In this paper, the stiffness of two materials with the same geological origin is presented, a silty sand, called
Perafita sand (D50=0.36mm) and a granite aggregate (0/12.5, D50=0.52mm). The stiffness in very small strains
( <10-5) of the compacted materials is studied by means of precision triaxial tests (with local strain measurements).
The influence of non-saturation on the stiffness is also studied through triaxial tests with measurement
of negative pore water pressures. Such measurements allow the analysis of the mechanical behaviour of the
unsaturated material in terms of effective stresses. For this purpose two approaches were used: the Terzaghi’s
and Bishop’s approaches. The results obtained show, for each material, a unique relationship between vertical
stiffness and vertical effective stress (constant void ratio = 0.5), independently of the saturation degree of the
studied samples.En este artículo se presenta la rigidez de dos materiales con el mismo origen geológico, una arena con limo,
llamada arena Perafita (D50=0.36mm) y un agregado granítico (0/12.5, D50=0.52mm). La rigidez para deformaciones
muy pequeñas ( <10-5) de los materiales compactados es estudiada mediante ensayos triaxiales de
precisión (con medidas locales de deformación). La influencia de la no-saturación en la rigidez se ha estudiado
también mediante ensayos triaxiales con medición de la presión negativa del agua en los poros. Estas medidas
permiten el análisis del comportamiento mecánico de materiales no saturados por lo que se refiere a tensiones
efectivas. Con este propósito fueron usados dos procedimientos: el de Terzaghi y el de Bishop. Los
resultados obtenidos revelan, para cada material, una relación única entre la rigidez vertical y la tensión efectiva
vertical (ratio de vacíos constante = 0.5), independientemente del grado de saturación de las muestras estudiadas

