An experimental investigation of the mechanical behaviour of an unsaturated gneiss residual soil

Transcription

1 Futai, M. M. & Almeida, M. S. S. (25). Géotechnique 55, No. 3, An experimental investigation of the mechanical behaviour of an unsaturated gneiss residual soil M. M. FUTAI* and M. S. S. ALMEIDA The paper presents compression and triaxial tests conducted under controlled suction in horizons B and C of a residual soil gneissic rock profile from south-east Brazil. Horizon B, found at the surface, consists of a 2 m thick reddish lateritic clayey soil layer, whereas horizon C is a saprolitic soil layer that reaches great depths. The block samples representing horizons B and C were manually taken from depths of and respectively. The test programme carried out consisted of isotropic and anisotropic compression tests as well as drained and constant water content triaxial tests. Tests were performed under saturated and unsaturated conditions at controlled suction. Strength parameters c and ö were shown to increase with matric suction. The critical state parameters were shown to vary with suction, which also expanded the yield curve. Data obtained may be useful for the development of soil constitutive models for unsaturated soils. KEYWORDS: compressibility; laboratory tests; residual soils; shear strength; suction Cet exposé présente des essais de compression et triaxiaux conduits sous une succion contrôlée dans les horizons B et C d un profil rocheux gneissique d un sol résiduel dans le sud-est du Brésil. L horizon B, trouvé à la surface, consiste en une couche de sol argileux latéritique rougeâtre de 2 mètres d épaisseur alors que l horizon C est une couche de sol saprolitique qui atteint de grandes profondeurs. Le blocs échantillons représentant les horizons A et B ont été prélevés manuellement à des profondeurs de et de respectivement. Le programme d essais effectué était constitué d essais de compression isotrope et anisotrope ainsi que d essais triaxiaux drainés et à teneur en eau constante. Les essais ont été effectués dans des conditions saturée et non saturée à une succion contrôlée. Les paramètres de résistance c et ö ont augmenté en fonction de l aspiration matricielle. Les paramètres d état critique ont varié en fonction de la succion, ce qui a également fait s étendre la courbe d écoulement. Les données obtenues peuvent être utiles pour le développement de modèles constitutifs pour des sols non saturés. INTRODUCTION Unsaturated soils may be divided into two categories: natural intact soils and compacted soils. Studies carried out on unsaturated soils are usually based on laboratory tests performed on compacted and reconstituted soils (Alonso et al., 1987; Maâtouk et al., 1995; Wheeler & Sivakumar, 1995; Cui & Delage, 1996; Rampino et al., 1999; Leroueil & Barbosa, 2; Blatz & Graham, 23). The behaviour of compacted and reconstituted soils may, however, be different from the behaviour of natural soils owing to different structures. Tropical unsaturated soils, in particular, have been studied less than soils from temperate climates. However, interest in the development of constitutive models for these soils has increased recently (e.g. Futai et al., 1999; Futai, 22; Machado et al., 22; Toll & Ong, 23). This paper presents the results of laboratory studies carried out on a natural intact unsaturated tropical soil. It is a residual soil from gneissic rock found near the city of Ouro Preto, south-east Brazil, where erosion is widespread and reaches large depths. This soil was recently studied by Futai (22) to improve understanding of the erosion mechanisms. Some of these experimental studies, comprising compression and triaxial tests conducted under controlled suction, are reported herein. Critical state and yield conditions, not usually investigated in tropical soils, were determined and may be implemented in constitutive models. Manuscript received 8 January 24; revised manuscript accepted 18 October 24. Discussion on this paper closes on 3 October 25, for further details see p. ii. * Polytechnical School, University of São Paulo, Brazil. COPPE, Graduate School of Engineering, Federal University of Rio de Janeiro, Brazil. SITE CHARACTERISATION The tropical profile studied is composed of