Geotechnical Testing Journal

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1 Geotechnical Testing Journal M. M. Farias 1,3 and M. A. Llano-Serna 2,3 DOI: /GTJ Simle Methodology to Obtain Critical State Parameters of Remolded Clays Under Normally Consolidated Conditions Using the Fall-Cone Test VOL. 39 NO. 5 / SEPTEMBER 2016

2 Geotechnical Testing Journal doi: /gtj Vol. 39 No. 5 / Setember 0000 / available online at M. M. Farias 1,3 and M. A. Llano-Serna 2,3 Simle Methodology to Obtain Critical State Parameters of Remolded Clays Under Normally Consolidated Conditions Using the Fall-Cone Test Reference Farias, M. M. and Llano-Serna, M. A., Simle Methodology to Obtain Critical State Parameters of Remolded Clays Under Normally Consolidated Conditions Using the Fall-Cone Test, Geotechnical Testing Journal, Vol. 39, No. 5, 2016,. 1 10, doi: /gtj ISSN Manuscrit received Setember 9, 2015; acceted for ublication May 5, 2016; ublished online July 28, Geotechnical Research Grou, Det. of Civil and Environmental Engineering, Univ. of Brasilia, Brasilia, DF, Brazil; and Camus Universitário Darcy Ribeiro, Faculdade de Tecnologia, Deartamento de Engenharia Civil e Ambiental ENC, Asa Norte, Brasilia, DF, Brazil, muniz@unb.br Geotechnical Research Grou, Det. of Civil and Environmental Engineering, Univ. of Brasilia, Brasilia, DF, Brazil; and Camus Universitário Darcy Ribeiro, Faculdade de Tecnologia, Deartamento de Engenharia Civil e Ambiental ENC, Asa Norte, Brasilia, DF, Brazil (Corresonding author), mallano@unb.br These authors contributed equally to this work ABSTRACT The falling cone is widely used as a laboratory test to determine the liquid limit for the characterization of clay soils. However, remolded undrained shear strength and deformability and strength arameters of critical state models can also be estimated. The objective of this aer is to show a simle methodology to determine these imortant arameters for engineering simulations. Controlled laboratory tests were carried out on kaolin clay samles using a cone with 30 of ti angle and 30 g of mass. Mini-vane tests were also erformed to determine the remolded undrained shear strength of the samles. The exerimental results were used to calibrate the Hansbo cone factor, K, from which it is ossible to relate the undrained shear strength and the cone enetration for different water contents. The study shows that a calibrated cone and the roosed methodology may be used to estimate strength and deformability arameters for reliminary stages of design involving remolded clays under normal consolidation conditions in a quick way and at very low cost. Keywords fall-cone test, normally consolidated clays, undrained shear strength, critical state arameters VC Coyright by 2016 ASTM by ASTM Int'l (all International, rights reserved); 100 Barr Mon Harbor Aug Drive, 8 02:06:15 PO Box EDT C700, 2016 West Conshohocken, PA

3 2 Geotechnical Testing Journal Introduction The remolded undrained shear strength (s u ) is a fundamental arameter for the design of geotechnical engineering works involving saturated clays under undrained conditions. Some ractical examles include the short-term bearing caacity of foundations on clays, retaining walls, embankment stability, ile driving, landslides, mudslides, and submarine soil structures (Vanaalli et al. 1996; Budhu and Mahajan 2009; Kayabali and Tufenkci 2010; Bai and Liu 2012). The fall-cone test was originally develoed in Scandinavia. Nowadays, it is widely used in several countries as a standardized test for the characterization of the liquid limit (w l )of cohesive soils (Koumoto and Houlsby 2001). The fall cone might be referable over the Casagrande cu method for determining the liquid limit, because it can better be exlained by the acceted theories. The fall-cone test results are indeendent of the oerator and, also, allow for measurements of both liquid limit, w l, and lastic limit, w, with the same aaratus (Koumoto and Houlsby 2001). Furthermore, according to the literature review erformed by Evans and Simson (2015), the coefficient of variation (COV) of fall-cone test measurements is lower than that of the Casagrande test measurements. However, the fall-cone test has some drawbacks, such as (see, e.g., Evans and Simson 2015) (1) the liquid limit may vary for the same material deending on both the geometry and roughness of the cone, and on the exerimental