Correia, A. Gomes

Ferreira, Sandra Reis

Fleureau, Jean-Marie

Universidade do Minho: RepositoriUM

Influence of non-saturation and particle size distribution on the stiffness of granite materialsInfluencia de la no saturación y granulometría en la rigidez de materiales de naturaleza granítica A.Gomes Correia & S. M. Reis Ferreira, University of Minho, Guimarães, Portugal J-M. Fleureau    Ecole Centrale Paris & CNRS, Châtenay-Malabry, France RESUMEN En este artículo se presenta la rigidez de dos materiales con el mismo origen geológico, una arena con limo, llamada arena Perafita (D50=0.36mm) y un agregado granítico (0/12.5, D50=0.52mm). La rigidez para defor-maciones muy pequeñas ( <10-5) de los materiales compactados es estudiada mediante ensayos triaxiales deprecisión (con medidas locales de deformación). La influencia de la no-saturación en la rigidez se ha estudia-do también mediante ensayos triaxiales con medición de la presión negativa del agua en los poros. Estas me-didas permiten el análisis del comportamiento mecánico de materiales no saturados por lo que se refiere a ten-siones efectivas. Con este propósito fueron usados dos procedimientos: el de Terzaghi y el de Bishop. Losresultados obtenidos revelan, para cada material, una relación única entre la rigidez vertical y la tensión efec-tiva vertical (ratio de vacíos constante = 0.5), independientemente del grado de saturación de las muestras es-tudiadas.ABSTRACT In this paper, the stiffness of two materials with the same geological origin is presented, a silty sand, calledPerafita sand (D50=0.36mm) and a granite aggregate (0/12.5, D50=0.52mm). The stiffness in very small strains ( <10-5) of the compacted materials is studied by means of precision triaxial tests (with local strain measure-ments). The influence of non-saturation on the stiffness is also studied through triaxial tests with measurementof negative pore water pressures. Such measurements allow the analysis of the mechanical behaviour of theunsaturated material in terms of effective stresses. For this purpose two approaches were used: the Terzaghi’s and Bishop’s approaches. The results obtained show, for each material, a unique relationship between vertical stiffness and vertical effective stress (constant void ratio = 0.5), independently of the saturation degree of the studied samples. Keywords: Unsaturated soils, Triaxial tests, suction, effective stress, Terzaghi’s and Bishop’s 1 INTRODUCTIONNowadays the great importance of the initial Young’s modulus or shear modulus (E0 or G0) is well established, since it is a reference value for sev-eral soil parameter correlations and numerical analy-ses. The investigation done in this field reveals that in the small strain domain the properties of the soils are not significantly affected by the cyclic, dynamic or static character of the actions. For this reason, the initial modulus of soils can be determined by dy-namic (resonant column), cyclic or static tests (pre-cision triaxial test).The soil behaviour, that interests the serviceabil-ity of structures depends on the maximum strain, which differs from work to work. In agreement with Biarez et al. (1999), the strain level is in the order of 10-4 in the subgrade soils and unbound granular ma-terials of pavements structures, around 10-3 for tun-nels, about 10-2 for foundations and nearly 10-1forembankments on soft soils. More generally, it can be concluded that the majority of structures, including buildings, presents values of strain in the order of 5x10-3. Therefore, the domain of the small strains is very important for the serviceability design of the structures. The linear elastic domain is generally found for strain levels lower than 10-5. From this value up to around 10-4, the behaviour of soil is re-versible but not linear, which means that the perma-nent strains are negligible although, in a loading-unloading cycle the stress-strain curve presents hys-teresis (Jardine et al., 1984).The main factors that affect the initial Young’smodulus of the granular materials are the void ratio and stress level. The influence of stress level is given by a power law. In agreement with several au-thors (Jiang et al., 1997; Hoque and Tatsuoka, 1998; Gomes Correia et al., 2001) the power law that de-scribes the vertical Young’s modulus (Ev) in thevery small strain domain is only a function of the vertical stress, !v, and not dependent on the horizon-tal stress, !h, and it is given by equation (1). Con-cerning the void ratio function, equation (2) pro-posed by Hardin and Richart (1963) is usually used. nvv CE )('!" (1))1()()(2eeBeF#$" (2)Another very important aspect is the evaluation ofsoil behaviour in terms of effective stresses.  