a reddish toplateritic soil layer (horizon B) about 2 m thick, followed by a saprolitic soil (horizon C), which may reach depths up to 4 m. The water level is at about 2 m depth. The present study concentrates on the top 7 m, in which block samples were manually taken at spacing. Samples of a nearby saprolitic soil slope exposed to erosion were also tested and compared with the intact saprolitic soil. Compression and strength tests under unsaturated conditions were performed in samples from and depths. Results of index tests and mineralogy data are summarised in Fig. 1. The amount of clay is greater in horizon B, and grain size analyses without deflocculant have revealed that all the clay is flocculated. Gravimetric water content is in the range 28 46%, between the liquid and plastic limits. The liquid and plastic limits (w L, w P ) and the void ratio (e) decrease with depth. The degree of saturation, S r, during sampling was in the range 8 96%, but in a drier season S r values were at a lower range: 4 7%. The mineralogical composition of the soil, shown in Fig. 1, was identified using various tests: X-ray diffraction, thermodifferential and thermogravimetric tests, and total and selective chemical analyses. Kaolinite is the predominant clay mineral, which is consistent with the cation exchange capacity, lower than 8 meq/1 g. Kaolinite was found in both clay and silt fractions. The amount of quartz is approximately constant with depth, which is in accordance with the relatively constant proportion of sand with depth. Gibbsite is found predominantly at shallow depths (horizon B). The values of the specific gravity of the soil grains (G s ) in horizons B and C were and respectively, which may be attributed to the different mineralogical composition of the two horizons. The pore-size distribution has been investigated by means 21

2 22 FUTAI AND ALMEIDA 1 2 B horizon Clayey sand Water content: % ã nat : kn/m 3 Void ratio Grain size: % Mineralogical content: % w P w nat w L I P 5 29% 22 Clay Sand Gibbsite Amorphous/Fe Depth: m C horizon Saprolitic soil Sandy silt Silt Kaolinite Quartz Other Exposed saprolitic soil Fig. 1. Index tests data and soil mineralogy (Futai et al., 24) of scanning electron microscopy (SEM) and mercury intrusion porosimetry (MIP). These studies were performed on oven-dried specimens. SEM studies for the deep and deep soils are shown in Fig. 2. The particles of the deep soil (Fig. 2) appear to be aggregated, and large pores may be observed, although the clay minerals are not clearly observed. SEM for the deep soil (Fig. 2) showed voids and large parallel plates of kaolin. Porosimetry measurements using the mercury intrusion technique are shown in Fig. 3, for cumulative (Fig. 3) and incremental inclusion (Fig. 3). The soil at depth presented a clear bimodal distribution of pores, with macro pores in the range 1 1 ìm and micro pores lower than. 1 ìm. The soil at depth presented just macro pores higher than 2 ìm, but concentrated in the ranges 2 1 ìm and 3 3 ìm. Porosimetry measurements appear to confirm the results of the grain size analysis: that is, horizon B possesses smaller pores and higher clay content than horizon C. The overall analysis of grain size, soil microscopy and porosimetry suggests a meta-stable structure for the horizon B soil comprising micro and macro pores. A good correlation between SEM and MIP has also been observed by Simms & Yanful (24) for a compacted soil with bimodal pore-size distribution. Figure 4 compares the retention curves of horizons B and C, measured using the suction plate for suction lower than 1 kpa and the filter paper technique (Chandler & Gutierrez, 1986) for higher suction. Curves are presented for both volumetric water content against matric suction (Fig. 4) and degree of saturation against matric suction (Fig. 4). The differences between the two soils regarding grain size distribution, mineralogical composition and microstructure directly influence the water retention capacity. The volumetric strains measured during the tests were about 12% and 6% respectively for the and deep specimens. The air entry values in both the and soils are ìm ìm ìm 1 ìm Fig. 2. Scanning electron microscopy of deep and deep soils