rocedure; and (2) the cone is overly sensitive to its surface roughness, which may vary because of wear or rust and may lead to incorrect results if not roerly calibrated. The drawbacks of the fall-cone test can be minimized if a calibration rocedure is regularly followed. For examle, the K factor must be re-determined if the condition of the aaratus changes. Besides characterization, the falling cone can also be used to determine other roerties, such as the undrained shear strength of clays. Some reresentative works have been ublished by Hansbo (1957), Karlsson (1961), Wood and Wroth (1978), Wood (1985), Leroueil and Le Bihan (1996), Koumoto and Houlsby (2001), Ayadat and Hanna (2007), Hazell (2008), Zentar et al. (2009), Azadi and Monfared (2012), Claveau- Mallet et al. (2012), O Kelly (2013), and Vardanega and Haigh (2014). The test has also been used to understand the ostfailure behavior of soils regarding viscosity, allowing to study the cree-related henomena (Budhu and Mahajan 2009; Cevikbilen and Budhu 2011; Bouketi et al. 2012) and, more recently, to study the alicability of time-dislacement cone motion using an innovative inexensive data-acquisition system for research and teaching uroses (Evans and Simson 2015). There are two widely used falling-cone configurations: the 60 ti angle and 60-g mass cone adoted in countries such as Sweden, Norway, Canada, and Jaan; and the 30, 80-g cone used in the United Kingdom, New Zealand, and France, for instance. The latter is known as the British cone, and will be used in this investigation. Koumoto and Houlsby (2001) recommend the 60, 60-g cone on the basis that its theoretical understanding is better than the 30 cone. However, many recent works using new numerical and exerimental aroaches have imroved the understanding of generic conical indenters, including the British cone (Hazell 2008). Under this ersective, the British 30, 30-g fall-cone aaratus was selected to show its otential as an alternative tool to determine deformability and undrained shear resistance of remolded clays. The authors roose a simle methodology to estimate the deformability and strength arameters of the well-known Camclay model (Wroth et al. 1958) based on the enetration results obtained with the British cone. As a first ste to validate the roosed methodology, kaolin was selected as a benchmark soil, taking advantage of its commercial availability around the world and the long existing database of tests in this tye of material (Rossato et al. 1992). The comressibility arameters were validated using the result of an odometer comression test. The shear strength arameters were calibrated using mini-vane tests and validated by consolidated undrained triaxial comression tests erformed in the same soil. Desite the limitations that the validations in one single soil suggest, the study showed a good agreement regarding deformability and undrained shear strength of remolded fine-grained soils. Furthermore, the aroach is theoretically consistent; the methodology is romising and ensures future research. Methodology to Obtain Parameters From the Fall-Cone Test Hansbo (1957) established the following relationshi between the undrained shear strength and the cone enetration: s u ¼ KQ h 2 (1) h ¼ cone enetration deth, K ¼ cone factor, Q ¼ total cone weight, and s u ¼ remolded undrained shear strength. More recently, Koumoto and Houlsby (2001) resented a theoretical study with an emhasis on the variables affecting the fall-cone factor. This factor deends on the cone surface s roughness, the cone geometry, and the rate of deformation imosed to the clay during the cone enetration; however, it is indeendent of the bluntness state as shown by Claveau-Mallet et al. (2012). One of the most recent equations to exress the