Whenthe soil is saturated or with a high degree of satura-tion, the effective stresses can be evaluated using Terzaghi’s effective stress concept (equation (3)).When the soil has a low degree of saturation, it is necessary to use another model, such as Bishop´s. In this simple model, the effective stress is given byequation (4), where % is a factor that depends on the saturation degree and ua and uw are the air and water pore pressures, respectively. wvv u$" !!'(3)& 'waa uuu $#$" %!! ' (4)The previous aspects are used in the present studydealing with the stiffness evaluation of a granite ag-gregate (0/12.5) by means of precision triaxial tests. Furthermore, this study also analyses the influence of the particle size distribution on the stiffness of two materials with the same geological origin, a granite aggregate (0/12.5, D50=0.52mm) and a silty sand, called Perafita sand (0/6.4, D50=0.36mm).2 MATERIALS AND TEST PROCEDURE Table 1 shows the geometric characteristics of theparticle size distribution curves for the two materials(granite aggregate and Perafita sand). Figure 1 shows the modified Proctor curves of the two mate-rials as well as the conditions of compaction of the granite aggregate samples.To carry out the study on the granite aggregatetwo kinds of tests were done: triaxial tests with measurement of the negative pore water pressure (TTu) to estimate the effective stress, and precisiontriaxial tests (PTT) to evaluate the stiffness of thematerial in the small strain domain. All the testswere done in the Soils, Structures and Materials Me-chanics Laboratory of the Ecole Centrale Paris(ECP) in France.Table 1 – Geometric characteristics of the particle size distribution curves.Graniteaggregate(0/12.5)PerafitaSandDmax 12.5 6.35D10 (mm) 0.040 0.033D30 (mm) 0.23 0.185D50 (mm) 0.52 0.36D60 (mm) 0.78 0.560CU 20 17CC 1.7 1.91,71,81,92,02,12,22,34 6 8 10 12 14Water content (%)Dry density(103 kg/m3)16Granite aggregate (0/12.5)Perafita sandTTU specimenPTT specimenModified Proctor curvesFigure 1- Modified Proctor curves and state conditions of thecompacted specimens for the triaxial tests. 2.1 Triaxial tests with negative pore water pressure measurements (TTu) The measurement of the pore pressure was done in a standard triaxial cell modifying the pedestal toaccommodate a semi-permeable porous stone (Figure 2-a). This porous stone has the capability to prevent the passing of the air into the water circuit.A thin layer of kaolinite slurry is placed between the soil specimen and the porous stone (Figure 2-b) in order to guarantee a perfect contact of interfaces.Kaolonite slurryPorous stoneb)a)Figure 2 – a) Porous stone; b) – Kaolinite slurry.The consolidated undrained tests with measurementof pore water pressure were performed in two steps: (i) isotropic consolidation under confining stresses of 0, 26, 52 and 78 kPa (the changes in negative pore water pressure were recorded until equilibrium wasreached), and for the last one (ii) axial compression,loading at constant strain rate up to failure.2.2 Precision Triaxial test (PTT)The granite aggregate, was tested using a single specimen, with 150 mm of diameter and 300 mm ofheight, through a precision triaxial test. Figure 3-a shows a picture of the axial displacement transduc-ers used for axial strain measurements (LDT - Local Deformation Transducer; Goto et al., 1991). Nowa-days, this equipment is also operational at Universityof Minho in Portugal (Gomes Correia et al., 2006 - Figure 3-b).The test procedure consists in submitting the specimen to different confining stresses (13, 52, 65 and 78 kPa). For each confining pressure five load-ing-unloading cycles of very small amplitude were applied. This amplitude was controlled to ensure that the cycles were closed and linear, in order to evalu-ate the elastic Young’s modulus. For the latest con-fining stress (78 kPa), the sample was submitted to aloading-unloading cycle of great amplitude. Duringthe unloading process, very small loading-unloading cycles of vertical stress were performed at differentsteps. Figure 4-a shows the test procedure for the lat-est confining pressure and Figure 4-b illustrates atypical result for a loading-unloading cycle of very small amplitude.Figure 3– Specimen and LDT’s: a) –at ECP; b) – at Universityof Minho.!3 = 78 kPa00,0E51015202530+00 1,0E-04 2,0E-04 3,0E-04Axial Strainq (kPa)Loading-unloadig cyclesof very small amplitudeEv = 87 MPa00.0E20040060080010001200140016001800+00 5.0E-06 1.0E-05 1.5E-05 2.0E-05Deformação axiaTensão Deviatq (Pa)lóricaAgregado Granítico(d = 2,164 g/cm3w  = 5.9 %e = 0.232!3 = 13 kPaFigure 4 – a) Test procedure for 78 kPa confining pressure; b)Young’s modulus (E) evaluation on loading-unloading cycles of very small amplitude.3 TEST RESULTS 3.1 TTuThe aim of the triaxial tests with measurements ofthe negative pore water pressure was mainly to esti-mate the effective stresses. For this estimation twoconcepts were applied: Terzaghi’s ( wupp $"' ) andBishop’s ( wupp .' %$" ). Figure 5 shows the aver-age trend line evaluated for all the compacted sam-ples at various water contents and densities (see Fig-ure 1). When analyzing each approach individually,values of 2.29 and 2.31 were obtained for the peak envelopes (ratio between maximum deviatoric stress (q) and effective mean stress (p’)), for Terzaghi’sand Bishop’s approaches, respectively. These values are very similar because the granite aggregate has low negative pore water pressures and the specimensare of low compressibility under the tested water content conditions.020040060080010001200140016000 100 200 300 400 500p'  (kPa)q (kPa)Terzaghi's Concept (p'=p-uw)Bishop's Concept (p´=p-Sr.uw)q=2.29 p'q=2.31 p'Figure 5 – Peak envelope of stress paths for compression triax-ial tests. Axial LDT Based on these data, the effective stress conceptprovides a simple means to model the failure crite-rion of the soil, in agreement with previous analyses (Biarez et al., 1994; Fleureau et al., 2003; Reis Ferreira 2003). 3.2 PTTThe very small strain Young’s moduli were ob-tained on one hand by very small loading-unloadingcycles in the isotropic state, and, on the other hand, on the unloading path at different anisotropic stresslevels (Figure 4-a). Young’s modulus (Ev) is calcu-lated as illustrated in Figure 4-b. The analysis has been done both in total stresses and in effective stresses. The values were normalized for a pa stress,of value equal to 100 kPa.As shown on Figure 6 the results follow a power law given by equation (5), similar to equation (1), but incorporating the stress normalizing value (pa).To interpret the results in terms of effective stresses,the negative pore water pressure values were derived from the measurements made in the TTu tests on theRadial LDT Axial LDT b)a)q (Pa)a) b)Axial Strainspecimens at the same water content and void ratio, under the same mean stress (Reis Ferreira, 2003). Once again, the effective stress was estimated usingthe two approaches. na'vpCE ))*+,,-. !" (5)Figure 6 shows the results obtained in terms oftotal and effective stresses. As we can see, the gran-ite aggregate behaviour is similar for both ap-proaches. This happens because the values of nega-tive pore water pressure are small, the material is oflow compressibility and the saturation degree of the sample is high (69%). 10100100010 100 1000!v//ou//!'v//&kPa'Ev (MPa)Granite aggregate (0/12.5)e = 0.232w = 5.9 %Total stressEv = 235.8(!v/pa)0.52Effective stressBishop´s ConceptEv(Bishop) = 233.3(!'v/pa)0.58Terzaghi's ConceptEv(Terzaghi) = 231.4(!'v/pa)0.61Figure 6 – Influence of total and effective stresses on the elas-tic Young’s modulus.4 COMPARISON OF STIFNESS IN TWOMATERIALS WITH SAME GEOLOGIC ORIGINThe influence of the particle size distribution on stiffness was analysed comparing the results ob-tained on the granite aggregate (0/12.5mm; D50=0.52mm) with the results obtained on Perafita sand (D50=0.36mm). The latter results were pre-sented by Fleureau et al. (2003) and were obtained under different conditions, using different experi-mental devices, on samples of different sizes and for water contents from 6.5% to 18.3%.All moduli values were corrected to eliminate theeffect of the different initial void ratio (e0) of thetested specimens. For this, a normalised moduluscorresponding to a reference void ratio of 0.5 was derived using expression 2. Following Iwasaki et al.(1978), a value of 2.17 was adopted for the parame-ter B (equation (2)).Results presented on Figure 7 show that Perafita sand has Young’s modulus values higher than the granite aggregate (0/12.5), for the same effectivestress. However, the use of equation (2) to take the changes in void ratio into account must be madewith precaution, as shown by Kokusho and Yoshida(1997, referred by Gomes Correia et al., 2001). These authors measured the shear velocity (vs) of dense gravels having densities varying from very loose to very dense states; they reported that the re-lationship between the vs values and void ratios of gravels having largely different uniformity coeffi-cient (Uc) values is not unique under otherwise sameconditions, but is largely affected by the gradation characteristics. That is, the rate of increase in Evwith a decrease in void ratio becomes larger when Uc increase. To clarify this point, there is an ongo-ing study at University of Minho to study the most adequate equation for this kind of materials. 