State Parameter Interpretation of Cone Penetration Tests in Agricultural Soils

Transcription

1 Biosystems Engineering (2002) 83 (4), doi: /bioe , available online at on SW}Soil and Water State Parameter Interpretation of Cone Penetration Tests in Agricultural Soils M. Z. Abedin 1 ; D. R. P. Hettiaratchi 2 1 Department of Farm Structure, Bangladesh Agricultural University, Mymensingh 2202, Bangladesh 2 Department of Agricultural & Environmental Science, The University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU, UK (Received 5 March 2001; received in revised form 18 September 2002) Cone penetrometer resistance in saturated sands has been shown by earlier workers to be an exponential function of a state parameter in critical state space. The present investigation demonstrates that this concept of a state parameter-penetrometer function (SPP-function) also holds good in a partly saturated agricultural soil. The two coefficients which characterize the SPP-function have been evaluated from extensive tests carried out in a miniature penetrometer calibration chamber. These coefficients were found to vary in a systematic manner with the moisture content of the sandy loam soil used in the experiments, as do the three basic parameters necessary to characterize the critical state boundaries of this soil. The paper presents a method of using this experimentally obtained information to interpret the pore space of the soil from measured penetrometer resistance in that soil. The performance of the proposed method was checked against penetrometer readings made under carefully controlled laboratory conditions in an indoor soil tank. The prediction accuracy was poor, but it is felt that this could be improved by using an iterative solution in place of the single step method used in the validation. The tedious and time consuming experimental work described in the paper is confined to a single sandy loam soil, typical of a light agricultural soil. In order to generalize the solution, it is necessary to test the procedure over a wide range of soils, including clay. If the SPP-functions can be established for these conditions then the state parameter concept could prove to be a powerful tool in the interpretation of cone penetrometer readings. # 2002 Silsoe Research Institute. Published by Elsevier Science Ltd. All rights reserved 1. Introduction Nearly four decades have elapsed since the Cambridge critical state concept was first developed as a model for explaining the behaviour of saturated sands and clays (Roscoe et al., 1958; Schofield & Wroth, 1968). In the intervening years, state space, delineated by this elegant model, has been extended empirically to cover partly saturated soils (see, e.g. Hettiaratchi, 1987; Wheeler & Sivakumar, 1993) and rocks (Gerogiannopoulos & Brown, (1978). In spite of steady development of the model, conspicuous practical applications have been sparse. A parallel inadequacy with cone penetrometer tests has been the complete lack of precision in the interpretation of penetrometer resistance data gathered from both saturated and partly saturated field soils. An opportunity to simultaneously bridge these two gaps in geotechnical practice has been made possible by Been & Jefferies (1985), who demonstrated that a state parameter, in critical state space, can be associated with the performance of cone penetrometers in sands. This powerful concept paves the way for a practical application of the critical state model to rationalize the interpretation of penetrometer data. This paper deals with a preliminary study in the application of the state parameter concept, devised by Been & Jefferies (1985), to data obtained from a cone penetrometer to predict the bulk density of a partly saturated loam soil. The experimental investigations discussed in the paper were confined to a single soil and must be construed as a tentative initial step in a broader attempt to provide a relatively simple general solution to a problem of extreme complexity. 2. Theoretical background 2.1. State parameter The state of a soil element is essentially its physical condition, which can be quantified by two parameters, its current pore space and its ambient stress level. The /02/$ # 2002 Silsoe Research Institute. Published by Elsevier Science Ltd. All rights reserved

