UNDRAINED SHEAR STRENGTH OF SATURATED COHESIVE SOILS DEPENDING ON CONSOLIDATION PRESSURE AND MINERALOGICAL PROPERTIES BOJANA DOLINRR About the author Bojana Dolinar University of Maribor, Faculty of Civil Engineering, Smetanova ulica 17, 2000 Maribor, SI-Slovenia, E-mail: bojana.dolinar@uni-mb.si Abstract It is well known that the relationship between the water content and the undrained shear strength of finely grained soils can be described with a non-linear function in which the type of soil is determined by two parameters. These parameters depend primarily on the size of clay minerals, their quantity in soil composition and the interlayer water quantity in expanding clay minerals. This article asserts that there exists the exactly defined relationship also between the water content and consolidation pressure. In the function describing this relationship, the type of soil is determined by two parameters. They can be expressed depending on the same mineralogical properties of soils as the values of parameters in the function showing the relationship between the water content and the undrained shear strength. These findings allow us to express the ratio between undrained shear strength and consolidation pressure depending on mineralogical properties of soils. Keywords clay, specific surface, undrained shear strength, compressibility 1 introduction Mechanical properties of cohesive soils depend on the quantity of contained water which, in turn, mostly depends on mineral compositions of soils. Few investigations have been undertaken about the above dependencies. The results of individual investigations are only known. Koumoto [5] and Koumoto and Houlsby [6] found that the relationship between the undrained shear strength cu and the water content w in soils could be expressed by the function w = acu-b (1) where a and b are soil-dependent parameters. a [%] is the water content in soils at the undrained shear strength cu = 1 kPa, and b is the slope of the linear function which represents the ratio between the logarithm of the water content w [%] and the logarithm of undrained shear strength cu [kPa]. Parameters a and b can be obtained experimentally with a few measurements of water content at different undrained shear strength. Dolinar [2] investigated the influence of mineralogical properties of soils on the values of both parameters in Eq. (1), water content and undrained shear strength. On the basis of theoretical and experimental tests, she established that the undrained shear strength only depends on the quantity of intergrain water, whilst interlayer water in expanding clay minerals, which is strongly bound between the layers of clay particles, can not influence it. To take into account this important fact, the equation (1) has been rewritten as follows w„ = a, c,, (2) where suffix e means that parameters ae and be are determined from the intergrain water content we only. It was found that soil-dependent parameters could be calculated in this case by Eqs. (3) and (4), from the known portion p and specific surface As [m2/g] of soils ae = p a + ß AS be = Y ■ AScA (3) (4) where a = 33.70, / = 0.99, Y = 0.05 and A = 0.27. Note that a, 3, y and A are equal for all cohesive soils. ASC [m2/g] is the external surface per one gram of clay minerals, while AS [m2/g] is the external surface per one gram of soil (AS = pASC ). ACTA GEOTECHNICA SLOVENICA, 2OO4 5. B. DOLINAR: UNDRAINED SHEAR STRENGTH OF SATURATED COHeSIVe SOILS DëPëNDING ON CONSOLIDATION PRESSURE AND MINËRflLOGICflL PROPERTIES This article presents the results of the research based on the above findings whilst being their logical continuation. The experimentally determined inter-dependence of the consolidation pressure and intergrain water quantity of saturated soils is studied. It was established that this dependence could be expressed by the non-linear function in which the type of the soil was described by two parameters. It was also established that the values of these parameters could be calculated from the same mineralogical properties of clays as are the values of parameters in Eq. (2). These findings allow us to express the ratio between undrained shear strength of saturated clays and consolidation pressure depending on mineral-ogical properties of soils. 