. 1 INTRODUCTION In situ testing has assumed increasing importance in determining the properties of soils, as the advantages of in situ testing have been recognised by practising engineers. The principal advantages are threefold: firstly in situ tests avoid the problems of sample recovery and disturbance, secondly some in situ tests are easier to conduct than laboratory tests which would yield the same information and thirdly in situ tests can offer more detailed site coverage than laboratory testing. Against these advantages there are of course drawbacks, the most important of which is the fact that the boundary conditions for an in situ test are less well-defined than those in laboratory tests. The result is that in most in situ tests the soil tested is not strained homogeneously, so that gradients of strain and stress exist around the testing device. Much of the soil is therefore deforming pre-failure and so its behaviour in this range becomes important. This complicates the interpretation of many in situ tests. The pre-failure deformation behaviour of soils is of course complex. It is now widely recognised that soil does not behave as a simple elastic-plastic material. At very small strains the behaviour of soils can be well approximated by elasticity theory, but at small and intermediate strains non-linear behaviour occurs long before failure. The non-linear behaviour cannot be modelled simply by non-linear elasticity, as this does not take into account the pathdependent and hysteretic effects that are observed in practice. A proper modelling of the non-linear response should be rooted in an understanding of the plastic (dissipative) processes that occur before failure. A comprehensive understanding of this problem has yet to be achieved, although some promising avenues are being pursued. For the purposes of this paper, however, we simply accept the empirical fact that soil almost universally exhibits non-linearity, certainly associated with plastic deformation, before failure occurs. The relevance of the non-linear pre-failure behaviour to in situ tests is twofold: The fact that non-linearity occurs in practice may conflict with simplifying assumptions which have been made to interpret the in situ test. The significance of the assumptions therefore needs to be assessed in relation to the effects of the non-linear response. Some in situ tests may allow measurements to be made which shed some light on the non-linear response of the soil. The above issues are treated separately in each of the following discussions, which are focussed on particular tests. 2 GEOPHYSICAL METHODS 2.1 Influence of non-linearity Geophysical methods usually subject the soil to very small strains, within the range for which the response of the soil can be regarded as truly elastic. If the soil does indeed remain elastic, then there will be no influence of non-linearity. Geophysical

methods are of course of great importance in assessing one particular aspect of the pre-failure behaviour: the shear modulus G 0 at small strain. If the strains applied to the soil become too large, then an accurate estimate of G 0 will not be obtained. Since the stiffness of the soil drops with increasing strain amplitude, the effect of this will be to reduce the apparent small-strain shear modulus. Such effects would be difficult to quantify without either detailed analysis, or the calibration of one testing technique against another. However, it appears that in general geophysical methods are little affected by the non-linear behaviour of soils. 2.2 Determination of pre-failure properties Apart from the (extremely important) determination of G 0, it is unlikely that geophysical tests will be of use in determining pre-failure behaviour of soils. 3 THE VANE TEST 3.1 Influence of non-linearity At the opposite extreme from geophysical tests, vane tests are used primarily to determine the undrained strength of clays. They subject the clay to very large strains, in fact sufficient to form a shear plane on a cylindrical surface enclosing the vane. The soil is certainly brought to failure on this surface, and the influence of the pre-failure deformation behaviour on the measured strength is likely to be small. The sensitivity of soils is often determined using the vane test, and in the case of sensitive soils the postfailure deformation behaviour of the soil has an important influence on the results. Although the geometry of the vane is such that the soil around the entire cylindrical surface is brought to failure at approximately the same time, there is some possibility that progressive failure could occur. In a sensitive soil this could result in some part of the failure surface reaching post-peak behaviour before another part had reached peak. The result would be that the observed peak strength would be lower than the true peak. Such a progressive failure would