3 35 3 MECHANICAL BEHAVIOUR OF AN UNSATURATED GNEISS RESIDUAL SOIL 23 6 Cumulative intrustion: ml/g Volumetric water content: % Incremental intrustion: ml/g Diameter: ìm Degree of saturation: % Suction, Diameter: ìm 5 Fig. 3. Pore size distribution: cumulative intrusion; incremental intrusion low, about 1 kpa and 5 kpa (Fig. 4) respectively, and may be explained by the macro pores observed in both soils (Fig. 3). The deep soil showed a sudden decrease in water content following 1 kpa suction as the macro pores desaturated and the suction reached 1 kpa. For the suction range 1 3 kpa a small decrease in water content with increase in suction was observed, which may be attributed to the deficiency of pores in the range.1 1 ìm (Fig. 3). The water content experiences another major decrease for suction higher than 3 kpa, which appears to be associated with desaturation of the micro pores. The bimodal retention curve presented by the deep soil is typical of tropical highly weathered soils (Carvalho & Leroueil, 2) containing aggregated particles uncemented or cemented by iron oxides linked by clay bridges. According to the same authors, these soils have two air entry points, corresponding to macro and micro pores. The deep soil presented a retention curve with two slopes but no plateau, which appears to be consistent with the two ranges of macro pores 2 1 ìm and 3 3 ìm (Fig. 3) Suction, Fig. 4. Soil water retention curves: volumetric water content; degree of saturation CONSTANT SUCTION TESTS Equipment and methods The equipment used for the tests reported herein included servo-controlled water pressure and air pressure devices, an electromechanically controlled press, and a data logger with filters and amplifiers, all placed in a temperature-controlled room (28C 18C). Instrumentation consisted of internal load cells, pore pressure transducers and external displacement transducers. Suction was controlled using the axistranslation technique (Bishop & Donald, 1961) with high air-entry ceramic porous discs (5 and 15 bar) installed at the base of the triaxial cell. The volume change of the specimens was controlled by means of measurements of the change in volume of the triaxial cell using a rolling diaphragm automatic volume change device. Air pressure

4 24 FUTAI AND ALMEIDA was applied at the top of the cell and water pressure was applied at the base of the cell, also controlled using another automatic volume change device. All the equipment was controlled by a computer. Suction-controlled isotropic and anisotropic compression tests and triaxial tests were carried out on specimens located at depths and respectively corresponding to the lateritic (horizon B) and saprolitic soil (horizon C). Isotropic compression tests were conducted at constant values of matric suction equal to 1 kpa, 3 kpa and 5 kpa. The values of constant suction adopted in the triaxial tests were 1 kpa and 3 kpa. Compression and triaxial tests were also carried out for two extreme conditions: saturated specimens and air-dried specimens. Initial suction values, s, measured with the filter paper technique for air-dried specimens from depth were in the range 6 9 MPa. The initial gravimetric water content, w, was in the range 3 5%. Values of s measured for the sample at depth were in the range 25 3 MPa with w in the range 4 6%. The values of the suction measured at the end of the tests with the filter paper technique were in the range MPa. Stabilisation of the applied constant suction The procedure adopted for suction control in the specimens (Futai, 22) consists of three steps. In the first step, specimens were left wet, or drying, in airtight boxes and suction was measured using the filter paper technique. The water content of each specimen was controlled by the previous determination of the initial water content and the subsequent control of the weight. The table in Fig. 5 presents data for step 1. In the second step, pressure was applied inside equalisation cells, at the top, and water was drained at the base, the sample volume being controlled by burettes connected to the base of the cell. Fig. 5 shows the data for step 2, in which positive volume corresponds to water drained from the specimen. It is seen that stabilisation in step 2 was achieved in less than 2 h. In