4 FARIAS AND LLANO-SERNA ON PARAMETERS OF REMOLDED CLAYS 3 fall-cone factor was also established by Koumoto and Houlsby (2001), which states: 3f K ¼ N ch tan 2 ðb=2þ N ch ¼ bearing caacity factor, b ¼ cone ti angle, and f ¼ ratio of the static overall the dynamic strength of the soil. The most commonly used rocedure to determine the undrained shear strength using the fall-cone test is based in revious exerimental observations as in Leroueil and Le Bihan (1996), Stone and Kyambadde (2007), and Das et al. (2013). Desite this fact, we consider that this is not a suitable ractice because of the high sensitivity of the K factor with changes on the surface roughness as observed by Koumoto and Houlsby (2001). Thus, in this aer, the value of K will be calibrated from exerimental results. Koumoto and Houlsby (2001) also roosed a rocedure to determine emirical arameters a and b to relate the water content and the undrained shear strength: w ¼ a s b u a a, b ¼ emirical fitting coefficients, a ¼ atmosheric ressure, and w ¼ water content. For the sake of comleteness, the key oints of the fall-cone formulation develoed by Koumoto and Houlsby (2001) will be described here. The emirical coefficients can be easily calibrated from a linear fitting of Eq 3 in a logarithmic sace (log w log s u ). Parameter a may be related to the water absortion and retaining caacity of the soil and b is related to soil comressibility (O Kelly 2013). Combining Eqs 1 and 3, the following exression is obtained: w ¼ a KQ b a h 2 Equation 4 can be further extended based on the critical state theory, which establishes a well-known relation for the critical state line (CSL). e ¼ e a k ln 0 (5) e ¼ void ratio, e a ¼ void ratio when 0 ¼ a, 0 ¼ mean effective stress 0 ¼ r 0 1 þ r0 2 þ r0 3 =3, a (2) (3) (4) a ¼ reference atmosheric ressure: 100 kpa (1 bar), and k ¼ comressibility coefficient. Instead of Eq 5, Koumoto and Houlsby (2001) use the following exression, which is linear in a bi-log (e- 0 ) sace: lnðeþ ¼lnðe a Þ kln 0 a 0 k or e ¼ e a (6) Using the relation (G s w ¼ Se), for the saturated test condition (S ¼ 1) and the water content w, exressed in ercentage, Eq 6 becomes: w ¼ 100 e a 0 k G s a G s ¼ secific gravity of the soil articles. But the mean effective stress 0 relates to the deviatoric stress at the critical state: a (7) q f ¼ M 0 (8) M ¼ inclination of the failure surface, and q f ¼ deviatoric stress at failure. The deviatoric stress can be exressed by: rffi 1 h 2þ i 2þ q ¼ r x r y ry r z ð rx r z Þ 2 þ6 s 2 2 xy þs2 yz þs2 xz r x, r y, and r z ¼ normal stresses, and s xy, s yz, and s xz ¼ shear stresses. For the conventional triaxial comression (CTC) test, the stress state is such that r x ¼ r y ¼ r 3, r z ¼ r 1, and s xy ¼ s yz ¼ s xz ¼ 0, then q ¼ (r 1 r 3 ) and stress q f ¼ 2s u at failure. This is the value used by Koumoto and Houlsby (2001). However, the normal stresses during the mini-vane shear test are negligible, and the stress state is better reresented by r x ¼ r y ¼ r z ¼ 0, s yz ¼ s xz ¼ 0, and s xy = 0, then q ¼ 3 sxy and q f ¼ 3 su at failure. The use of the mini-vane shear equiment had the intention of roviding better constitutive data because the influence of anisotroy is largely removed in remolded samles. Both cases can be reresented by the following relation between deviatoric stress q f and the undrained shear strength (s u ): (9) q f ¼ as u (10) a ¼ 2 for CTC, or a ¼ 3 for the mini-vane test. Note that Eq 10 imlies that M is constant. This means that for each a value assumed an aroximation of the cross-section of the failure enveloe is comuted. This also imlies a circular

5 4 Geotechnical Testing Journal (von Mises) failure enveloe because the fall cone is considered to haen under undrained conditions. In contrast, drained conditions can lead to different enveloe shaes. Finally, substituting Eq 10 in Eq 8, and the resulting exression for 0 in Eq 7, the following exression is obtained: w ¼ 100 e a G s a k s u M a k By comaring Eqs 3 and 11, the following exressions relating coefficients a and b and the Cam-clay arameters (e a, k, and M) can be found: a ¼ 100 e a G s (11) a k (12) M b ¼ k (13) The revious exressions are almost the same derived by Koumoto and Houlsby (2001) excet for a. Then the results of cone enetration and mini-vane tests can be used to calibrate the deformability and strength arameters of the Cam-clay model roosed by Wroth et al. (1958). The coefficient b according to Eq 13 gives the first arameter (k), but arameter a rovides a single Eq 12 for two unknowns (e a and M). The derivations erformed here do not account for the effect of anisotroy on the undrained shear strength, which means that the roosed methodology can only be alied to remolded soils. The methodology to obtain the deformability arameters can be summarized as follows: 1. Using Eq 1, calibrate the cone factor (K), based on exerimental results with the falling-cone tests to obtain the enetration (h) and mini-vane shear tests to obtain the undrained strength (s u ) for different water content (w). 