Estimation of Coefficient of Earth Pressure at Rest Using Modified Oedometer Test
SOILS AND FOUNDATIONS Vol. 47, No. 2, 349–360, Apr. 2007 Japanese Geotechnical Society
ESTIMATION OF COEFFICIENT OF EARTH PRESSURE AT REST USING MODIFIED OEDOMETER TEST
NIPON TEERACHAIKULPANICHi),SATOSHI OKUMURAii),KAZUAKI MATSUNAGAiii) and HIDEKI OHTAiv)
ABSTRACT
A series of experimental trial for estimating the coe‹cient of earth pressure at rest, K0, is presented. The developed apparatus is a modiˆed Oedometer covered with pressurized chamber specially designed for K0 determination based on the principle of eŠective stress originally proposed by Ohta et al. (1979). K0 is estimated from the developed apparatus primarily by means of load cell and auxiliary by means of pore pressure transducer aiming at conˆrming the test results. K0 triaxial consolidation is carried out to verify the result of purposed method. K0 values are obtained using Oedometer tests on two samples one of which is taken horizontally and the other is taken vertically from a block sample and K0 values from empirical equation are also estimated for comparison. It was found that the proposed method gives a comparable K0 of kaolin to K0 triaxial consolidation method but somewhat higher than those from empirical equations and lower than K0 obtained using Oedometer.
Key words: coe‹cient of earth pressure at rest, consolidation, eŠective stress, friction, kaolin (IGC:D5)
Nevertheless, there are published research measurements INTRODUCTION of K0 with methods chosen to provide the condition that In many geotechnical problems, the initial state of the lateral strain is zero. These methods can be classiˆed stress existing in the ground is an important parameter in two categories: (1) in-situ methods; (2) laboratory that must be known for designs and analysis. The in-situ methods. vertical eŠective stress, s?v at any depth can be simply estimated from the proˆles of overburden pressure and In-situ Methods pore water pressure. On the contrary, the in-situ horizon- The in-situ tests to evaluate K0 have been proposed by tal eŠective stress, s?h, is di‹cult to directly measure and many researchers that can be grouped into three also di‹cult to estimate empirically because it depends categories. The direct tests involve very small disturbance not only on the soil properties but also on the geological in the soils caused by the insertion of test devices such history of soil deposits and is most often approximated. as Self-boring Pressure meter (Baguelin et al., 1972; The relationship between the vertical eŠective stress Jezequel, 1972; Wroth and Hughes, 1973; Hamouche and the horizontal eŠective stress under conditions of et al., 1995). The semi-direct tests involve inserting zero lateral deformation is usually expressed by probes in the ground without any precaution for avoiding coe‹cient of earth pressure at rest K0＝s?h Ws?v . disturbance such as, A large pile instrumented with total The coe‹cient of earth pressure at rest, K0, has been pressure cell (Kenney, 1967), Hydraulic Fracturing studied by geotechnical engineers for many years for its (Bjerrum and Andersen, 1972; Bozozuk, 1974; Lefebvre being an essential parameter in designs and analysis of et al., 1991; Hamouche et al., 1995), Total Pressure Cells many geotechnical problems such as earth retaining (Massarsch, 1975; Massarsch and Broms, 1976; Tavenas, structures, piles, and slope stabilities. Moreover, in the 1975), Dilatometers (Marchetti, 1980; Hamouche et al., last few decades, K0 represents an essential step in any 1995), K0 Stepped Blade (Handy et al., 1982; Handy numerical analysis of soilWwater coupled geotechnical et al., 1990), and Cone penetration test (Masood et al., boundary value problems involving constitutive stress- 1993). The non destructive method involves measuring strain-time formulations. shear wave velocity of cohesionless soils (Fioravante
The information of K0 in soft soils is limited by the et al., 1998; Hatanaka et al., 1999). di‹culty of sample handlings and measurements under However, the diŠerent methods of in-situ evaluation of the strictly deˆned condition of no lateral displacement. K0 gave some variations on K0 due to many uncertainties
i) Doctoral Candidate, Department of Civil Engineering, Tokyo Institute for Technology, Japan (nipon＠ide.titech.ac.jp). ii) Engineer, Obayashi Corporation, Japan. iii) Engineer, Chuoh Consultants Co., Ltd., Japan. iv) Professor, Department of International Development Engineering, Tokyo Institute of Technology, Japan. The manuscript for this paper was received for review on March 27, 2006; approved on November 17, 2006. Written discussions on this paper should be submitted before November 1, 2007 to the Japanese Geotechnical Society, 4-38-2, Sengoku, Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.