the third step, the specimen was transferred to the triaxial cell, and a final verification of the equilibrium of the volume change was made. Times varying between 2 and 6 h were necessary for the start of the test, as shown in Fig. 5. Isotropic and anisotropic compression tests Isotropic compression tests under constant suction were carried out by increasing the mean net stress p, where p ¼ (ó 1 +2ó 3 )/3 and is the constant air pressure. Fig. 6 shows the compression curves of the (Fig. 6, ) and deep (Fig. 6(c), (d)) specimens for three given values of suction (, 1, 3 kpa), together with that of the saturated and air-dried specimens (drained to the air). As shown in the plots of void ratio against p (Figs 6 and 6(c)), specimens had different initial void ratios owing to the intrinsic heterogeneity of the natural soil, but also to contraction during drying, which was a function of the applied suction. Thus the same data have been plotted in terms of e/e against p, where e is the change in void ratio during the test and e is the initial void ratio. This plot isolates the influence of suction on the compressive behaviour. Table 1 presents the compressibility parameters of specimens located at and depths in terms of specific volume v ¼ 1+e. N(s) and º(s) in Table 1 are the standard critical state parameters of the virgin isotropic compression line defined by v ¼ NðÞ s º ðþln s ðp Þ (1) Drained water volume: cm 3 Drained water volume: cm Depth: m Depth: m Suction: kpa Suction: kpa ó 3 2 : kpa ó 3 2 : kpa w after 1st equalisation: % w after 2nd equalisation: % Time: min The other parameters presented in Table 1 are k(s), the slope of the recompression line, and p (s), the yield stress determined by the Casagrande construction. Data for tests on saturated and unsaturated specimens (s ¼ 5 kpa), presented in Fig. 7, show that, below yield, the compression strain of the deep specimen is greater than that of the deep specimen. However, once yield has been reached, the deep specimen is stiffer, as shown by the smaller values of º(s) presented in Table 1. Isotropic yield stresses p (s) against suction for the and deep specimens are shown in Fig. 8. Values of p (s) at each depth define the load collapse yield curve, LC (Alonso et al., 199), as shown in Fig. 8. A number of multistage isotropic compression tests have been carried out (Futai, 22) with the purpose of probing the ( u w ) (p ) space. These tests, not shown here for lack of space, confirm the LC curves, inside which the soil behaves in a pseudoelastic fashion. The pseudoelastic region of the specimen at depth is smaller than that of the deep specimens. However, at very high suction (air-dried specimens) the pseudoelastic region of the specimens is larger, as shown in Table 1. This can be explained by the structure of the soil, which enables it to retain larger suctions, as also shown by the data of the retention curves (Fig. 4). The compression index, º(s), and recompression index, k(s), shown in Table 1 are plotted against suction in Fig. 9. Values of º(s) increase with suction, and the curves appear to converge at higher net stresses. An increase in º(s) with w : % w after drying: % w after equalisation: % Time: h Fig. 5. Stabilisation of suction applied to specimens

5 1 3 MECHANICAL BEHAVIOUR OF AN UNSATURATED GNEISS RESIDUAL SOIL Void ratio, e Void ratio, e ( ) 5 1 kpa ( ) 5 3 kpa 6 ( ) 5 1 kpa ( ) 5 3 kpa ( ) 5 5 kpa (c) 1 1 Äe/e 2 Äe/e ( ) 5 1 kpa ( ) 5 3 kpa ( ) 5 1 kpa ( ) 5 3 kpa ( ) 5 5 kpa (d) Fig. 6. Isotropic compression curves under different constant suction values for specimens from, 1. m and (c), (d) 5.m depths Table 1. Compressibility parameters: isotropic compression Depth: m Suction e k:s º: s N: s p (s) increased suction (Fig. 9) has been observed by Araki & Carvalho (1995), Wheeler & Sivakumar (1995), Futai (1997), Machado & Vilar (1997) and Chiu & Ng (23), but the opposite behaviour has also been observed (Alonso et al., 199; Maâtouk et al., 1995); most of these studies were for the same limited range of suction tested here. Values of k(s) (Fig. 9), are greater for the 5. m deep specimens, which also show a greater decrease with increase in suction, s. Data for k(s) against suction for natural soils are scarce in the literature.