2 tested soil samples data Three monomineral samples (Table 1) were used in tests: a well crystallized kaolinite (Sample 1), a poorly crystallized kaolinite (Sample 2) and Ca-montmorillonite (Sample 3). The investigated clays originate from the United States regions. Being intended for fundamental studies, these clays have a known mineral composition, structural formula of a unit cell and specific surface As (Tab. 1). The below properties of tested samples are taken from literature [8]. expanding mineral thus needed to be reduced. 3.1 THE CALCULATION OF INTCAGAAIN WATER IN AN EXPANDING MINERAL The montmorillonite structure consists of an octahedral sheet sandwiched between two silica sheets. The layers thus formed are continuous in the a and b directions and stacked one above the other in the c direction. Bonds between layers are weak, thus water or other polar molecules can enter the space between the unit layers causing the lattice to expand in the c direction. The basal spacing (spacing between the center of two neighboring layers) in the c direction which is d1 = 0.96 nm for dry calcium montmorillonite (dried at 1050 C) rises to d2 = 1.54 nm after the adsorption of water. In case of a calcium exchangeable cation in montmorillonite, the adsorption of water between layers is completed already at very low water content and the basal spacing is then practically constant. The volume of interlayer water Vwi can thus be calculated in accordance with [3] using Eq. (5) V= ASi(d2 - dl) = 0.1817 cm3Ig (5) where ASi [m2/g] is the internal specific surface of montmorillonite. It was determined from the total specific Table 1. Mineral composition of clays, specific surface and structural formula of the unit cell. Mineral composition I portion of clay in sample A [m2Ig] Structural formula of the unit cell 1 - Kaolinite I p =1 10.05 (Mgo,Cao,Nao,Ko.l)[Al3,6Fe(III)o,MnslTio,l][Si3,3Alo,7]Olo(OH)8 2 - Kaolinite I p =1 23.50 (Casl.Ksl.)[Al3.66Fe(III)o.07MnslMgslTi0.16][Si4.o]O1o(OH)a 3 - Montmorillonite I p =1 97.42 (Cao.39Nao.36Ko,)[Al,7lMg,llFe(III)o,2Mno,Tio,3][Si8,]O2o(OH)4 3 methods and results of laboratory tests The water content w , which is determined by drying soils at the temperature of 105° C, equals the intergrain water content we of non-expanding clay minerals (Samples 1 and 2). With the montmorillonite clay, the interlayer water w{, which is bonded to internal grain surfaces, also appears besides the intergrain water. It is known that the interlayer water cannot be drained from an expanding mineral at usual stresses, which leads to the conclusion that the intergrain water quantity and consolidation pressure can only be compared. The total water content for the interlayer water portion in the surface of one gram of clay ASt reduced for the value of the measured external specific surface AS (Eq.