2 470 M.Z. ABEDIN; D.R.P. HETTIARATCHI Notation C 1, C 2, C 3 c K 0 M m m 0 p p c p n p 0 q q c Q Q 0 S S c S p u v coefficients cohesion intercept in Mohr Coulomb equation, N m 2 coefficient of earth pressure at rest slope of critical state line in q p space slope of SPP function slope coefficient mean normal stress, N m 2 mean normal stress at critical state, N m 2 pre-compression pressure, N m 2 cell pressure, N m 2 principal stress difference (deviatoric stress), N m 2 cone penetrometer resistance, N m 2 normalized cone resistance intercept of SPP function degree of saturation of soil degree of saturation at quasi-saturation limit partial degree of saturation pore pressure, N m 2 specific volume of soil, m 3 m 3 v c w z g g d G l s s a, s c s H, s V s 1, s 2, s 3 j c specific volume of soil at critical state, m 3 m 3 gravimetric water content of soil, kg kg 1 embedment depth of penetrometer cone, m bulk unit weight of soil, N m 3 dry unit weight of soil, N m 3 intercept of critical state line in v ln(p) space slope of critical state line in v ln(p) space total normal stress, N m 2 axial stress and confining stress, N m 2 stress on vertical and horizontal planes, Nm 2 major, intermediate and minor principal stresses, N m 2 critical state angle of friction, deg state parameter, m 3 m 3 Superscript 0 effective stress former can be represented by its specific volume v and the latter by its mean effective stress p 0. This is basically the octahedral normal effective stress which, expressed in terms of the three principal stresses, is p 0 ¼ 1 3 s0 1 þ s0 2 þ s0 3 ð1þ The state parameter of a soil element can be defined either on a stress or on a volumetric basis. For example, in the v ln p 0 projection of critical state space shown in Fig. 1(a), the state parameter of the element X can be represented either by the distance XA=ln p 0 - ln p 0 c =ln (p 0 /p 0 c ) or by the distance XB=v v c where v c 0 and p c are the specific volume and mean normal stress at the critical state wall, respectively. An attractive feature of the parameter is that it is non-dimensional. Following the original definition proposed by Been & Jefferies (1985), the state parameter based on specific volume is used in this investigation. On this basis the state parameter c of the soil element, at its ambient stress p 0 and its current specific volume v, is defined as c ¼ v v c ð2þ The specific volume v c at the critical state wall at the ambient stress p 0 is obtained from the equation characterizing the critical state line v c ¼ G l ln p 0 ð3þ where: G is the value of v c at p 0 =10 kpa and l is the slope of the critical state line on a v c -ln p 0 plot. The element X, considered in the above definition, was located in the super-critical zone of state space (i.e. on the so-called dry side of critical), where v5v c, so that c is negative. For elements located within the subcritical zone (i.e. on the so-called wet side of critical), the state parameter is positive and when the element lies on the critical state line, the state parameter is zero [see Fig. 1(b)]. The sign of the state parameter thus gives us an indication as to whether the soil element will dilate (c50), compact (c>0) or deform without volume change (c=0). By definition, the state parameter of the soil element is the distance of the soil element from the so-called critical state wall. This single parameter, therefore, embodies quantitative information on both the current state of the soil element and the volume change potential of the soil itself. Clearly, the state parameter concept constitutes a significant simplification in the use of a complex model which requires a plethora of defining parameters Effective Stress The original work relating the state parameter to the performance of penetrometers was developed for saturated soils. The present paper attempts to extend this concept to partly saturated agricultural soils. The major change required in dealing with partly saturated soils is the move from effective stresses in saturated soils

3 CONE PENETRATION TESTS 471 v v ICL v c v Ψ X B A CSL CSL Ψ (-ve) Sub-critical domain Super-critical domain Ψ= 0 Ψ (+ve) (a) p p c ln p (b) ln p Fig. 1. (a) Volumetric v and effective stress p 0 basis for defining a state parameter; (b) sign of volumetric state parameter c in the two domains of critical state space; CSL, critical state line; ICL, isotropic compression line; v c and p 0 c, specific volume and mean effective stress at the critical state wall to total stresses in de-saturated soils. Considerations of space preclude a comprehensive discussion for making this change, but the main factors involved are outlined below. Consider the case of a soil sample in which the degree of saturation S is gradually reduced from saturation (S=1). At the start of de-saturation, the gaseous phase enters the free water in the pore space and occupies it in the form of discrete bubbles. As the soil dries out further, to a degree of saturation S c, the bubbles join up and the liquid phase retreats into the contact sites of the grains and the pressure in the gaseous phase now approximates to atmospheric pressure. At around this degree of saturation, the liquid phase changes from being predominantly free water within the pore space to mainly capillary water at the contact sites. The consequences of this transition are two-fold. Firstly, the liquid phase cannot impose any hydrostatic constraints on pore volume change because the compressible gaseous phase is capable of accommodating part or all of the pore space change. In contrast, at higher degrees of saturation (S>S c ), pore space cannot change without