6 26 FUTAI AND ALMEIDA Void ratio, e 9 Void ratio, e (c) Äe/e 2 Äe/e (d) Fig. 7. Isotropic compression curves for 1. m and 5. m specimens:, saturated; (c), (d) 5 kpa The deep specimens were also subjected to anisotropic tests (K ¼ ó 3 /ó 1 ¼. 75). Data for the yield conditions, summarised in Table 2, will be subsequently used for the definition of the yield curve of the soil. Anisotropic tests were not performed for the specimen, as the yield curve obtained for saturated conditions (Futai, 22) was shown to be isotropic in the p q plot. Triaxial shear tests Consolidated drained triaxial tests (CID) (air and pore water drainage allowed) were carried out under two values of controlled suction: s ¼ 1 kpa and s ¼ 3 kpa. Constant water content triaxial tests, (CW) (Fredlund & Rahardjo, 1993), with air drained and no water drained have also been performed on air-dried specimens with the purpose of obtaining the strength data under maximum soil suction. Suction was not measured in CW tests in air-dried specimens, as suction values were quite high, in the range 25 9 MPa. Five isotropic consolidation stresses p were used to obtain the strength envelope at each constant suction. The strain rate used in the tests was.m/min. Triaxial tests under saturated conditions have also been performed, the data for which have already been presented elsewhere (Futai et al., 24a). The results of the CID and CW tests are shown in Fig. 1 for specimens extracted at 1. m depth. Dilatant behaviour is noticed for the CID tests (Figs 1, (d)) at values of p ¼ 25 kpa, in which the peak deviator stress is achieved at relatively small axial strains (4 7%). Under saturated conditions the soil did not present any dilation, even under low stresses (Futai et al., 24a). It is seen in Fig. 1 that the soil behaviour changes from dilation to compression with increase of confining stress (p ), which also increases the axial strain at peak. For some tests performed at high values of p the peak is not achieved, even at the final axial strain of about 25% (Fig. 1, (c)). For the air-dried soil (CW tests; Fig. 1(e), (f)) dilatant behaviour is noticed

7 8 6 MECHANICAL BEHAVIOUR OF AN UNSATURATED GNEISS RESIDUAL SOIL Suction, 4 ë(s) Fig. 8. Yield stresses p against suction load collapse curve for 1. m and 5. m specimens Suction, 5 even for high values of p. Results of CID and CW tests are shown in Fig. 11 for specimens extracted at 5.m depth. The behaviour differs slightly from that of specimens located at depth. As for the CID tests (Fig. 11 (d)), dilation is noticed at larger values of p, and the peak deviator stress is better defined. However, for the air-dried soil (CW tests, Fig. 11(e), (f)) specimens located at and depths have similar behaviour. k(s) TEST DISCUSSION AND INTERPRETATION Strength envelopes The failure envelopes at peak deviator stresses are presented in Fig. 12 for: (i) the saturated samples (Futai et al., 24); (ii) two suction values, s ¼ 1 kpa and 3 kpa; and (iii) the air-dried condition. The failure envelopes of the and deep specimens (Fig. 12) are almost linear for each suction value. The effect of the suction increase on the failure envelopes may be seen in Fig. 12. For the deep soil the envelopes for s ¼ 1 kpa and 3 kpa are not so far apart, but they are higher than for the saturated specimens, and below that of the dried specimens. Values of cohesion intercept, c, and friction angle, ö, as a function of suction are shown in Fig. 13. It is noticeable that both c and ö increase with suction, although the latter does not increase so much in the range s ¼ 1 3 kpa for the deep specimen. The increase of the cohesion intercept c with suction is well known (e.g. Escário & Jucá, 1989), but the increase in ö with suction is less common. The apparent cohesion, c, of the specimens (Fig. 13) increases non-linearly up to the air-dried condition (c ¼ 125 kpa). The apparent cohesion for the deep specimens (Fig. 13) shows behaviour similar to that of the deep specimens until 3 kpa, but then stabilises. The variation of the friction angle with suction for the deep specimens (Fig. 13) is similar to the apparent cohesion (Fig. 13). The friction angle for the deep specimens increases almost linearly with suction (Fig. 13). The overall increase in strength for the deep specimens is not as great as for the deep specimens, which is consistent with the soil water retention curves (Fig. 4) Suction, Fig. 9. Variation of compression and recompression indexes with suction for 1. m and 5. m specimens Table 2. Yield stress, anisotropy compression: specimens Suction e Yield Critical state parameters Critical state conditions were determined by means of the triaxial test data presented above. Only the data close enough to the critical state conditions were considered. The critical state used is that defined by Roscoe et al. (1958): that is, no variation of deviator stress q, net stress p and volumetric strain at large strains. Table 3 presents a description of the shape of the specimens at the end of the triaxial tests. It is observed that for moderate suction (s ¼ 1 and 3 kpa) failure planes were, in general, formed at lower p y q y

8 28 FUTAI AND ALMEIDA Deviator stress, q kpa 5 kpa 1 kpa 2 kpa 4 kpa Deviator stress, q kpa 5 kpa 1 kpa 2 kpa 5 kpa Deviator stress, q kpa 1 kpa 2 kpa 4 kpa 6 kpa 8 kpa (c) (e) Volumetric strain 4 Volumetric strain 4 Volumetric strain (d) (f) Fig. 1. Constant suction triaxial tests performed on specimens:, 1 kpa; (c), (d) 3 kpa; (e), (f) air dried Deviator stress, q kpa 1 kpa 2 kpa 4 kpa 8 kpa Deviator stress, q kpa 1 kpa 2 kpa 4 kpa 8 kpa Deviator stress, q kpa 1 kpa 2 kpa 4 kpa 8 kpa (c) (e) Volumetric strain Volumetric strain Volumetric strain (d) (f) Fig. 11. Constant suction triaxial tests performed on specimens:, 1 kpa; (c), (d) 3 kpa; (e), (f) air dried

9 MECHANICAL BEHAVIOUR OF AN UNSATURATED GNEISS RESIDUAL SOIL kpa 5 3 kpa kpa 5 3 kpa Deviator stress, q kpa 15 1 Deviator stress, q kpa Fig. 12. Failure envelopes for different suction conditions: ; Apparent cohesion intercepts, c Peak friction angles: degrees Suction, Suction, Fig. 13. Cohesion intercept c and friction angle ö against suction for and specimens Table 3. Shape of specimens at end of tests Depth: m Suction, s: Shape of specimens at end of test kpa 1. Barrel shape for all values of p9 1 and 3 Failure plane just for 25 kpa; barrel shape for higher values of p Failure plane at all confining stresses p 5. Failure plane for confining stresses p9 <1 kpa; barrel shape for higher values of p9 1 and 3 Failure plane for confining stresses p < 2 kpa; barrel shape for higher values of p Failure plane for confining stresses p < 4 kpa; barrel shape for higher values of confining stresses. values of confining stresses p. At higher values of p barrel-shaped specimens were observed. However, airdried specimens developed failure planes for most of the confining stresses. The equation of the critical state line in the p q plane for unsaturated conditions can be given by (Toll, 199; Wheeler & Sivakumar, 1995) q ¼ ìðþþ s MðÞp s ð Þ (2) where the parameters ì(s) and M(s) vary with the matric

10 21 FUTAI AND ALMEIDA Table 4. Critical state parameters Depth: m Suction M(s) ì(s) e (ave) suction s as follows: ì(s) is the intercept of the critical state line with the q axis as a function of suction s; M(s) is the slope of the unsaturated critical state line as a function of suction s. The critical state lines (CSL) of the and deep specimens under different constant suctions are shown in Table 4 and Fig. 14. The CSL in the p q plane show that the suction has a greater influence on the slope M(s) than on the intercept ì(s). As the initial void ratios e of natural intact soils presented some scatter, the critical state line was defined in the plot of e/e against p plot, and subsequently converted into specific volume using the average value e (ave) (see Table 4). This was computed by averaging the values of e for all specimens following equalisation under the applied suctions. The CSL data in the plot of e/e against p (Fig. 14, (d)) show that the CSL in unsaturated conditions are not straight lines for the specimens at depth. Considering these uncommon and unclear features of the critical state line in the void ratio against