349 350 TEERACHAIKULPANICH ET AL.
Fig. 1. COWK triaxial apparatus ESTIMATION OF COEFFICIENT OF EARTH PRESSURE 351
relatedtosensitivityofderivedK0 to the small distur- bance caused by inserting the probe into the ground.
Laboratory Methods The laboratory methods fall into two distinct classes. The ˆrst uses a rigid lateral boundary; consolidometer type, which provides the required ``zero lateral strain'' condition but also allows undeˆned friction between the wall and the soil such as Semi rigid Conˆning Ring (Newlin, 1965), Null Type Conˆning Ring (Brooker and Ireland, 1965; Singh et al., 1973), COWK (Ohta et al., 1979), Semi-rigid Consolidometer (Abdelhamid and Krizek, 1976; Edil and Dhowain, 1981; Mesri and Hayat, 1993; Ting et al., 1994). The second uses a ‰exible lateral boundary with a feedback system to maintain the position of boundary; triaxial types such as Rigid Cell (Davis and Poulos, 1963), Controlled Volume Triaxial (Lewin, 1970), Null Type Triaxial Test (Bishop, 1958;
Moore and Spencer, 1972) Automatically simulating K0 Fig. 2. Concept of K0 estimation consolidation and K0 swelling in triaxial cell (Menzies et al., 1977), A Simple K0 Triaxial Cell (Campanella and
Vaid, 1972), Double cell K0 triaxial apparatus (Okochi tion, supplying with cell pressure (CP) and back pressure and Tatsuoka, 1984), K0 consolidation test in triaxial (BP) in order to eŠectively dissolve any small volume of apparatus (Fukagawa and Ohta, 1988), Triaxial strain entrapped air in the specimen. path testing (Lo and Chu, 1991), Automated K0-consolia- The total stress becomes equal to the eŠective stress tion apparatus in triaxial cell (Tsuchida and Kikuchi, plus the back pressure after the completion of primary 1991; Watabe et al., 2003). The advantage of using a consolidation as shown in Fig. 2 ‰exible lateral boundary is the absence side friction but sv0＝s?v0＋u0 (1) the disadvantage is how to control the soil specimen to be zero lateral strain as well as ensuring the uniformity of sh0＝s?h0＋u0 (2) eŠective stress in the specimen. in which u0＝BP (back pressure) Most of the presently employed laboratory methods After completion of primary consolidation, the are rather complicated and usually time consuming in drainage valve is closed and the container ring is to be consolidating a specimen. In this study, a method for eliminated by withdrawing downwards. During this estimating K0 is examined by using the modiˆed process, the constant eŠective stresses are needed to be Oedometer covered with a pressurized chamber. The kept unchanged under undrained condition by means of method employed in this investigation can be categorized having no additional deformation. Thus, the specimen as an indirect semi-rigid ring type. The advantages are volume and vertical displacement are kept constant after that soil can be consolidated under conditions of perfect- closing the drainage valve and by means of ˆxing the ly no lateral deformation, lesser time and low operational movement of york (9) shown in Fig. 1(b). cost. No volume change and no vertical displacement provide no lateral displacement resulting in no deforma- tion at all. This ensures that no change in eŠective stress TESTING APPARATUS state takes place during the process of container ring Concept withdrawal. The concept of modiˆed Oedometer with a pressurized After withdrawal of container ring, the specimen is chamber mounted on a consolidation machine was exposed to the rubber membrane being pressurized by cell invented and developed by Ohta et al. (1979). The acro- pressure (CP). The total horizontal stress becomes equal nym ``COWK (Cambridge-Ohta-Wroth-Kyoto) triaxial to the cell pressure and the pore water pressure changes to apparatus'' was coined to call the developed apparatus as u1 while the eŠective stresses remain constant as shown in shown in Figs. 1(a) and (b). The soil specimen (1) is Eqs. (3) and (4): placed in the container ring (2). The outside of container sv1＝s?v0＋u1 (3) ring is covered with a rubber membrane (3). Two of rubber o-rings (4) and (5) are ˆtted over the membrane sh1＝s?h0＋u1 (4) and the other o-ring (6) is in the groove of the pedestal (7) Substitution of sh1＝CP into Eq. (4) yields: to provide the seals. Additionally, the vertical drainage is s? ＝CP－u (5) provided by a cast-in-place high air-entry ceramic disk (8) h0 1 sealed in the top portion of the pedestal. The soil speci- in which u1 is pore water pressure measured by pressure men is consolidated in the container ring; K0 consolida- transducer (10) after the withdrawal of the container ring 352 TEERACHAIKULPANICH ET AL.