altering the pressure in the virtually incompressible liquid phase. Secondly, sharply curved menisci develop between the gaseous, liquid and mineral phases within the soil fabric. The curvature of the liquid surfaces constrains the pressure in the liquid phase to drop below atmospheric pressure. The resulting liquid phase suction, acting at the inter-granular contact sites, increases the grain contact forces by an appreciable amount. Generally, this capillary pore water suction is comparatively insensitive to pore space changes. Clearly, these conditions have an impact on effective stress, but its direct influence on the behaviour of the soil is difficult to quantify. Further reduction of moisture to a degree of saturation S p results in the amount of water at the contact sites shrinking to the point where physico-chemical forces now predominate in the soil skeleton. This is particularly significant if the soil contains an appreciable amount of fines. At these levels of saturation, bonding and cementing between the grains control the intergranular forces required to initiate sliding. The direct influence of these factors on the relevant effective stress is even more difficult to quantify. The above greatly simplified categorization of soil saturation levels leads us to two distinct approaches. For saturated soils (S=1) and soils in the quasisaturated state (S c 5S51), soil behaviour is governed by the relevant combination of total stress s and pore pressure u, and the effects of a change in stress or pore volume are a direct result of changes in effective stress s 0 =(s u), which can be readily quantified. For unsaturated soils in the range S5S c, the influence of pore water suction u, cementation and other physicochemical effects on the effective stress at the intergranular contact sites cannot be accurately quantified or evaluated in a meaningful way. Under these circumstances, the overall external effect of all these factors on the volume change behaviour of the soil is reflected in the relative magnitudes of the parameters quantifying critical state space (such as l, G, etc.) established on a total stress basis. The corresponding influence on soil strength is represented by the Mohr Coulomb parameters c, the cohesion intercept,

4 472 M.Z. ABEDIN; D.R.P. HETTIARATCHI and the angle of internal friction j. This expedient does not violate the principle of effective stress but, as distinct from the approach for saturated and quasi-saturated soils, no attempt is made to actually infer what the actual effective stresses are from difficult to measure pore water suction, only their indirect influence on soil behaviour is quantified in terms of total stress. An example of this approach is the establishment of the geometry of the state boundaries in p q v state space (where p is the mean normal total stress, q the deviator stress and v the specific volume of the soil) for partly saturated soils. The shape of these surfaces and their controlling parameters, established in terms of total stress, can be shown to vary systematically with the degree of saturation below S c (see, e.g. Hettiaratchi & Abedin, 1994). Broadly speaking, it can be assumed that the degree of saturation of light agricultural soils below field capacity rarely exceeds the quasi saturation limit S c. Under these circumstances, it is reasonable to work in terms of total stress and the customary prime used to designate effective stress will be dropped in all future references in this text. 3. State parameter concept and cone resistance 3.1. Cone resistance Cone resistance, or cone index, is defined as the equivalent uniform stress q c, which when distributed uniformly over the projected area of the cone balances the vertical load on it. Wroth (1984, 1988) suggested that penetrometer data should be normalized with respect to the effective vertical stress in the soil at the level of the cone. In the present analysis, the reference stress is taken as the mean normal stress p [Eqn (1)]. The values of p for the boundary conditions encountered in the present investigation are discussed in Section 4.1 In the present context, the normalized cone resistance Q is given by the following expression: Q ¼ q c p p 3.2. Experimental connection between the normalized cone resistance and the state parameter From their experimental work on cone resistance measurements in sands, Been et al. (1986, 1987) have established the exponential relationship between the state parameter c of the sand in the neighbourhood of the cone to normalized cone resistance Q by the ð4þ following relationship: ln Q ¼ ln Q 0 mc ð5þ The coefficients Q 0 and m in Eqn (5) depend on the volume change characteristic of the sand. Been et al. (1986, 1987) have shown that for sand these coefficients are functions of the slope l of the critical state line m ¼ m 0 ln l ð6þ Q 0 ¼ C 1 þ C 2 ð7þ ðl C 3 Þ where m 0, C 1, C 2 and C 3 are coefficients unique to a particular soil. 4. Parameters required for