(6)). Asi = Ast - As = 626.80 m2/g (6) The total specific surface ASt was calculated in accordance with [9] by Eq. (7) A» = — Na 2J,«, = 724.22 m2/g (7) m where m = 762 is the calculated relative molecular weight of the unit cell, NA = 6.022 x 1023/mol is Avoga-dro's number, sw = 0.515 nm is the width of the unit cell and sl = 0.89 nm is the length of the unit cell. 2 10. ACTA GEOTECHNICA SLOVENICA, 2004 B. DOLINAR: UNDRAINED SHEAR STRENGTH OF SATURATED COHeSIVe SOILS DëPëNDING ON CONSOLIDATION PRESSURE AND MINËRflLOGICflL PROPERTIES 3.2 THE RELATIONSHIP BETWEEN THE INTERGRAIN WATER CONTENT AND CONSOLIDATION PRESSURE The quantity of intergrain water in saturated clays was measured at different effective stresses by an oedometer consolidation test in accordance with BS standard [1]. The initial moisture content in the samples was near the liquid limit. The void ratio e and the corresponding water content w after consolidation of the clays were determined at axial stress a' = 50 kPa, 100 kPa and 200 kPa. The total water content w was decreased for the portion of interlayer water wi (we = w — wi) in order to determine the intergrain water content we in the expanding mineral (Table 2). It is established that the relationship between the void ratio e and vertical stress a' is approximately linear for normally consolidated saturated soils when using a semi-logarithmic scale (e, log a'). In this case, the 50 100 a-1 fkPal Figure 1. Intergrain water content we as a function of effective stress a'. Table 2. The relative water content w before the test, specific weight 7s, void ratio e and intergrain water content we after consolidation at different axial stresses a ', and soil dependent parameters ie and je. Sample 1 - kaolinite 2 - kaolinite 3 - montmorillonite w [%] 39.60 54.56 120.00 7. 2.58 2.50 2.30 a ' [kPa] 50 100 200 50 100 200 50 100 200 we [%] 33.29 31.15 29.19 41.32 38.09 35.12 86.25 76.62 67.88 e 0.859 0.804 0.753 1.033 0.952 0.878 1.984 1.762 1.561 ie [%] 48.20 65.42 169.63 Je 0.094 0.117 0.172 slope of the straight line is the compression index Cc. A complete linear relationship, however, was only established when both variables were shown on a double logarithmic scale (Fig.1). The inter-dependence of the quantity of intergrain water we = (e/js ) [%] and the effective stress a' [kPa] can thus be expressed using the function logwe = logie — je loga' ^ Wg = ie a'—je (8) where ie (the water content in the soil at a' = 1 kPa) and je (the slope of the linear function) are soil dependent parameters (Table 2). It is evident from Fig. 1 that parameters ie and je increase with the increase of the specific surface As of clays. 3.3 THE RELATIONSHIP BETWEEN PARAMETERS i AND j AND e J e MINERALOGICAL PROPERTIES OF CLAYS Parameters i and j vary with the type of soil, yet they can also be influenced by temperature, the structure of the soil, organic additions and chemical composition of the pore water. To adjust test conditions as much as possible, laboratory tests were performed at the temperature of 20° C using distilled water on samples without organic matter having a parallel arrangement of clay particles. In accordance with previous findings [2], it was expected that parameters ie and je depended on the size and quantity of clay grains in samples. ACTA GEOTE^NI^ SLOVENICfl, 2004 7. B. DOLINAR: UNDRAINED SHEAR STRENGTH OF SATURATED COHeSIVe SOILS DëPëNDING ON CONSOLIDATION PRESSURE AND MINËRflLOGICflL PROPERTIES by the function ie = be = Y • Ascx (10) where Y = 0.05 and A = 0.27. 3.4 APPLICATION OF THE RESULTS TO NATURAL SOILS The calculation of parameters ie and ie from mineral-ogical properties was based on test results obtained on monomineral clays. To adopt this criterion to practical applications, it was however necessary to investigate the validity of the test results for heterogeneous soils. Five samples of natural soils were chosen for this purpose. The quantity of intergrain water in saturated clays was measured at different effective stresses by an oedometer consolidation test in accordance with BS standard [1]. The mineralogical composition of the soils was analyzed using an X-ray diffractometer (Philips 1820) with Cu-Ka radiation. Powdered samples were used to determine the bulk sample composition (Table 3). Clay minerals were characterized with the help of oriented clay mineral aggregates (Tables 4 and 5). The results of