(2). Top Cap Interlocking
Consequently, K0 is determined by Eq. (6): The main objective of the newly designed apparatus is to build the simple apparatus for K measurement. The s? CP－u 0 K ＝ h0＝ 1 (6) simple design of the loading system of COWK triaxial 0 s? s? v0 v0 apparatus is shown in Fig. 1(a). This kind of loading sys- since s?v0 is already known as the consolidation pressure tem performs properly when the load is increasing. during the preceding consolidation process. However, the withdrawal of the container ring causes
Moreover, substitution of u1 from Eq. (5) into Eq. (3) slight inclination of the top cap. This is due to a slight yields: inhomogeneity of the consolidated specimen which then produces some interlocking between the top cap and the s ＝s? ＋CP－s? (7) v1 v0 h0 hole in the upper plate through which the top cap comes Then,Eq.(7)minusEq.(1)yields: out of the triaxial chamber. Therefore, the change in
vertical total stresses, sv0－sv1,inEq.(9)isveryoften sv1－sv0＝(s?v0＋CP－s?h0 )－(s?v0＋u0) (8) reduced by the interlocking. The method for estimating s?h0＝CP－u0＋(sv0－sv1) the actual change in sv0－sv1 by eliminating the eŠect of Thus, K0 is also determined by Eq. (9): interlocking will be described later.
s?h0 CP－u0＋(s?v0－sv1) K0＝ ＝ (9) Description of Main Components s?v0 s?v0 Figure 1(a) shows the apparatus with all essential
The diŠerence of vertical total stresses (sv0－sv1)is details. The apparatus is made from a precision- measured by means of load cell (11) attached on the top machined rigid stainless steel consisting of Perspex cylin- cap (12) as well as by the load cell (13) which detects the drical chamber (14), (200 mm in diameter, 200 mm in change of reaction to the york. Both of pressure trans- height, and 20 mm in thickness), upper and lower end ducer (9) and load cell instrumentations (11) and (13) are plates (15) and (16) which are connected by three of riser used to conˆrm the estimation of K0 value. legs (17), shown in Fig. 1(b), located inside the chamber. Thechamberissealedbymeansofrubbero-rings(18), Friction (19) and silicone grease sealant. The cell is supported by Side Friction Cut the base plate (20) connected by three of riser legs (21). In reality, the side friction between the container ring The pedestal (7) is screwed in the lower end plate (16). and the consolidating soil exists along the container ring. Rubber o-rings are used to provide the seals; one (6) The side friction directly aŠects the estimation of located in the groove at 25 mm from the top of pedestal coe‹cient of earth pressure at rest due to the reduction of and the other one (19) in the bottom of pedestal. A vertical eŠective stress. In order to transfer most of the ceramic disk (8) (air entry value＝300 kPa) is installed at vertical load to the specimen, change of direction of the the top portion of the pedestal to provide the vertical friction from upward to a little bit of downward is drainage. required. Downward pre-withdrawal of container ring The dimension of container ring (2) is 60 mm in inter- after the completion of the primary consolidation is the nal diameter, 90 mm in height, and 6 mm in thickness. technique to change the friction direction. Several steps The inside surface of the container ring is coated with of pre-withdrawal of container ring are performed in chromium in order to reduce the friction. With this order to make the vertical eŠective stress as equal as the diameter size, undisturbed sample taken by thin-walled applied load. tube, diameter 75 mm, is also applicable. Furthermore, the thickness of container ring is thick enough for
Excess Pore Water Pressure due to Side Friction preventing any lateral stain during K0 consolidation. The During withdrawal of container ring under undrained top cap (12) dimensions are 60 mm in diameter and 90 conditions, some excess pore water pressure is also mm in height. Weight of top cap is 1.972 kg causing the generated. It is believed that this pore water pressure uf is addition of axial vertical pressure of about 7 kPa once it caused by side friction. This excess pore water pressure is placed on top of the specimen. causes the decrease in eŠective stresses. Therefore, it is K0 value must be measured under conditions of no unavoidable to obtain a K0 value of slightly over volume change and no deformation with the purpose of consolidation in which slightly higher than K0 of normal keeping the eŠective stresses unchanged. In order to consolidation. The change of pore water pressure due to satisfy these conditions, the rubber membrane (3), 0.025 the