interpreting bulk densityfrom cone resistance The object of the current investigation is to establish a connection between the current specific volume v of the soil, in which the penetrometer is embedded, to its cone resistance q c and the moisture content w of the soil. Equations (2) (5) contain the necessary information for establishing this correlation. Eliminating Q and v c from these expressions gives v ¼ðG lln pþ 1 m ln ðq c pþ ð8þ Q 0 p It is clear from Eqn (8) that, to evaluate v from measured values of q c, a knowledge of the parameters p, Q 0, m, G and l for the soil, at its existing moisture content w, are required. A brief outline of the significance of these parameters in the present investigation is set out below and their experimental evaluation is discussed in Sections 6 and 7. It is interesting to note that the second term in Eqn (8) is a function of penetrometer data only and represents the amount by which the specific volume v c at critical state has to be modified to predict the in situ specific volume from measured cone penetration data The ambient total normal stress Under field conditions, this stress can be approximated by assuming that the stress s V0, acting on horizontal planes at the embedment depth z of the cone, is the geostatic stress gz, where g is the unit weight of the moist soil. The corresponding stress s H acting on vertical planes at this depth is K 0 s V, where K 0 is the coefficient of earth pressure at rest [ (1 sin j)]. Substituting these values in Eqn (1) gives: p ¼ gz ð1 þ 2K 0Þ ð9þ 3

5 CONE PENETRATION TESTS 473 Under controlled laboratory conditions, for example in the triaxial cell and the calibration chamber discussed in Section 6, this parameter is obtained from the axial stress s a applied to the sample end platens and the cell pressure p 0 which becomes the confining stress s c. Substituting in Eqn (1): p ¼ ðs a þ 2s c Þ ð10þ 3 The tacit assumption in both Eqns (9) and (10) is that the intermediate principal stress s 2 is equal to the minor principal stress s 3. For purely hydrostatic loading s a = s c = p 0 and hence p = p Intercept and slope of the state parameter-penetrometer (SPP) function The state parameter coefficients of the cone penetrometer probing the soil at different moisture contents w have to be evaluated under laboratory conditions. Ideally, this requires a very large calibration chamber. In the present investigation, a less than ideal test procedure had to be employed where a specially adapted standard large diameter triaxial test apparatus was used in conjunction with a miniature penetrometer Intercept and slope of the critical state line These parameters have to be evaluated from carefully conducted triaxial compression tests on desaturated remoulded soil samples at different moisture contents. Details of these tests are set out in Section Strategyfor interpreting cone penetrometer data 5.1. Calibration In this phase of the investigation, a cone penetrometer is used to probe a cylindrical soil mass, whose boundaries are subjected to carefully controlled stress levels s V and s H. Details of the calibration chamber used in this investigation are given elsewhere (Abedin, 1995) and a brief description of the equipment used is set out in Section 6. The stages in the analysis are set out diagrammatically in Fig. 2. The pre-determined current specific volume v of the sample is set by isotropically consolidating the soil loaded into the chamber at specific volume v 0 by increasing the cell pressure to the pre-compression pressure p n. The sample is allowed to swell back to the chosen stress level p by reducing the cell pressure to p and thereafter held constant at this value. Because the sample is subjected to isotropic confinement at the boundaries, the ambient mean normal total stress given by Eqn (10) for s c = s a is simply the cell pressure p 0. The penetrometer is then advanced into the sample and the cone resistance q c measured. The normalized cone resistance Q is calculated from Eqn (4) at the value of p set in the procedure described above. The value of v c at the selected level of p is obtained from Eqn (3), where the critical state parameters l and G have been independently obtained from separate triaxial compression tests. The relevant state parameter c can then be estimated from Eqn (2). This yields companion pairs of values of Q and c for the soil at each selected moisture content w. The procedure is repeated for a series of initial specific volume settings and the pairs of values of Q and c thus obtained are used to evaluate the state parameter coefficients Q 0 and m in Eqn (5). This estimation has to be repeated to cover the entire range of moisture contents selected Interpretation The data gathered in the calibration process outlined in the previous section can now be employed to predict the specific volume of a partly saturated soil from cone resistance. The main steps involved are set out diagrammatically in Fig. 3. The cone resistance