the p plane, the critical state interpretation and parameter definition will be restricted here to the q: (p ) plane. The critical state parameters M(s) and ì(s) are shown in Table 4 and Fig. 15 for each suction. Values of M(s) present a monotonic increase with suction. Values of ì(s) also increase with suction, but then drop for very high suctions (air-dried condition). It was shown in Fig. 13 that for peak conditions the cohesion intercept kept increasing for higher suctions. However, as the soil gets stiffer under high suction values, values of ì(s) decrease for large-strain post-peak critical state conditions, where a fragile behaviour is achieved. Experimental data about critical state lines for unsaturated soils reported in the literature do not show a clear pattern of variation with suction. Critical state lines in the p q plane may show different types of behaviour, such as: M constant and ì(s) increasing with suction (Alonso et al., 199); M(s) decreasing and ì(s) increasing with suction (Maâtouk et al., 1995); or both M(s) and ì(s) increasing with suction (Wheeler & Sivakumar, 1995; Cui & Delage, 1996). Data for critical state lines in the p v plane presented in the literature show that critical state lines for different suctions converge as the net stress p increases kpa 5 3 kpa kpa 5 3 kpa Deviator stress, q 1 5 Deviator stress, q (c) Äe/e 2 Äe/e kpa 5 3 kpa kpa 5 3 kpa (d) Fig. 14. Critical state lines in (p 2 ): q and ( e/e ): (p 2 ) planes:, ; (c), (d) 5m

11 M(s) ì(s) Suction, MECHANICAL BEHAVIOUR OF AN UNSATURATED GNEISS RESIDUAL SOIL Suction, Fig. 15. Critical state parameters against suction for 1. m and 5. m specimens: M(s); ì(s) Yield and limit state The shape of the yield curves of natural clays has been studied by many authors (e.g. Tavenas & Leroueil, 1977; Graham et al., 1983; Smith et al., 1992). However, the shape of the yield curve of tropical soils is not yet well known, as limited data are available. Leroueil & Vaughan (199) suggested that residual soils and soft rocks may have yield curves centred on the hydrostatic axis. Futai et al. (24a), however, showed that the yield curves of tropical soils under saturated conditions may be isotropic or anisotropic with respect to the hydrostatic axis, depending on the degree of weathering, the nature of the mother rock, and diagenesis. The shape of the yield curve of unsaturated soils has also been investigated with respect to change in suction. Yield curves not centred on the hydrostatic axis have been obtained for compacted and artificially cemented soils (Maâtouk et al., 1995; Cui & Delage, 1996; Leroueil & Barbosa, 2). Machado et al. (22) obtained yield curves centred on the hydrostatic axis for a sandy shale residual soil, probably due to the isotropic characteristic of the mother rock. Yield curves were determined for saturated conditions, for suction values equal to 1 kpa and 3 kpa and in air-dried conditions. The yield curves are based on data from isotropic and anisotropic compression tests, and from CID triaxial tests. Yield points were determined following Graham et al. s (1988) suggestion to define the inflexion point in the deviator stress against axial strain space. The complete limit state curves also include failure data for specimens in the overconsolidated condition to provide data for low values of p in the limit state curve. Yield curves under different suctions of specimens of and depths are shown in Fig. 16. It can be seen that suction has a strong effect on the increase in size of the yield curves. The yield curves of the specimens (Fig. 16) appear to be isotropic, as previously observed in saturated specimens of the 2 m horizon B (Futai et al., 24). Machado et al. (22) also obtained isotropic yield curves for an intact sandstone residual soil collected at a depth of 8 m and subjected to suctions of s ¼, 1 and 2 kpa. These isotropic yield curves could be a consequence of the isotropic mother rock. The deep specimens presented anisotropic yield curves, as also observed (Futai et al., 24) in saturated specimens from other depths at horizon C. Yield curves of the deep specimens have