specimen exposure to the cell pressure deˆned as u* is mm thick, is wrapped on the container ring and top cap. measured as the summation u1＋uf. In order to obtain u1 Three of rubber o-rings are used to provide the seals; the for Eq. (6), uf has to be estimated by measuring the pore ˆrst one (4) is located on the container ring and ˆxed its water pressure during pre-withdrawal of container ring. vertical movement by o-ring holders (22), the second It should be noted that the pore water pressure due to o-ring (5) is on the top cap, and the last o-ring (6)) is friction uf gives no eŠect on Eq. (9). located in the groove on the pedestal. The withdrawal of container ring is performed by screwing three of the jacking bars (23) against the ESTIMATION OF COEFFICIENT OF EARTH PRESSURE 353 container ring by means of wrenches. the water content. The top cap is placed on top of the specimen separated by a ˆlter paper. The container ring is Control System slide up about 12 mm with the aim of providing the Figure 1(b) illustrates the typical COWK triaxial distance for pre-withdrawal. The silicone oil is used for apparatus test set-up. The apparatus is mounted on the lubricating the surfaces between container ring, top cap consolidation machine. The cell pressure and back and rubber membrane. An entrapped air is taken out as pressure tube are connected to the outlets located at the much as possible after placing the membrane. Two of the lower end plate and the pedestal outlet respectively by rubber o-rings are placed on the container ring and top means of 1W8 inch (3.2 mm) copper tube and ˆtting. cap. The cream silicone grease is painted on the outside of Pressure transducers (10), (24) (TEAC 1 MPa model membrane in order to minimize intrusion of the air TP-BR1MP) are attached to the BP and CP drainage through the membrane into the specimen during the test. paths. The cell pressure and back pressure are controlled The o-ring holders and riser rods are placed in order to by the precision regulator (25) and air supply compressor prevent the movement of o-ring at the middle of contain- (26). er ring during withdrawal of container ring. The axial vertical loading is applied by means of dead For the cell assembler, the double o-rings are ˆrst weight (27) on loading system of consolidation frame. A placed in the groove of the upper and lower end plate load cell (11) (TEAC model TT-FR 10 kN) is connected lubricated and sealed by the silicone grease sealant. Three to the top cap (12) and attached to the york (9) for poles of riser rods are screwed on the lower end plate. The vertical stress measurement. The specimen deformation is Perspex cylindrical chamber is placed on the lower end measured by the axial dial gauge transducer attached to plate and then the upper plate is placed on the top by the stand bar (28) and its tip is sitting on the top of york. orienting the direction of holes right to the riser rods and The movement ˆxing of the loading ram is set by top cap. All bolts are screwed into the riser rods to supporting the loading plate (29) with a load cell (13) assemble all parts together. Next, the load cell is attached (Kyowa model LC-20KA) mounted on the screwed jack on the top cap. The COWK triaxial apparatus is then (30) in order to resist and prevent the downward mounted on the consolidation machine. The center of movement of the loading plate shown in Fig. 1(b). For loading ram is adjusted right to the center of york. The the upward movement prevention, an additional dead jacking bars are placed and ˆxed on the upper plate. The weight is placed on the loading plate. The withdrawal cell pressure and back pressure lines are connected to the distance is monitored by the axial dial gauge transducer water pressure supply system. At this stage, the pressure (31) placed on top of the jacking bar. transducer and load cell are set the reading to zero All data are measured by electronic load cell, electronic relative to atmospheric pressure. The york is lowered pressure transducers, and axial dial gauge transducers. down to sit on the load cell and connected together. The The signals from these measuring devices are set to collect water is ˆlled into the chamber via the air-bleed valve. at every one second and then are saved to data logger (32) Finally, the chamber is fully ˆlled by silicone oil (Shinetsu (Kyowa EDX-1500A Digital Memory RecorderWAnalyz- KF-96-3000CS) in order to retard the cell water to leak er) in which data are acquired and stored. out through the small gap between the top cap hole on the upper plate.