2. With the calibrated value of the cone factor (K) for a given equiment, the cone test can be used on its own to estimate the undrained shear strength (s u ). 3. Use the values of water contents (w) and undrained strength (s u ) to obtain the coefficients a and b by fitting the exerimental data according to Eq Equation 13 corresonds to sloe of the normal comression line (NCL), i.e., the virgin comressibility coefficient (k). The results of a calibrated fall-cone test, or those obtained directly from the mini-vane test, can now be used to estimate the osition critical state line (e a ) and its strength arameters (M or / cs ), as follows: 5. The sloe of the critical state (k), assumed arallel to the NCL, was already determined; thus, the CSL becomes totally determined if a oint, X ¼ (e X, X ) is given (the initial guess for this oint will be discussed later). 6. Using the values of k and X ¼ (e X, X )ineq5, the value of the void ratio (e a ) for the reference ressure ( a )is determined. 7. As the fall-cone test (and the mini-vane test) is considered undrained, the initial void ratios e i are the same at failure (e f ¼ e i ). 8. Using the values of void ratio (e f ¼ e i ) and the CSL, and then the values of effective mean stresses at failure (f 0 ) are obtained, by means of Eq Now for each initial void ratio condition, the corresonding deviatoric strength (q f ) is obtained from the comuted (or exerimental) undrained strength (s u ), Eq Find the best linear regression through the origin and through the oints (f 0, q f ) to obtain the sloe M of the critical state line, from which the critical state friction angle can be comuted if necessary. 11. Finally, use the comuted value of the sloe M (and value of k) to obtain a new value of e a from the coefficient a, according to Eq 12. This means that a new osition of the CSL based on the new value e a is established. 12. Comare the new reference void ratio e a with the value reviously estimated; if the difference is not accetable assume the last comute value of e a as inut value and go back to ste 7 and iterate until convergence is obtained. These rocedures will be demonstrated and validated in the next sections. Materials and Exerimental Methods The material used in this study was a kaolin, which was commercially acquired. Test results of the Atterberg limits were obtained following ASTM D (2000). Finally, the secific gravity of the soil articles was measured using an electronic helium-based ycnometer. The results are shown in Table 1. The fall-cone equiment used here comlies with BS (1990). The weight of the cone is Q ¼ 80 g and the ti angle is b ¼ 30. The cone enetration is measured by a dial gauge with a recision of 0.01 mm. The mini-vane shear tests were erformed according to ASTM D4648M-10 (2010). The test aaratus is equied with a calibrated sring and a dial gauge to measure the angular strain. The rotation velocity was between 60 and 90 er minute, and the vane ti measured 13 mm in height and width. Three samles for seven different water contents were reared, beginning from aroximately the lastic limit and gradually increasing u to values greater than the liquid limit of the TABLE 1 Material characteristics. Liquid limit, w L (%) 54 Plastic limit, w P (%) 39 Secific gravity of the soil articles, G s 2.61

6 FARIAS AND LLANO-SERNA ON PARAMETERS OF REMOLDED CLAYS 5 clay (40 % w 63 %). The samles were later stored overnight. The fall-cone tests and mini-vane tests were erformed for each one of the three samles, and the final result is the average of all tests. To avoid bias errors, all tests were erformed using the same equiment and oerator. To obtain the critical arameters, a odometer comression test following ASTM D2435/D2435M-11 (2011). The test was erformed in a samle reared with a water content w ¼ 50 % within the range described before and assuring the full saturation condition; the samle was also loaded incrementally until reaching the normally consolidated line at 1000 kpa aroximately. Accordingly, three samles with a water content w ¼ 45 % and under normally consolidated conditions were molded to erform a conventional triaxial tests according ASTM D (2011) with initial mean stress ( i 0 ) of 75, 150, and 600 kpa. The lower values (75 and 150 kpa) intend to embrace lower mean stresses develoed in fall-cone test and mini-vane, whereas the