of course be influenced by the pre-peak behaviour. The pre-peak behaviour will also have a very minor influence through the distribution of stresses on the ends of the vane. 3.2 Determination of pre-failure properties Whilst in principle some information on the prepeak stress-strain curve could be obtained from the torque-rotation curve for a vane test before peak, in practice the corrections necessary to account for the twist of the shaft are likely to be large compared to the measured rotations. For all practical purposes the vane cannot be used to give information on the nonlinear behaviour of soil pre-peak. 4 CONE PENETRATION TESTS 4.1 Influence of non-linearity The cone penetration test is recognised primarily as a strength-measuring device. Thus the tip resistance in clay would be expressed as qt = Nktsu + σvo (1) Given an estimate of N kt and of the overburden stress σ vo. The undrained strength can be estimated. Alternatively in sand: q t = Nqσ vo + uo (2) so that given estimates of σ vo and u o it is possible to estimate N q, which can in turn be related to the angle of friction of a sand. Unfortunately the above is an over-simplification. It is well recognised that the factor N kt is a function of other variables, for instance it is affected by the relative magnitudes of the horizontal and vertical stresses, and is also significantly affected by the stiffness of the soil (see for example Houlsby and Teh (1988), Teh and Houlsby (1988), Houlsby and Wroth (1989), Teh and Houlsby (1991)). In sands it is also recognised that the bearing capacity factor N q for the cone will be a function of variables other than the strength. The analysis of the cone in sand is complex, but it may partly be idealised as the expansion of a cylindrical cavity of zero initial size in the soil. The factor N q will therefore be closely related to the solution of the equivalent cylindrical cavity expansion problem. Such solutions were obtained by Yu and Houlsby (1991), and demonstrated that again the horizontal stress and the soil stiffness have a strong influence on the expected cavity expansion pressure. A further complication in sands is that the pressure depends on the angle of dilatancy as well as the angle of friction. Since, however, the angles of dilatancy and friction for a given soil are related (see for example Bolton (1986)), then provided that the critical state angle of friction is known, then friction and dilation can be taken together as a single variable. The above analyses, whilst recognising the influence of horizontal stress and stiffness on the CPT, are still simplifications in that the behaviour of the soil itself

is assumed to be described by a simple elasticplastic model. They do, however, point the way to more complex analyses. If the soil could be represented by a more realistic model, accounting fully for the non-linearities, then it is clear that the shape of the stress-strain curve would affect the calculated cone resistance, as well as the initial stiffness and the ultimate strength. Analysis of cavity expansion problems using more complex models have been carried out (see for example Collins and Yu (1996), Yu et al. (1996)), but the author is not aware of any analysis of the CPT in which detailed modelling of soil non-linearity across the full range of strains is attempted. 4.2 Determination of pre-failure properties One might expect that if the results of a test depend on some feature of soil behaviour (in this case the nature of the non-linearity) then the results could be interpreted to provide information about that feature. Unfortunately this is not the case. The tip resistance in the CPT test is effectively an integration of a (weighted) function of the soil stress-strain curve. If the stress-strain behaviour were known in detail, then the cone resistance could be predicted, but the reverse is not true. One cone resistance can result from many different combinations of soil properties. Of course the cone tip resistance can be supplemented by other information (e.g. the sleeve friction and pore pressure measurements). Although this gives important clues about soil properties, and so narrows down the range of possibilities, there are still many possible forms of non-linearities that could give rise to any given set of measurements. Unfortunately the CPT test is not therefore of any value in determining the non-linear stress-strain curve for a soil. 5 PRESSUREMETER TESTS 5.1 Influence of non-linearity The pressuremeter test is quite closely related to the CPT in that it too involves expansion of a cavity in the soil. In fact cylindrical cavity expansion theory is even more appropriate to the pressuremeter test. The great advantage, however, of the pressuremeter test is that a complete pressure-expansion curve is obtained. Some of the following discussion was presented by Houlsby (1998), but the points