EXPERIMENT PROGRAM Consolidation Clay Investigated Consolidation is performed by step-wised incremental In this study, kaolin is used as the specimen to verify loading. The specimen is loaded by the dead weight. Since the proposed methods because of many research evi- the specimen is preconsolidated at 39.2 kPa, the total ver- dences, convenient in a preparation, homogeneity when tical stresses of 100, 200, and 300 kPa are selected to con- purchased commercially, and generally low degree of solidate the specimens before withdrawal of container creep. The type of kaolin used in this study is a white ring to measure K0. powder marketed ASP100. The liquid limit, plastic limit The loading preparation is suggested by following and speciˆc gravity are 77z,28z and 2.61, respectively. procedures. Firstly, for example of consolidation at The slurry kaolin is prepared by mixing kaolin powder vertical eŠective stress of 100 kPa, gradually increase the with the distilled water at water content of 120–130z by cell pressure to 300 kPa while the drainage valve is closed. weight. The mixture is then thoroughly stirred by means Secondly, the vertical loading of 200 kPa is applied to the of a motor-driven rotary mixer at atmospheric pressure specimen by means of dead weight. Thirdly, gradually for one hour and de-aired under vacuum for another one increase the back pressure to 200 kPa and then open the hour. drainage valve. The specimen is under the equilibrium condition because the previous vertical loading is Specimen Preparation canceled by the back pressure. Finally, the additional The slurry kaolin is poured into the container ring and vertical loading of 100 kPa is applied to consolidate the pre-consolidated at 39.2 kPa for one day. The specimen specimen. istrimmedinto20mminheight.Theexcesssoilis The measurement of pore water pressure in undrained extruded out and taken for three samples to determine condition allows calculating the pore pressure coe‹cient 354 TEERACHAIKULPANICH ET AL.
B indtroduced by Skempton (1954). B value is measured after the primary consolidation is completed and before withdrawal of the container ring. The use of B value will be described later.
Withdrawal of Container Ring The withdrawal of container ring as stated in previous section will be explained here in detail. The pre- withdrawal procedure is needed to perform in order to make the specimen fully consolidated under the applied (intended) vertical load and to estimate the pore water pressure generated by the cut of side friction. After the primary consolidation is completed, the drainage valve is closed to provide the undrained condition. Then, the Fig. 3. Correction of u1 using coe‹cient of pore water pressure B jacking bars are gradually screwed downward against the container ring. The withdrawal distance is monitored by a dial gauge transducer attached on the top of jacking bar. The change in pore water pressure uf is recorded during the pre-withdrawal of container ring. After ˆnishing the pre-withdrawal at each step, the drainage valve is opened to allow the specimen to further consoli- date. Total length of pre-withdrawal is determined by the set up level of container ring plus the specimen deforma- tion after consolidation (12＋Dd ) mm. Two times of pre- withdrawal of averagely 5 mm are performed at each step. Finally, the last step is the full withdrawal of container ring to expose the specimen to the cell pressure directly applied to the specimen through the rubber membrane. The drainage value is closed out of back pressure. The Fig. 4. Principal stress diŠerence and axial strain movement of loading ram is ˆxed as described earlier. At this stage, there is a small change in pore water pressure loading to the specimen under undrained condition and possibly due to a slight disturbance in the mechanical then the response of the pore water pressure is measured. loading system of the consolidation machine. Therefore, The response curve for not fully saturated specimen the new record of pore water pressure and vertical load could be obtained from these data. This response curve are updated to use in the calculation. will be used for u1 correction later.