chemical analyses were used to determine the quantity of individual minerals in the soils. The external surface area was measured by the five-point BET method with N2 (Table 3). The obtained results allowed a comparison between the experimentally determined parameters ie and ie and those that were calculated from the mineralogical properties of samples by Eqs. (9) and (10). Table 3. Mineral composition of the powder bulk samples. Mineral composition [%] Sample 1 2 3 4 5 Illite + MLC illite/montmorillonite 25 35 28 35 34 Chlorite + MLC chlorite/montmorillonite 8 14 16 0 18 Kaolinite 5 0 0 12 0 Ca-montmorillonite 14 0 0 34 0 Quartz 34 25 42 18 43 Plagioclase 9 3 9 0 3 Microcline 5 0 4 0 3 Calcite 0 22 0 0 0 Go ethite/hematite 0 1 0 1 0 Specific surface As [m2/g] 30.1 28.5 16.7 54.1 32.6 Note: MLC - mixed layer clays 10. ACTA GEOTECHNICA SLOVENICA, 2004 It is evident from Fig. 2 that the relationship between parameter ie [%] and the specific surface AS [m2/g] is linear. This can be shown by the expression ie = p n + K As (9) where n = 33.46 and k = 1.39. Note that the weight portion of clay minerals in tested samples was p =1. 200 180 160 140 120 100 1) 80 60 40 20 0 \ 3 - Ca-rnofitmorillonite — kaolinite j 1 - kaolinite ; ; 20 40 60 [m2/g] 80 100 Figure 2. Parameter ie as a function of external specific surface AS. It was established that parameter je totally equaled parameter b in Eq. (4) and could therefore be expressed B. DOLINAR: UNDRAINED SHEAR STRENGTH OF SATURATED COHeSIVe SOILS DëPëNDING ON CONSOLIDATION PRESSURE AND MINËRflLOGICflL PROPERTIES Table 4. Mineral composition of the clay fraction < 0.002 mm. Sample Illite, MLC illite / Ca-montmorillonite, Ca-montmorillonite [%] R1 R1 R3/1 R1 R0 R0 R0 R0 ILL I/ZI1 I/ZI2 I/ZI3 I/ZI4 I/ZI5 I/ZI6 I/ZI7 I/ZI8 Ca-M 1 4 0 0 0 60/2 0 0 23/2 0 6 2 7 0 82/6 0 0 55/5 0 0 0 2 3 2 0 0 78/1 0 0 42/1 0 0 1 4 6 0 0 78/4 0 0 42/3 0 0 16 5 7 84/5 0 78/4 0 0 42/3 0 15/2 0 LEGEND R0, R1, R3/1 ordering of layers in MLC I percent of illite in ILL Illite MLC illite/Ca-montmorillonite Ca-M Ca-montmorillonite ZI1-ZI8 percent of MLC illite/Ca-montmoril- lonite in sample Table 5. Mineral composition of the clay fraction < 0.002mm. Sample Kaolinite, MLC kaolinite/Ca-montmorillonite, MLC chlorite/Ca-montmorillonite [%] R1 R1 R1 R1 Ka Ch K/ZKa1 C/ZC1 C/ZC2 C/ZC3 < 0.002 mm 1 1 0 0 0 0 0 14.54 2 3 2 0 0 68/1 0 26.21 3 0 3 0 76/2 0 63/2 12.84 4 2 0 90/2 0 0 0 33.02 5 4 0 0 0 0 0 24.96 LEGEND R1 Ka Ch K ordering of layers in MLC Kaolinite Chlorite percent of kaolinite in MLC kaolinite/Ca-montmorillonite C ZKal ZC1-ZC3 percent of chlorite in MLC chlorite/Ca-montmorillonite percent of MLC kaolinite/Ca-montmorillon-ite in fraction < 0.002 mm percent of MLC chlorite/Ca-montmorillon-ite in sample In determining parameters ie and je experimentally, it was necessary to consider only the intergrain water content in the soil. The interlayer water in the tested samples, however, resulted from the presence of Ca-montmorillonite. Its quantity was calculated by Eq. (5) considering the internal specific surface of montmoril-lonite grains Asi = 626.80 m2/g and adequate mass portions of this mineral in individual soils. The research results are given in Table 6. It is evident that parameters ie and je and the quantity of water after consolidation at different vertical stresses calculated from the results of a mineralogical analysis are almost equal to the experimentally obtained values. Minor differences probably appear due to the presence of organic substances in the soils (1-3 %). 