higher confining ressure (600 kpa) was chosen with the aim of aroaching the level of stresses develoed in the odometer comression test. Higher stresses could not be achieved inside the triaxial chamber because of equiment limitations. Test Results and Discussion According to Eq 1, there must be a linear relationshi between the inverse of the fall-cone enetration squared (1/h 2 ) and the remolded undrained shear strength of the clay (s u ) measured in the mini-vane test aaratus. Fig. 1 shows the calibration with the sloe reresenting the roduct KQ ¼ , which corresonds to a cone factor of K ¼ for the cone weight Q ¼ mg, with m ¼ 0.08 kg (80 g), and g ¼ 9.81 m/s 2. There is a good agreement between the exerimental data and the Hansbo (1957) exression (solid line) with a correlation coefficient R 2 ¼ The relationshi between w and the remolded undrained shear strength is exressed by Eq 3. Fig. 2 exlores the linear relationshi of Eq 3 in a bi-logarithmic sace, where the abscissa is the remolded shear strength measured in the minivane test aaratus. ATTERBERG LIMITS According to Kayabali and Tufenkci (2010), estimates from different authors for the undrained shear strength at the liquid limit range from kpa, with 1.7 kpa as the best estimate given by several researchers. Furthermore, the undrained shear strength at lastic limit ranges from kpa, with 170 kpa as the most acceted estimate. According to the results resented in Fig. 1, the enetration exected at the liquid limit, considering s u ¼ 1.7 kpa would be around 15 mm. From a different ersective, considering the BS (1990), which secifies a enetration of 20 mm (see Fig. 1), the strength measured at the liquid limit would be around 1.0 kpa, which is within the bounds reorted by Kayabali and Tufenkci (2010). Furthermore, in Fig. 2, it can be determined that the water content for s u ¼ 1.7 kpa is 58 %, an absolute difference of 4 % when comared with the exerimental value obtained following the ASTM standard (Table 1). A similar analysis could be made for the case of the lastic limit. According to Fig. 2, the exected water content for a theoretical lastic limit with strength s u ¼ kpa would be FIG. 1 Exerimental calibration of the cone factor. FIG. 2 Relationshi between remolded undrained shear strength and water content.

7 6 Geotechnical Testing Journal 30 % 32 %, It imlies an absolute difference between 7 % 9 % when comared with the results (w ¼ 39 %) obtained using the ASTM standard (see Table 1). Moreover, when the calibrated cone in Fig. 1 is used for w measurements, a enetration deth between mm is exected. It is worth of noting that this value might be very close to the equiment tolerance. Thus, a heavier cone to increase the enetration may be an alternative (Koumoto and Houlsby 2001). It is also ointed out that different methodologies and standards may lead to quite different Atterberg limit values. Therefore, it is not ossible to define a unique liquid or lastic limit value for such different testing rocedures as the fall cone, rolling rocedures, and Casagrande tests, because whereas the former enetration deth is used as a reference, in the Casagrande cu and rolling rocedure, the number of dros and oerator judgment are used resectively. These measures are totally unrelated and hard to control. It would be referable to relate the Atterberg limits to a hysical quantity or roerty of the material, for instance, the shear strength. The K factor could actually hel in determining this quantity. ESTIMATION OF THE DEFORMABILITY PARAMETERS k AND j Based on Fig. 2, the coefficients a and b of Eq 3 are calculated and summarized. The determination coefficient is very high (R 2 ¼ 0.990), which shows the good agreement between Eq 3 and the exerimental observations. The b coefficient corresonds to the comressibility coefficient k, according to Eq 13, so the fitting gives an estimated k ¼ To validate the result obtained here based on the falling-cone results, the traditional one-dimensional odometer FIG. 3 Void ratio, ln 0 curve from odometer comression test. 0 is given in kpa. test on the same kaolin soil is shown in Fig. 3, where the obtained results are lotted in a grah of void ratio e versus ln 0. To calculate 0 for the odometer comression, it is necessary to know the lateral stress. For this goal, we used an analytic solution based on the modified Cam-clay model for normally consolidated soils