Pore Pressure Measurement Estimation of Top Cap Interlocking The response of pore pressure induced by change in As state earlier, due to a slight inclination of the top total stress under undrained condition is usually ex- cap caused by inhomogeneity of the consolidated speci- pressed by Skempton's pore pressure coe‹cient A and B men, some interlocking results around the top cap and its (Skempton, 1954): hole in the upper plate after withdrawal of container. This amount of interlocking can be checked after Du＝B [ Ds ＋A( Ds －Ds )] (10) 3 1 3 withdrawal of the container ring by applying the vertical In partially saturated soils, the compressibility of the load to the specimen. This additional application of the pore ‰uid is appreciable due to the presence of pore air vertical load brings the specimen into a state of undrained resulting in a pore pressure parameter lower than 1.00. compression. The relationship of principal stress The value higher than 0.95 is generally accepted as diŠerence Dq and the axial stain during this undrained satisˆable enough for any practical test. However, the compression process is used to estimate the total stress change in u1 is somewhat in‰uential to K0 value in Eq. (6) change, sv0－sv1 in Eq. (9), because the axial strain starts when the vertical eŠective stress is low. To obtain more to increase only after the vertical compressive load reliable K0 from Eq. (6), the correction of pore pressure becomes large enough to overcome the interlocking measurement is needed to apply. between the top cap and the hole in the upper plate of the For the fully saturated and partially saturated speci- cell through which the load is transmitted to the top cap men, the response of pore water pressure is illustrated in asshowninFig.4. Fig. 3. In this study, the pore pressure parameter is measured while specimen is covered by the container ring. EXPERIMENTAL RESULTS AND DISCUSSIONS Thus, Eq. (10) is reduced to Du＝BDs1. The incremental dead weight of 10 kPa is used to apply the vertical Some of the results obtained by the new apparatus are ESTIMATION OF COEFFICIENT OF EARTH PRESSURE 355
Fig. 5. Pre-withdrawal of container ring after completion of consoli- dation described in this section. Since the measured quantities show the similar characteristic, only the result for the case of s?v ＝105 kPa is described in detail here. Fig. 6. Full withdrawal measurements
Estimation of uf Figure 5 shows the pore water pressure induced by pre-withdrawal under undrained condition. Also, the other tests show the similar characteristics. It can be seen that pore water pressure increases after each of pre- withdrawal of container ring. The ˆrst step of pre- withdrawal gives the peak and subsequently increasing residual values of the pore water pressure generation. After opening the drained valve to release the excess pore water pressure, the specimen further consolidates as shown in Fig. 5 for the vertical displacement of specimen and time relation. This further displacement is large in the ˆrst step and smaller in the next step indicating the success of the side friction cut.
Full Withdrawal of Container Ring Figure 6 shows the measurement of load cell and pore pressure transducer for the full withdrawal of container ring. The pore water pressure and load cell increase while Fig. 7. Pore pressure curve response in case of s?＝105 kPa the container ring is being withdrawn. Very small amount v of vertical displacement in the extension side is observed after completion of withdrawal. It is inevitable to have kPa) on specimen under undrained condition by means this type of displacement because a change of force of dead weights in order to estimate B value as described makes the diaphragm inside the load cell to deform. earlier. The data points were used for constructing a ˆtting curve based on linear relationship as shown in
K0 Determination Fig. 7. Substitution of u1 in the curve ˆtting equation By Pore Pressure Transducer yields the corrected u1 equal to 223 kPa. Then, substitu-
From Figs. 5 and 6, uf is about 32 kPa and u* is about tion of corrected u1 in Eq. (6) yields K0 by means of
254 kPa. Thus, u1 obtained by u＝u*－uf is 222 kPa. pressure transducer equal to 0.72. Nevertheless, it is necessary to correct the value of u1 by considering the saturation of specimen. After the By Load Cell completion of primary consolidation but before The correction of K0 values by means of load cell is performing pre-withdrawal of container ring, the pore performed after pore water pressure change due to full pressure parameter was measured by applying ˆve withdrawal of container ring becomes constant. Figure 8 incremental vertical loadings of 10 kPa (total Ds1＝50 shows the increment of principal stress diŠerence Dq 356 TEERACHAIKULPANICH ET AL.
Table 1. COWK triaxial test summary
Test 12345
Initial water content, wiz 71.85 77.71 78.44 79.77 78.59
Initial void ratio, e0 1.88 2.03 2.05 2.08 2.05
Void ratio at s?v , es?v 1.58 1.49 1.41 1.55 1.41 B value 0.96 0.90 0.84 0.71 0.69
s?v (kPa) 105 203 301 105 105 OCR 11123
K0 by means of pore pressure transducer
uf (kPa) 3224291321 u* (kPa) 256 264 263 300 291
(a) Deviator stress and axial strain Corrected u1 (kPa) 224 246 277 304 299 CP (kPa) 300 399 499 399 399
K0 from Eq. (6) 0.71 0.75 0.74 0.90 0.95
K0 bymeansofloadcell Lower1433559184 Corrected Most s?v0－s?v1 24 41 74 94 90 (kPa) likely Upper 32 49 85 100 94
CP-BP 95 196 291 193 193