are also relevant here. All the theories for the interpretation of the pressuremeter make use of (a) the in situ horizontal stress (b) the soil stiffness and (c) strength (and dilation) parameters. The commonly-used theories mainly use simple elastic-plastic idealisations of the soil to allow derivation of a theoretical pressuremeter curve. This is then matched against observations to deduce the material parameters. There are many complicating factors in this process (e.g. the finite length of the pressuremeter, Houlsby and Carter (1993)), but clearly an important on is the fact that the real soil does not behave in a simple elastic-plastic manner. If a complete model of the stress-strain behaviour were to be available it is clear that the details of the non-linearities would affect the derived pressuremeter curve. Setting aside the interpretation of the whole pressuremeter curve, consider just the interpretation of unload-reload loops in a pressuremeter test, where a conventional analysis would indicate that the behaviour would be entirely elastic. Use of these loops is in principle a useful way to measure shear stiffness since it avoids many of the problems of disturbance that are associated with laboratory testing. In practice, however, the equivalent shear stiffness will vary significantly with radial distance from the pressuremeter. Firstly 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 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 self-boring pressuremeter 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 1 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,

G 1 G 0 a r 1 Figure 2, Pressuremeter in soil with stiffness varying with radius Figure 1, Typical variation of shear modulus with strain (data for Todi Clay, after Georgiannou et al., 1991) then it is impossible to put measurements of stiffness in context with other results. It is useful to 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 2, which represents a highly idealised test. A pressuremeter of radius a is surrounded by elastic soil with stiffness G 1 out to radius r 1, and outside that the soil has modulus G 0. It is straightforward to show that the measured shear modulus (for an undrained test in which ν = 0. 5) will be given by: 2 a G m = G1 + ( G0 G1 ) (3) 2 r1 Selecting for example 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 2 2 factor a r1 at this radius is also 1/10. The measured shear modulus would therefore be G m = 0.9G1 + 0. 1G 0. This demonstrates that the measured modulus is very much dominated by the stiffness of the material close to the pressuremeter. However, if the strain at the pressuremeter surface were 0.1%, and the strain at r 1 0.01%, Figure 1 shows that the ratio G 0 G1 would be about 2.5. This would result in G m being about 15% higher than G 1. It is difficult to judge the shear strain that would be relevant to this stiffness, but it is perhaps 0.08%, which is the strain that occurs about 5mm from the surface of the pressuremeter. The shear strain at the pressuremeter surface is a reasonable estimate of an appropriate value for interpretation of the stiffness values, but the measured stiffness will be a little higher because of the stiffer material further away from the pressuremeter. Although the above analysis is highly simplified, it demonstrates that not only does the non-linear behaviour of the soil influence the pressuremeter test, but that the magnitude of the influence can be assessed, and the results placed in a proper context. 5.2 Determination of pre-failure properties Unlike the tests previously discussed, the pressuremeter test offers the possibility of measurement of features of the pre-failure deformation behaviour. This can be achieved by decoding the pressure-expansion curve to obtain the shear stress-strain curve for the soil. The first, and well-known, example of this was the sub-tangent method of analysis of the undrained pressuremeter test (independently discovered by Palmer (1972), Ladanyi (1972) and Baguelin et al. (1972)). The details are not given here, but the key result is that (for small strains) the mapping: dψ τ = ε, γ = 2ε dε (4a,b) allows derivation of the shear stress-shear strain ( τ, γ) curve from the pressure-cavity strain ( ψ,ε) curve (where cavity strain is defined as the hoop strain at the pressuremeter surface). The method can be applied either graphically or algebraically. Manassero (1989) published an elegant application of a very closely related concept to the interpretation of pressuremeter tests in sands. By exploiting the relationship between the mobilised angle of friction and the current rate of dilation (Manassero used Rowe s stress-dilatancy relationship, but in principle other relationships could be used), he was able to derive a numerical procedure which allows derivation of the stress-strain curve from the pressure-expansion curve.