assuming that the elastic deviatoric strain is different from zero. This aroach was roosed by Wood (1990) to obtain the following exression: and g k0 ð1 þ Þð1 KÞ þ 3g k 0 K 3ð1 2Þ M 2 g 2 ¼ 1 (14) k 0 K ¼ k j k (15) g k0 ¼ 31 ð k 0Þ (16) 1 þ 2k 0 K ¼ lastic volumetric strain ratio, ¼ Poisson s ratio assumed as 0.498, aroximately 0.5 to ensure the saturated undrained condition in clay, j ¼ elastic coefficient of comressibility, g k0 ¼ stress ratio q/ 0 under conditions of zero lateral strain, and k 0 ¼ lateral stress coefficient. Note that the comutation of k 0 imlies knowing the values of k, j, and vice versa. To solve this issue, a first estimate of k and j was obtained by assuming k 0 equal to one. Afterward, using Eqs 14 and 15, a new lateral stress coefficient was calculated. (This rocedure imlies knowing the value of M, which is shown later in the text.) Note also that if ¼ 0.5, the first term in Eq 14 is undefined, meaning that the constrained modulus is infinite and no deformation occurs. The iterative rocess was reeated and after two iterations the calculation converged. A value k 0 ¼ 0.78 was obtained and used to calculate and lot Fig. 3. In Fig. 3, it is also ossible to see the high comressibility of the kaolin clay. The mean stress was increased u to 1400 kpa aroximately. Whereas in OED01, it was not clear that the normal consolidation line was achieved, a linear regression in the last stretch of the comression curve shows a sloe of k 1 ¼ 0.147, matching very closely the aroximation given by Eq 13, k ¼ In the other hand, OED02 erforms a quicker transition to the NCL. A best fit through the last four oints measured gives a sloe k 2 ¼ Desite the difference of the initial void ratio, both tests converge to the NCL as the mean effective stress increases, obtaining a mean value of k ¼ 0:150 used as reference in the comutations therein.

8 FARIAS AND LLANO-SERNA ON PARAMETERS OF REMOLDED CLAYS 7 Desite the ositive results described above, it must be highlighted that the aroximation obtained using the fall-cone test uses the definition of lambda given in Eq 6 rather than the traditional formulation, given by Eq 5. The difference between the void ratios comuted using Eqs 5 and 6 is not significant to low stress levels. Nevertheless, this difference is not constant, and the consequences of assuming Eq 6 in our derivations will be discussed later in this section. Schofield and Wroth (1968) also roosed that the virgin coefficient of comressibility (k) is highly correlated with the elastic coefficient of comressibility uon unloading and reloading, and the relation established in Eq 15 should be constant for a given soil. According to Federico (1989), K ¼ 0 stands for a erfectly elastic soil, whereas K ¼ 1 means a erfect lasticity, and, in the case of kaolin, a highly comressible clay, a value of K ¼ 0.85 may be assumed. This value is relatively close to K ¼ 0.81 roosed by Schofield and Wroth (1968) for kaolin. The mean exerimental values of k and j, in the semi-ln sace in Fig. 3, gives the value K ¼ for the kaolin tested in this investigation. The establishment of this constant K in Eq 15 considers the e- 0 relation given in Eq 5. Nevertheless, if we use the ln ln relation as described in Eq 6, the value K ¼ is obtained, which is less than a 1 % error comared to K ¼ Assuming K constant and considering the value of k obtained from the fallcone test, the elastic coefficient of comressibility would be estimated around j ¼ This value is not very far from the exerimental value j ¼ obtained from the unloading section of the odometer test (see Fig. 3). Furthermore, it should be emhasized that j is not a critical arameter for normally consolidated clays because most of the volumetric strains (more than 80 %) in this case are lastic. Note, however, that this statement considers that the materials are submitted to comression aths and the assumtion must be taken carefully when analyzing different loading aths. e i ¼ The initial void ratios were obtained by measuring the samles water content and calculating the void ratio for the known volume and weight of the casule used in the fall-cone test, furthermore individual measurements of the mass of the casule and samle set were made to erform the void ratio calculations. All of the obtained values are listed in Table 2. The values in this table corresond to the first estimates (oen symbols in Fig. 