Lower 0.77 0.80 0.78 0.97 1.04 Most K0 from Eq. (9) 0.68 0.76 0.72 0.94 0.98 likely
Upper 0.60 0.72 0.68 0.89 0.94
bit lower than the others. The B value tends to low as the vertical eŠective stress and overconsolidation ratio increase. K values of normally consolidation are falling (b) Ds? and Dd with time 0 in the range of 0.71–0.75 for Eq. (6) and 0.68–0.76 (most Fig. 8. Correction of load cell measurement likely value) for Eq. (9) both pore pressure transducer
andloadcellmeasurements.Also,K0 values of over- against axial strain in triaxial compression after measur- consolidated specimens are higher as expected from the ing K0 based on the pore pressure transducer. It can be past studies (Brooker and Ireland, 1965; Wroth, 1972; clearly seen that principal stress diŠerence is increasing Abdelhamid and Krizek, 1976; Edil and Dhowian, 1981; while the axial strain is zero. However, the principal Mayne and Kulhawy, 1982; Garga and Khan, 1991; Mesri stress diŠerence calculated by using the average cross and Hayat; 1993; Ting et al., 1994). sectional area; A＝A0(1－ev )W(1－ea) shows a band as shown Fig. 8(a) due to resolution of the dial gauge transducer within the range of about 0.008 mm (in COMPARISON
Fig. 8(b)). The position that the specimen started to Veriˆcation of K0 by means of K0 Triaxial Consolidation deform is not obviously noticeable from Fig. 8(b) but Test shows the transitional trend instead. Thus, the lower (14 InordertoverifythetestresultsofCOWKtriaxial kPa) and upper (32 kPa) possible values were considered apparatus, the estimation of K0 value,basedonthe as interlocking (sv0－sv1). Additionally, the authors also concept that the ratio of the volume of water dissipated chose the mostly likely value of (sv0－sv1)as24kPa.K0 from the specimen to cross sectional area of specimen values by means of load cell obtained by substitution into equals to the specimen vertical displacement, is carried Eq. (9) were 0.77, 0.60, and 0.68 for lower, upper and out; Dh＝DVWA,whereDh＝specimen height change, most likely values of respectively. DV＝volume of dissipated water measured by burette, Table 1 shows the summary of test results both normal and A＝specimen cross sectional area. and overconsolidated kaolin specimen. The initial water K0 triaxial consolidation test is performed on the contents are comparable except for Test 1 which is a little specimen after COWK triaxial test without experiencing ESTIMATION OF COEFFICIENT OF EARTH PRESSURE 357
Fig. 9. Stress path undrained compression described in the previous section.
The result is shown in Fig. 9. The specimen prior to the K0 triaxial consolidation is in K0 condition after completion of the withdrawal of the consolidation ring. The process is as follows. The increment of cell pressure laterally consolidates the specimen. In order to make the specimen return to K0 condition, the vertical loadings are applied to the specimen until the vertical displacement becomes equal to the ratio of the volume of dissipated water to specimen cross sectional area after primary consolidation completed. Consequently, the specimen is returned to K0 condition again at higher stress level. Three steps are performed at the cell pressure of 300, 350 and 400 kPa.
It is found that K0 values are falling in the range of 0.72–0.74, agreeing well with the previous method using COWK apparatus. Considering the time consumption and cost of operation, K0 triaxial consolidation test requires longer time for consolidating the specimen returning to K0 condition per one step; more than ten times as shown in Fig. 10. e－log s? for estimation of vertical and horizontal maximum Fig. 9 as the data points on the path, while the proposed past pressure method required only few steps of consolidation; for estimating K0 value. Moreover, for those complicated apparatuses for K0 triaxial consolidation, listed in labora- Table 2. Interpretation of preconsolidation pressure tory methods in INTRODUCTION, it should be more Interpreter 1 Interpreter 2 Interpreter 3 expensive than the simple apparatus used in this study. Test s?vc s?hc K0 s?vc s?hc K0 s?vc s?hc K0
Compare to K0 Estimated from Conventional Oedometer O-1 132 123 0.93 135 125 0.93 140 125 0.89 Tests O-2 132 113 0.86 140 135 0.96 140 135 0.96 Tavenas et al. (1975) suggested that the value of the ratio of horizontal to vertical preconsolidation pressures O-3 131 109 0.83 157 145 0.92 150 135 0.90 is a practical solution to the problem of K0 determination. The same slurry kaolin is preconsolidated in a con- solidometer, 200 mm in diameter, at a pressure of about test O-1 and O-2 are tested under the same loading 145 kPa. Then, the specimen is half divided with 100 mm condition. It can be seen that the preconsolidation in height and ˆlmed with para‹n before use. The samples pressure on the vertical and horizontal planes are in the are trimmed in horizontal and vertical planes and tested range of eŠective stresses 100–160 kPa. Thus, the special in the Oedometer. Figure 10 shows the test results of three sub loading steps are paid in Test O-3 by applying specimens. The vertical line, appeared in e－log s?v incremental loading of 10, 10, 20, 20, 20 kPa to the speci- between 100–200 kPa, (10 kPa of interval) can be used as men in the range of the vertical stress of 80 to 160 kPa. a guide line for reading preconsolidation pressure. The The interpretations of preconsoliadtion pressure shown 358 TEERACHAIKULPANICH ET AL.