q c is measured at a known depth of penetration z. This represents the field use of the penetrometer. The ambient mean normal stress p in the zone occupied by the cone at its current depth z is estimated from Eqn (9) and the normalized cone resistance Q is obtained from Eqn (4). The state parameter c of the soil is calculated from Eqn (5). The coefficients Q 0 and m used in this estimation must match the moisture content of the soil under test. This information is obtained from the calibration procedure outlined in Section 5.1 All the independent variables in Eqn (8) are known and hence the specific volume v can be estimated. The bulk density of the soil can then be calculated from known values of moisture content w and the specific gravity of the mineral particles. 6. Calibration chamber 6.1. Apparatus and experimental procedure The calibration chamber used in the experimental work was a specially adapted standard triaxial compression testing machine taking 100 mm diameter by 185 mm specimens. The top loading platen of the machine was

6 474 M.Z. ABEDIN; D.R.P. HETTIARATCHI Fig. 2. Diagrammatic representation of steps (1) (5) in the calibration procedure; left, calibration chamber; centre, critical state data; right, derivation of the SPP function; CSL, critical state line; ICL, isotropic compression line; p, mean normal stress; q c, cone penetration resistance; Q, normalized cone resistance; v, specific volume; Q 0 and m, intercept and slope of the SPP function; s H and s V, stresses on vertical and horizontal planes, respectively; c, state parameter Fig. 3. Diagrammatic representation of the basic steps (1) (6) in the interpretation procedure: left, soil tank (or field) measurement of the cone penetration resistance q c ; centre, use of SPP function to evaluate the state parameter c: right, interpretation of soil specific volume v from critical state data; CSL, critical state line; ICL isotropic compression line; p, mean normal stress; Q, normalized cone resistance; v, specific volume; K 0, coefficient of earth pressure at rest; g, bulk unit density of soil; z, embedment depth; subscript 1 indicates test value of parameter drilled to accommodate the shaft of a miniature 10 mm diameter cone penetrometer. The diameter ratio of this combination of penetrometer and sample is 10. This is clearly less than the recommended value of for dense soil (Parkin & Lunne, 1982). The laboratory facilities available precluded the use of larger specimens to meet this requirement. However, the disadvantage of this size limitation is somewhat compensated for by the

7 CONE PENETRATION TESTS 475 fact that more uniform and repeatable initial density and moisture content values can be set up with confidence in samples of the size used in the present experiments. A remoulded soil sample was set up at a predetermined initial density and moisture content and then compressed isotropically to 250 kpa. Cell pressure was then relaxed to the desired value of p and held constant whilst the penetrometer was advanced into the sample at a rate of mm s 1. Cone resistance, sample volume change and depth of penetration were continuously recorded over the full 55 mm penetration depth. A total of six penetration tests were conducted at cell pressures of 25, 50, 100, 150, 200 and 250 kpa for each moisture content. Three replications were made at each of six selected soil moisture contents Results The experimental data obtained from the calibration chamber tests provide pairs of values of Q and c. A loglinear plot of these values is shown in Fig. 4 and the coefficients Q 0 and m in Eqn (5) derived from this data are tabulated in Table 1. The graphs in Fig. 4 show good linearity for the soil at moisture contents ranging fron 7 to 22%. These figures show that the coefficients Q 0 and m vary in a systematic manner with moisture content w. Table 1 Cone resistance and state parameter coefficients in Eqn (5) Moisture content (w),% 7. Triaxial compression tests 7.1. Experimental work Intercept (Q 0 ), kpa Slope, m The critical state parameters l, G and M of the soil at various moisture contents were measured on a standard triaxial compression testing machine taking 38 mm diameter by 81 mm samples. Axial compression load, platen displacement and sample volume change were monitored continuously during each drained tests. The cell pressure was maintained at the selected value throughout each run. The experimental procedure employed generally followed the steps set out for consolidated drained tests (Head, 1986). The sample was initially set up at known initial density and moisture A B ln Q 5 6 C 4 D E State parameter Ψ Fig. 4. Summary of experimental results for the normalized cone resistance (Q) in calibration chamber experiments; moisture content w: A, 7%; B, 11%; C, 15%; D, 18%; E, 22%