4). Then the values of q f, according to Eq 10, are obtained and listed in the same table for a ¼ 2 and a ¼ 3. Using Eq 8, it is ossible to fit a straight line on a tyical -q lot and calculate the M arameter. This is shown in Fig. 5, for the first estimate, from which it was ossible to obtain values M ¼ 1.06 (for a ¼ 2) and M ¼ 0.92 (for a ¼ H3). The corresonding values of e a, based on Eq 12, are in both cases, which are very close to the initial guess (e a ¼ 0.916) based in oint X. The error between the initial guess and the first iteration was around 0.8 %. Nevertheless, to check the roosed methodology, the authors carried out the iterative rocedure using the new values of e a to obtain new estimates of the values of M, and new ositions of the CSL, until the difference between two comuted values of e a was less than 0.01 %. During the iterative rocedure, the values of e a decreased, and the values of M increased gradually. The rocess converged slowly and reached the desired accuracy (0.01 %) after 47 iterations, giving the final values e a ¼ 0.903, M ¼ 1.16 for a ¼ 2, and e a ¼ 0.903, M ¼ 1.00 for a ¼ 3. The final estimates are also shown in Fig. 5. It is worth mentioning that different researchers reort M values for kaolin in the range of (Schofield and Wroth 1968; Rossato et al. 1992; Terzaghi et al. 1996; Khalili et al. 2004; Nuth and Laloui 2008), which matches fairly well with our results. FIG. 4 Void ratio, ln 0 curve for CSL determination. 0 is given in kpa. ESTIMATION OF THE STRENGTH PARAMETER M AND REFERENCE VOID RATIO e a For calibrating the sloe (M) of the critical state line in a ( 0, q) sace, it is necessary to locate initially the rojection of the CSL in the e-ln( 0 ) sace. According to Schofield and Wroth (1968), the exerimental observations of critical state lines of several soils can be geometrically extended to a single reference oint X ðe X ffi 0:25; X ffi kpaþ, where all of the critical state lines (e ln 0 sace) seem to ass through, or very near. Passing a line through oint X with sloe k, from the fall-cone test (k ¼ 0.144), the critical state line becomes totally defined in the e-ln( 0 ) sace, and the reference value e a ¼ is obtained from Eq 5. Using the initial void ratios and the CSL determined above, the values of 0 at failure are obtained as shown in Fig. 4 for

9 8 Geotechnical Testing Journal TABLE 2 Estimated stresses at failure from mini-vane tests. e i s u (kpa) 0 f (kpa) q f ¼ 2s u (kpa) q f ¼ 3 su (kpa) FIG. 6 Comarison between the results from the roosed methodology and a CTC effective stress ath. Again, is ossible to evaluate the effects of using Eq 6 instead of Eq 5 in the derivations resented. Adoting a calibrated e a ¼ and the arameter k ¼ from the fallcone test is ossible to calculate the void ratio using Eq 6 and Eq 5. Is also ossible to consider the range of mean stresses described along this aer and the results show that the difference in void ratio when Eq 6 is considered instead of Eq 5. The related difference is u to 5 % for kpa, 10 % for 0 750, 15 % for , and 18 % for The estimated values of friction angles were validated, a osteriori, using consolidated undrained (CU) conventional triaxial comression (CTC) tests, using the same kaolin clay. Fig. 6 shows the effective stress aths obtained from the CU-CTC tests and the critical state failure line estimated from our methodology (dashed line and oen circles). During the CTC tests, the kaolin samles initially showed a contractive behavior, with increasing ore water ressures, u to a certain dislacement. The ore ressure eaks were observed in the range of 3 % 4 % of axial strain for the three tests. The contractive behavior is shown by the branch of the stress aths heading to the left and uwards in Fig. 6. Then the aths make a turn to the right, corresonding to an exansive behavior with a decrease of ore ressure. The decrease of ore ressure leads to an increase in effective mean stresses and consequent gain of strength. Only the test for i 0 ¼ 600 kpa reached the critical state line; for the lower confining stresses the samle showed excessive bulging and the tests had to be stoed when strains reached 13 %, as shown in Fig. 7, because of limitations in the course of the measuring devices [linear variable differential transformers (LVTDs)]. FIG. 5 Critical state line on a q- 0 sace. FIG. 7 Stress strain curves of CTC test for kaolin clay.