Table 3. Indirect determination of K0 for normally consolidated soils Table 4. Indirect determination of K0 for overconsolidated soil
K0 for Kaolin K0 for Kaolin
K0 equation Reference q?＝259, q?＝259,PI＝49 K0 equation Reference I ＝49 p OCR＝2OCR＝3 ＝ － K0 1 sin q? Jaky (1948) 0.57 K ＝1－sin (1.2q?)(OCR)sin(1.2q?) Schmidt 0.71 0.87 ＝ － 0 K0 0.9(1 sin q?) Jaky (1944) in Ref. 1), 0.52 (1967) Fraser (1957) K0＝(0.19＋0.233 log PI) Kenney 0.80 0.96 －PI 0.54 exp (1959) K＝ ×OCR 281 2 Alpan 1＋ sin q? (1－sin q?) Ø 3 » (1967) Jaky (1944) in Ref. 1) 0.51 K ＝1－sin q?(OCR)sin q? Mayne and 0.77 0.92 1＋sin q? 0 Kulhawy
K0＝ (1982) 1.15(q?－99) tan2 459－ Rowe (1957), 0.52 Ø 2 » Abdelhamid and Krizek (1976) researchers as shown in Table 4.
By comparison, the laboratory K0 values are higher K0＝0.95－sin q? Brooker and 0.52 Ireland (1965) than the correlation equations for normally consolidated PI soil. Moreover, K0 value of OCR＝2 from the laboratory K ＝0.44＋0.42 Massarsch (1979) 0.65 0 100 test does not match well with those equations. On the contrary, very good matching is obtained in the case of OCR＝3. For the overconsolidated soil, the empirical
equation proposed by Alpan (1967) gives K0 value reason- ably close to the experiment results in this study. However, more investigation at higher overconsolidation ratio are needed.
It can be seen that the correlation equations give K0 estimation which are close to each other but those values are lower than the laboratory result in this study. Since
Jaky (1944) proposed the equation for estimating K0 value as a function of critical state parameter (internal angle of friction), some researchers; Hendron (1963), Wroth (1972), Mayne and Kulhawy (1982) also proposed the equations as a function of critical state parameter. Recently Watabe et al. (2003) noticed that the deˆnition
of q? should be concerned in order to estimate K0 value. They reported that the use of q? corresponding to a
critical state and peak state gives ±0.05 diŠerence of K0 value from their laboratory results. Nevertheless, Fig. 11. t－s? of Kaolin clay Michalowski (2005) revised Jaky's equation and con- cluded that this equation is a reasonable prediction which in Table 2 are obtained by Casagrande's (1936) sugges- is somewhat coincidental due to the state at rest of soil tion by three of staŠs in the laboratory who are not below the critical state level. Consequently, it can be seen involved with this study. It can be seen that K0 values that the use of empirical equation to estimate K0 value is from this method vary due to preconsolidation pressure still ambiguous and seems not to be precise enough diŠerently estimated by each of the interpreters. The K0 especially for the work such as the initial conditions for values 0.83–0.96 with the average of 0.89 are higher than soilWwater coupled ˆnite element analysis in which K0 is those obtained by the two previous methods. an essential input parameter such as Sekiguchi and Ohta (1977), Hashiguchi and Chen (1998), Asaoka et al.
K0 from Empirical Equation (2002), and Dafalias et al. (2003). Many researchers have proposed empirical or semi Consequently, from the test results, it can be con- empirical correlations of K0 with the angle of shearing cluded that the performance of COWK triaxial apparatus resistance and plastic limit as shown in Table 3. In this is practical enough for estimation of K0 both normally study, the eŠective angle of friction obtained from and overconsolidated soil with many advantages over the constant volume shear box test shown in Fig. 11 is q?＝ existing K0 estimation methods such as less time con- 259and the plasticity index Ip of kaolin from the labora- sumption, and low cost of operation. tory test is Ip＝LL－PL＝77－28＝49.
Moreover, the correlation equations of K0 for over- consolidated soil have also been proposed by some ESTIMATION OF COEFFICIENT OF EARTH PRESSURE 359
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