8 476 M.Z. ABEDIN; D.R.P. HETTIARATCHI Table 2 Critical state parameters for Ryton sand [Eqn (3)] Moisture content (w), % Slope on v ln(p) plane (l) Intercept (G), kpa Slope on q-p plane (M) v, specific volume; p, mean normal stress; q, deviatoric stress. content, then consolidated isotropically to 250 kpa and allowed to swell to the required cell pressure before shearing. Six cell pressures were used at each moisture content. The highest degree of saturation used was well below the expected quasi-saturation limit S c of this soil and pore fluid was not observed in the drainage line during all the tests Results The values of the critical state parameters obtained from the extensive programme of triaxial compression testing on this particular soil (see Section 9) are summarized in Table 2. The slope M in the relation q=mp, where q is the principal stress difference, is also given in the table. It will be seen that all three parameters vary in an ordered manner with moisture content. 8. Cone penetration tests The performance of the state parameter model, as applied to a standard penetrometer, was checked under carefully controlled conditions in an indoor soil tank, 6 m long, and filled to a depth of 400 mm with the same soil used in the laboratory experiments. An instrumented penetrometer having interchangeable cones, with 30 and 608 apical angles, was attached to the vertical motion carriage of the test facility. This carriage, which can translate the full length of the tank, was used to advance the penetrometer vertically into the soil at different points along the tank. Unfortunately, the minimum lowering speed of the vertical motion carriage was in excess of the penetration rate used in the calibration chamber. An independent check was therefore carried out to assess the effect of the rate of loading on cone resistance in this unsaturated soil. No significant effect on cone resistance due to the higher loading rates was observed. Cone resistance and depth readings were recorded at 500 mm horizontal intervals along the soil tank. The tank was prepared for each run by excavating the soil and re-constituting its entire contents according to a strict routine. The process involves the sequential use of a plate vibrator and skim and levelling blades. The moisture content and bulk density were monitored before each run and these were maintained at 17.5% and 1.2 Mg m 3 respectively. 9. Particulars of the soil used The soil used in soil tank and all the experimental work was a sandy loam obtained from the Tyne valley at Ryton (65.2% sand, 14.5% silt, 20.3% clay). The cone penetrometer plastic limit of the soil was 18% and its liquid limit was 33%. The laboratory experiments were carried out at moisture contents of 7, 11, 15, 18 and 22%. The highest moisture content was well below the quasi-saturation limit of S c 0.8 as discussed in Section Interpretation of penetrometer readings Quantifying experimental values The values of the critical state parameters l, G and SPP coefficients m and Q 0 appearing as independent variables in Eqn (8) are all functions of a particular soil and its moisture content w. Their variations with moisture content for Ryton sand have been established experimentally and were shown to be continuous functions of w. Of the remaining pair of variables, q c is the measured cone resistance in the field and is therefore the known input variable. The magnitude of the remaining stress level parameter p is a function of the depth of penetration z of the cone. However, as discussed in Section 4.1 and as set out in Eqn (9), p is a function of the critical state angle of internal friction j and the in situ bulk density g of the soil. The variation of

9 CONE PENETRATION TESTS z = 200 mm A B Cone resistance q c, MPa 1.0 C D E Dry density, Mg m -3 Fig. 5. Typical interpretation chart for embedment depth z of 200 mm; moisture content w: A, 7%; B, 11%; C, 15%; D, 18%; E, 22%. Broken line indicates a typical prediction of dry density from known cone resistance in a soil at 18% moisture content. Interpolate linearly for intermediate moisture contents 1. 6 Dry density, Mg m Penetration depth z, mm Fig. 6. Experimental validation of prediction procedure (soil tank experiments). Predicted values: *, 608Cone; *, 308Cone. Sampled value in tank, m j (and hence K 0 ) with w can be deduced from the critical state parameter M given in Table 2 from the following expression: j ¼ sin 1 3M ð11þ 6 þ M A difficulty arises with regard to g in that it is, in turn, a function of the specific volume v, which is the dependent variable in Eqn (8) that is to be determined. For a rigorous solution an iterative solution is required, where an initial trial value of g is specified and improved on in subsequent iterations. In the present context, a single step solution is presented with an estimated value for g. In order to prepare a general solution to Eqn (8), it is necessary to quantify the variation of the independent variables with moisture content. As these are all continuous functions of w, a NAG FORTRAN Library subroutine was employed to fit a fourth degree polynomial to the relevant variables.