G Thus, for either undrained or drained tests, the pressuremeter curve provides direct information about soil non-linearity. It is useful to explore the implications of the above analyses for the presentation the variation of stiffness with strain. In a laboratory test we can define a secant modulus G s = τ γ, and a tangent modulus G t = dτ dγ. Similarly in a pressuremeter test one can define secant and tangent moduli G ps = ( ψ σho ) 2ε and G = 1 pt ψ dε 2 d. The definitions of the moduli can be used to show that: dg = + γ s Gt Gs dγ (5) dg ps G pt = G ps + 2 ε 2dε (6) Muir Wood (1990) showed that, for an undrained pressuremeter test, the Palmer (1972) subtangent analysis leads to the result: Gs = G pt -dg ps /dx -dg s /dx G ps G pt = G s x = ln(γ) or x = ln(2ε) Figure 3: Links between definitions of the shear modulus dg ps = G ps + 2 ε (7) 2dε 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 for particular forms of variation of shear modulus with strain. Here we explore the more general relationships. It is common to plot modulus against logarithm of strain (as in Figure 1), and it is useful to relate the moduli in this plot. Define x = ln γ for a laboratory test and x = ln( 2ε) for a pressuremeter test (the maximum shear strain in the soil in a pressuremeter test is 2 ε ). It follows that: dgs Gt = Gs + (8) dx G t dg ps Gs = G pt = G ps + (9) dx The relationships between the moduli are shown on Figure 3 (note that the horizontal scale uses natural logarithms, not logarithms to base 10). The different definitions of the modulus give rise to different curves. The values only coincide if the shear modulus is constant. This will only be the case at very low strains (typically γ < 10 5 ). For a substantial range of intermediate strains, the stiffness (however defined) 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 3 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 THE MARCHETTI DILATOMETER TEST 6.1 Influence of non-linearity The Marchetti dilatometer tests is another in the general class of cavity expansion devices, although this time the cavity is blade-shaped rather than cylindrical. It would be expected that the results of the dilatometer test would be affected in broadly the same way as those of the CPT: the shape of the nonlinear stress-strain curve will influence the results. 6.2 Determination of pre-failure properties The dilatometer is in a certain sense a highly simplified type of pressuremeter (with a slightly complex geometry). If the standard dilatometer readings are taken then they represent in effect two points on the stress-strain curve, and so in principle may give some information about non-linearity, although how to relate the detailed readings to numerical values is far from clear. Some research has been done with a research dilatometer in which a complete dilatometer pressure-expansion relationship is obtained. Clearly this offers a rather more realistic possibility of obtaining information about non-linearity, but again the interpretation is not yet established.

Table 1: In situ tests and soil non-linearity Test Test influenced by Test able to measure Soil non-linearity soil non-linearity Geophysical No No Vane Test No No CPT Yes No Pressuremeter Yes Yes Dilatometer Yes No? Plate Load Test Yes No 7 PLATE LOAD TESTS 7.1 Influence of non-linearity It is self-evident that the load-deformation curves in plate load tests will depend on the pre-failure behaviour of the soils concerned. 7.2 Determination of pre-failure properties Since the plate load test involves (like the pressuremeter) the recording of a complete loaddeformation response, it might be expected that it would be possible to decode this curve to determine the non-linear response of the soil. This is not, however, possible because the test differs from the pressuremeter in a very important way. Each element of soil under the plate undergoes a different strain history, unlike the case in an (idealised) pressuremeter test, in which elements of soil at different radii all undergo the same stain history. It is this simplifying feature of the pressuremeter test which makes the decoding possible. It is well known that the plate load test is further complicated if it is on a vertically inhomogeneous soil. Such complications of course also affect the interpretation of other in situ tests. 8 CONCLUSIONS The above discussion addresses two issues (a) how the pre-failure behaviour of soils affects the results and interpretation of in situ tests, and (b) to what extent in situ tests can be used to determine prefailure deformation behaviour. The results of the discussion are summarised in Table 1. At one extreme geophysical tests are at such small strain that they are neither affected by soil nonlinearity, nor are they useful for measuring nonlinear behaviour. At the other extreme the vane test measures only failure conditions and is again relatively unaffected by non-linearity. In between are several tests which are strongly affected by soil non-linearity. These are all tests where, by one means or another, a cavity is expanded within the soil (e.g. CPT tests, the pressuremeter or the dilatometer). Large zones of soil in a pre-failure condition influence these tests. Although affected by non-linear behaviour, most of the cavity-expansion type tests do not provide sufficient information to be able to deduce anything about the nature of the non-linearity. Only the pressuremeter, because it involves recording of a continuous pressure-displacement curve, offers a realistic possibility of in situ determination of nonlinear response. REFERENCES Baguelin, F, Jézéquel, J.F., Lemèe, E and Le Méhauté, A. (1972) Expansion of Cylindrical Probes in Cohesive Soils, Proc. ASCE, J. Soil Mech. Found. Eng. 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