similar shapes, and the top left part appears to be tangent to a single envelope. Cui & Delage (1996) obtained anisotropic yield curves of the same shape for a compacted silt soil, with suctions in the range 2 15 kpa. The yield curves obtained at the same suction of the and deep samples are compared in Fig. 17. The elastic region of the specimens is much larger than that of the specimens. This trend continues as suction increases up to s ¼ 3 kpa, although the difference in sizes of the elastic regions decreases. However, this pattern is inverted for very high suctions. This may be explained by the microporous formation of the horizon B soil, which consists basically of clay particles with aluminium and iron oxides, as SEM, mineralogical and porosimetry tests have shown. Thus as the deep soil dried it could no longer be broken with the fingers, and it behaved similarly to a porous ceramic brick. CONCLUSIONS A tropical residual soil from south-east Brazil derived from a gneissic rock has been studied to define the behaviour of the soils in horizons B and C under controlled suction. Intact block samples were collected at depths and from horizons B and C respectively, and were subjected to isotropic and anisotropic compression tests, CID triaxial tests under controlled suction, and constant water content triaxial tests. Isotropic compression tests for different suctions have indicated that the yield stress p9 ðþ s increases with suction. The slope of the virgin compression line º(s) increases with suction, within the limited suction range tested here, and the curves tend to converge for higher net applied stresses. Analysis of the strength envelopes evidenced an overall strength increase as matric suction increased. The cohesion intercept showed, for the specimen, a continuous increase with the increase in suction. The deep specimen showed just a small increase in cohesion up to a suction of 1 kpa. The internal links created by the larger amount of clay in the horizon B soil could be the reason for this difference. The triaxial data have also been interpreted using critical state concepts. An increase in the slope M(s) of the critical state line in the p q diagram with an increase in

12 212 FUTAI AND ALMEIDA kpa 5 1 kpa 5 3 kpa u 16 a 5 3 kpa 12 Deviator stress, q 12 8 Deviator stress, q Fig. 16. Yield curves under constant suction values: ; Deviator stress, q 3 2 Deviator stress, q Fig. 17. Comparison of yield curves of samples from and depths: saturated; air dried suction was noticed. The critical state lines in the plot of void ratio against p plot could not be clearly identified. The data obtained confirmed that suction has a strong effect on the expansion of the yield curves of the specimens studied. For moderate values of suction the elastic region of the deep soil is much greater than that of the 1.m deep specimen. For very high suctions the opposite is observed. This should be related to the different grain size, mineralogy and soil structure. Yield curves of the horizon B specimens appear to be isotropic, but anisotropic behaviour is clearly seen for the horizon C specimens. The material presented here provided a new database on natural soil, which may be useful for the development of further constitutive modelling. ACKNOWLEDGEMENTS The present study had the financial support of PRONEX and CNPq (Ministry of Science and Technology), FAPERJ (Rio de Janeiro Secretary of Science and Technology) and the FUJB Foundation (Federal University of Rio de Janeiro). The authors are indebted to Serge Leroueil for the critical review of the paper and to Orêncio Villar for the general comments presented. NOTATION c cohesion intercept e void ratio e void ratio following applied suction G s specific gravity of soil grains K anisotropic stress ratio ó 3 /ó 1 M(s) slope of unsaturated critical state line, in p q plane, as function of suction N(s) void ratio at p ¼ 1 kpa, the virgin isotropic compression line p ¼ (ó 1 +2ó 3 )/3 p9 ðþ s yield stress under isotropic compression s matric suction ¼ u w S r degree of saturation pore air pressure

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