10 478 M.Z. ABEDIN; D.R.P. HETTIARATCHI Solution charts The proposed interpretation requires a prediction of v (or the dry unit weight of soil g d ) from measured values of q c and known moisture content w and cone penetration depth z together with an initial guess of g. Because a single graph can display only three variables, two of the above variables have to be fixed in presenting a solution in the form of a chart. Fig. 5 shows a solution chart for a fixed penetration depth of 200 mm and initial g d =1.2 Mg m 3. The ordinate represents the measured cone resistance q c, the abscissa the required in situ density g d, and the solution curves of the chart are presented for a range of moisture contents w. Other combinations are feasible. The alternative to the use of a chart is a self-contained computer programe or spreadsheet Validation The above solution technique, embodied in a FOR- TRAN program, was employed to interpret the cone penetrometer readings obtained in the soil tank experiment described in Section 8. The results are summarized in Fig. 6. The predicted densities are consistently low, but generally follow the trend with increasing penetration depth. Unexpectedly, the error is greatest with the 308cone, whose apical angle is identical to the calibration chamber penetrometer. 11. Conclusions (1) The log-linear relationship between the state parameter c of the soil and the normalized cone resistance Q holds good for a partly saturated sandy loam soil. It is not unreasonable to expect the relationship to hold good for most light agricultural soils (2) The coefficients for the intercept Q 0 and slope m of the state parameter-penetrometer function governing (1) above show a systematic variation over a wide range of moisture contents of the soil. Mathematical relationships of these coefficients as a function of moisture content can therefore be established for a given soil. If these coefficients show only minor variations over a given range of soil types, then the concept could prove to be a powerful tool in generalizing the interpretation of penetrometer tests. (3) A small-scale calibration chamber using a scaleddown penetrometer can be used successfully to evaluate the coefficients Q 0 and m. (4) With a knowledge of the critical state parameters, it is possible to use the penetrometer-state paramater function to predict the specific volume v of the soil from known penetrometer resistance q c and embedment depth z. The experimental validation carried out under controlled conditions was encouraging, but the accuracy was not particularly good. Improvements may be possible with the introduction of an iterative solution in place of the single step solution presented here. (5) The work described in the present investigation demonstrates that the background work required to develop the proposed interpretation procedure is excessively tedious and extremely time consuming. This may detract from the proposed procedure becoming a practical tool. (6) The investigation concentrated on a single sandy soil. There is no evidence at present to show that the procedure will work in clay soils. If the procedure can be generalized for both sands and clays, then much of the background data gathered from tedious experimental work can be a once and for all estimation which can be used in a data bank. References Abedin M Z (1995). The characterization of unsaturated soil behaviour from penetrometer performance and the critical state concept. PhD Thesis, The University of Newcastle upon Tyne, UK. Been K; Jefferies M G (1985). A state parameter of sands. G!eotechnique, 35(2), Been K; Crooks J H A; Becker D E; Jefferies M G (1986). The cone penetration test in sands: part I, state parameter interpretation. G!eotechnique, 36(2), Been K; Jefferies M G; Crooks J H A; Rothenburg L (1987). The cone penetration test in sands: part II, general inference of state. G!eotechnique, 37(3), Gerogiannopoulos N G; Brown E T (1978). The critical state concept applied to rock. International Journal of Rock Mechanics, Mining Science & Geomechanics Abstracts, 15, 1 10 Head K H (1986). Manual of Soil Laboratory Testing. Pentech Press, London, Plymouth Hettiaratchi D R P (1987). A critical state soil mechanics model for agricultural soils. Soil Use and Management, 3, Hettiaratchi D R P; Abbedin M Z (1994). Computer simulation of the mechanical behaviour of partly saturated soils. In: Proceedings 13th International Conference ISTRO, Vol. 1, Aalborg, Denmark, pp Parkin A M; Lunne T (1982). Boundary effects in the laboratory calibration of a cone penetrometer in sand. In: Proceedings, 2nd European Symposium on Penetration Testing, ESOPT-II, Vol. 2, Amsterdam, pp

11 CONE PENETRATION TESTS 479 Roscoe K H; Schofield A N; Wroth C P (1958). On the yielding of soils. G!eotechnique, 8(1), Schofield A; Wroth P (1968). Critical State Soil Mechanics. McGraw-Hill, London Wheeler S J; Sivakumar V (1993). Development and application of a critical state model for unsaturated soil. Wroth Memorial Symposium on Predictive Soil Mechanics, Oxford Wroth C P (1984). The interpretation of in situ soil tests. 24th Rankine Lecture. G!eotechnique, 34(4), Wroth C P (1988). Penetration testing}a more rigorous approach to interpretation. Proceedings of the International Symposium on Penetration Testing ISOPT-I, Vol. 1. Orlando, pp