3.5 UNDRAINED SHEAR STRENGTH TO CONSOLIDATION PRESSURE RATIO Substituting the quantity of intergrain water we in Eq. (2) by Eq. (8), which determines the relationship between the quantity of intergrain water we and effective stress a ', and considering that parameter je = be, we obtain Eq. (11). a , ^ ^ a (H) 10. ACTA GEOTECHNICA SLOVENICA, 2004 B. DOLINAR: UNDRAINED SHEAR STRENGTH OF SATURATED COHeSIVe SOILS DëPëNDING ON CONSOLIDATION PRESSURE AND MINËRflLOGICflL PROPERTIES Table 6. Specific surface As and portion p of clay minerals in soil composition, water content w before and after the test, calculated interlayer water quantity wi, measured and calculated intergrain water quantity we after consolidation at different axial stresses a ', and calculated and experimentally determined soil dependent parameters ie and je. Sample 1 2 3 4 5 As [m2/g] 30.1 28.5 16.7 54.1 32.6 P 0.52 0.49 0.44 0.89 0.52 w [%] before the test a '= 50 kPa 49.36 45.92 31.20 70.13 37.77 a '= 100 kPa 49.36 44.43 30.38 69.35 37.70 a '= 200 kPa 44.99 44.05 27.95 66.22 35.25 w [%] after the test a' = 50 kPa 37.47 36.76 25.82 66.04 34.72 a '= 100 kPa 33.67 34.23 22.56 60.12 31.51 a '= 200 kPa 30.85 32.68 23.42 55.16 27.87 wi [%] 4.05 1.02 0.55 8.14 0.93 we = w - wi [%] measured a '= 50 kPa 33.42 35.74 25.27 57.90 33.79 a '= 100 kPa 29.62 33.21 22.01 51.98 30.58 a '= 200 kPa 26.80 31.66 22.87 47.02 26.94 we = ie aj' [%] calculated a '= 50 kPa 33.06 31.26 22.54 57.92 34.60 a '= 100 kPa 29.82 28.20 20.50 52.13 31.14 a '= 200 kPa 26.89 25.43 18.74 46.91 28.02 ie [%] calculated 59.23 56.01 37.93 104.98 62.71 ie [%] measured 62.10 55.14 39.60 104.04 64.26 j calculated 0.149 0.149 0.133 0.152 0.152 1 measured 0.159 0.111 0.115 0.150 0.163 e Due to the known relationships between the soil-dependent parameters and the mineralogical properties of clays, the relationship cu/ a 'can be expressed by Eq. (12). = (0.05 Asc 33.70 + 0.99AS 33.46+1.39AS (12) 4 conclusion The article illustrates the interdependence of the quantity of intergrain water in saturated clays and consolidation pressure. It has been established that this relationship can be described by the non-linear function (8), where ie and je are soil-dependent parameters. According to previous findings, the parameters can be expressed depending on the quantity and size of clay minerals. These relations are shown by Eqs. (9) and (10). The known relationships between the intergrain water content, undrained shear strength, consolidation pressure and the mineralogical properties of soils allow us to express the cuja' ratio depending on the specific surface and the quantity of clay minerals in soil composition as shown by Eq. (12). c u a 10. ACTA GEOTECHNICA SLOVENICA, 2004 B. DOLINAR: UNDRAINED SHEAR STRENGTH OF SATURATED COHeSIVe SOILS DëPëNDING ON CONSOLIDATION PRESSURE AND MINËRflLOGICflL PROPERTIES references [1] British Standards Institution (1990). Methods of test for soils for civil engineering purposes. BS 1377, London. [2] Dolinar, B. (2004). Physical properties of saturated cohesive soils depending on their mineralogical composition. PhD Thesis, University of Maribor, Faculty of Civil Engineering. [3] Fink, D.H. and Nakayama, F.S. (1972). Equation for describing the free swelling of montmorillonite in water. Soil Science, 114, No. 5, 355-358. [4] Fripiat, J.J., Letellier, M. and Levitz, P. (1984). Interaction of water with clay surfaces. Philosophical Transactions of the Royal Society of London, A311, 287-299. [5] Koumoto, T. (1990). Determination of the both liquid and plastic limits of clay by the fall cone test. J. Jpn Soc. Irrigation, Drainage and Reclamation Engng, 146, 95-100. [6] Koumoto, T. and Houlsby, G.T. (2001). Theory and practice of the fall cone test. Geotechnique, LI, No. 8, 701-712. [7] Mitchell, J.K. (1993). Fundamentals of Soil Behaviour. John Wiley & Sons, New York. [8] Van Olphen, H. and Fripiat, J.J. (1979). Data handbook for clay minerals and other non-metallic materials. Pergamon press. [9] Van Olphen, H. (1977). An Introduction to Clay Colloid Chemistry. 2nd ed., Wiley Interscience, New York. 10. ACTA GEOTECHNICA SLOVENICA, 2004