10 FARIAS AND LLANO-SERNA ON PARAMETERS OF REMOLDED CLAYS 9 The oints corresonding to the limit between contractive and exansive behavior are used to draw through a straight solid line as seen in Fig. 6. The sloe of this line is M ¼ This sloe is smaller than the estimated here considering a CTC condition (a ¼ 2). However, we note that the late dilative art of the effective stress aths has an ambiguously large inclination, with a tangent that indicates an effective critical state friction angle larger than Furthermore, the differences in the inclination of the dilative stretch of the stress aths may be attributed to the rearation rocess and the rocedure to lace the samle inside the triaxial chamber. As a matter of fact, dealing with normally consolidated and high comressible clays can make this rocess highly challenging. Coincidentally, the sloe obtained in CTC is close to the one comuted for a ¼ 3 from the vane test condition, but we do not see a hysical relation between these facts. Conclusions The aer shows a simle methodology to estimate imortant deformability (k and j) and strength (M) arameters for remolded soils, such as those used in the well-known Cam-clay model, based solely on the enetration of a falling cone on clay samles at different water content. The methodology is based on the relation between fall-cone enetration and remolded undrained shear strength (s u ) of clays, as roosed by Hansbo (1957) and the lastic volumetric strain ratio (K). It should be emhasized the imortance of a revious and roer calibration of the fall-cone factor (K) roosedhansbo (1957). Ad hoc assumtions about this fundamental characteristic of the equiment may lead to inaccurate results. Here, the calibration of the fall-cone factor was achieved using data of fall-cone enetration (h) versus the corresonding remolded undrained shear strength (s u ) obtained from mini-vane shear tests. The methodology was alied to determine deformability and strength arameters of kaolin using a 30, 80 g cone (also called British cone). The choice of this aaratus was because of the relative lack of research about its fall-cone factor comared to the alternative falling cone with 60 of ti angle and 60 g of mass, adoted in countries such as Sweden, Norway, Canada, and Jaan. The good correlation between the exerimental data and the theoretical curve of enetration versus remolded undrained strength, roosed by Hansbo (1957), and the emirical relationshi between the water content (w) and the remolded undrained shear strength (s u ), roosed by Koumoto and Houlsby (2001), corroborate the accuracy of these models. Moreover, the values of deformability arameter comuted for the kaolin using the fall-cone enetration data matches closely with the values obtained from conventional laboratory tests. The exression roosed by Koumoto and Houlsby (2001) was adjusted with a factor a ¼ 3 instead of a ¼ 2, to account for the stress state of the mini-vane test. The use of the minivane shear equiment allows to obtain better constitutive data because the influence of anisotroy is largely removed in remolded samles. This means that the alicability of the rocedures described here may not be suitable for its use in undisturbed soils. The authors also roosed further stes to obtain the strength arameters (M). This includes an initial estimate of the osition (e a ) of the critical state line in the e-ln( 0 ) sace, which is later adjusted using an iterative rocedure. Using the aroriate relation between the deviatoric stress invariant at failure (q f ) and the remolded undrained shear strength (s u ), the authors comuted strength arameter comatible with those reorted in the literature for kaolin. The estimated values were also checked by comaring with the strength arameters obtained from undrained triaxial comression tests. However, the comarisons erformed here are limited, and further tests are required to firmly validate the roosed methodology. The study shows that the falling cone if roerly calibrated is a reliable tool to estimate the remolded undrained shear strength and deformability of remolded clays. Desite the limited validation, the simlicity of the methodology roosed and the low cost of the falling-cone test may rovide an attractive tool to obtain arameters for reliminary analyzes. The simlicity of the rocess might also be attractive for engineering roblems where large testing involves remolded clays under normally consolidated conditions. ACKNOWLEDGMENTS The writers acknowledge the financial suort of the Brazilian National Research Council (CNPq) and the Coordination for the Imrovement of Higher Level Education Personnel (CAPES). 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