10100100010 100 1000!'vEnor(e=0.5) (MPa)Perafita sandEv = 200(!'v/pa)0.68Granite aggregateEv = 142.3(!'v/pa)0.58e = 0.232w = 5.9 %Figure 7 - Influence of particle size distribution on the normal-ised Young’s modulus.5 CONCLUSIONSStiffness properties of two materials with thesame geological origin, a granite aggregate (0/12.5, D50=0.53mm) and a silty sand, so called Perafita sand (D50=0.36mm), were evaluated. In the very small strain domain ( <10-5) the stiffness was deter-mined by means of precision triaxial tests, using lo-cal strain measurements (LDT´s - Local Deforma-tion Transducer (Goto et al., 1991)). The influence of non-saturation on the stiffness was studied through triaxial tests with measurementsof negative pore water pressures. Such measure-ments allowed the analysis of the mechanical behav-iour of the unsaturated material in terms of effectivestresses. For this purpose two approaches were used: Terzaghi and Bishop. For the granite aggregate (0/12.5) the estimated effective stresses values, us-ing the two approaches, were similar. This was due to the small values of negative pore water pressureand the low compressibility of the material under the water content test conditions.The results obtained for the granite aggregate(0/12.5) show a unique relationship between elastic vertical Young’s modulus and the vertical effective stress. Fleureau et al., 2003 also found for Perafita sand a unique relationship between vertical stiffnessand vertical effective stress (constant void ratio = 0.5), independently of the saturation degree of the studied samples. These findings show the relevance of the use of effective stress analysis in the smallstrain behavior of geomaterials and the importanceof negative pore water pressure measurements for the state conditions of the samples.  The influence of the particle size distribution on the stiffness was studied by comparing the results obtained on the granite aggregate (0/12.5 mm; D50=0.52mm) with those obtained on Perafita sand (D50=0.36mm). The stiffness values obtained for Perafita sand were higher than those for the granite aggregate, for the same void ratio and stress level. However, this result must be considered with some reserves, until the question, of which is the void ratio function that best describes the behaviour of materi-als with very low values of void ratio and high val-ues of Uc, be clarified. ACKOWLEGEMENTS This work was performed under the umbrella of GRICES/CNRS project – “Security of road and railway infrastructures versus climatic changes”. The authors would like to thank GRICES/CNRS for the financial support to perform this bilateral coop-eration work. REFERENCESBiarez, A., Fleureau, J. M., and Taibi S. 1994. Critère de résis-tance maximale des sols non saturés: approche expérimen-tale et modélisation. Proc. XIII Int. Conf. on Soil Mechani-cal and Foundation Engineering, Oxford & I. B. H. Pub. Co., New-Delhi. 385-388. Biarez, J., Liu, H., Gomes Correia, A., and Taibi, S. 1999. Stress-strain characteristics of soils interesting the service-ability of geomaterials structures. Proc. II Int. Conf. on Pre-failure Deformation Characteristics of Geomaterials, IS Torino 99, Jamiolkowski, Lancellotta and Lo Presti Eds. Balkema, Rotterdam. (1) 617-624. Fleurau, J. M., Hadiwardoyo, S., and Gomes Correia, A. 2003. Generalised effective stress analysis of strength and small strains behaviour of a silty sand, from dry to saturated state. Soil and Foundations. (43) Nº 4 21-33. Gomes Correia, A., Anhdan, L. Q., Koseki J.,and Tatsuoka, F. 2001. Small strain stiffness under different isotropic and anisotropic stress conditions of two granular granite materi-als. Advanced Laboratory Stress-Strain Testing of Geoma-terials, Tatsuoka, Shibuya and Kuwano Eds. Balkema, Swets and Zeitlinger. 209-215. Gomes Correia, A., Reis Ferreira, S. M. , and Araújo, N. 2006. Triaxiais de precisão para determinação das características de deformabilidade. 10º Congresso Nacional de Geotecnia.Goto, S., Tatsuoka, F., Shibuya, S., Kim, Y-S., and Sato, T. 1991. A simple gauge for local small strain measurements in the laboratory. Soils and Foundations. (31)1, 169-180. Hardin, B. O. & Richart, F. E. Jr. 1963. Elastic wave velocities in granular soils. Journal of the Soil Mechanics and Foun-dations. Division, ASCE, (89) Nº SM1 33-65.  Hoque, E. & Tatsuoka, F.1998. Anisotropy in the elastic de-formation of materials. Soils and Foundations. (38)1 163-179. Iwasaki, T. & Tatsuoka, F. 1978. Effects of grain size and grading on dynamic shear moduli of sands. Soils and Foun-dations. (17)3 19-35. Jardine, R. J., Simes, M. J. and Burland, J. B. 1984. The meas-urement of soil stiffness in the triaxial apparatus. Géotech-nique. (34)3 323-340. Jiang, G. L., Tatsuoka, F., Flora, A. and Koseki, J. 1997. Inher-ent and stress-state-induced anisotropy in very small strain stiffness of a sandy gravel. Géotechnique. (47)3 509-521. Reis Ferreira S. M. 2003. Influência da não saturação e da gra-nulometria nas características de deformabilidade de um Agregado Granítico. Master Thesis, Instituto Superior Téc-nico, Portugal. 

Influencia de la no saturación y granulometría en la rigidez de materiales de naturaleza granítica

http://repositorium.sdum.uminho.pt/bitstream/1822/12280/1/Influence%20of%20non-saturation%20and%20particle%20size%20distribution.pdf

Influencia de la no saturación y granulometría en la rigidez de materiales de naturaleza granítica

Abstract

Similar works

Full text

Available Versions

Universidade do Minho: RepositoriUM