Otober 12-17, 28, Beijing, China THE EFFECT OF CONSOLIDATION RATIOS ON DYNAMIC SHEAR MODULUS OF SOIL J. Sun 1 and X.M. Yuan 2 1 Assoiate Professor, Institute of Civil Engineering, Heilongjiang University, Harbin, China 2 Professor, Institute of Engineering Mehanis, China Earthquake Administration, Harbin, China Email: iemsunj@163.om, yxmiem@163.om ABSTRACT : The dynami shear modulus (DSM) is the most basi soil parameter in earthquake or other dynami loading onditions and an be obtained through testing in the field and in the laboratory. By using the resonant olumn tests, the effet of the onsolidation ratios on the maximum DSM of the soil is investigated and an inremental formula for alulating the maximum DSM for the ases of the anisotropi onsolidation is presented. The silty lay, silt and sludgy soil of China are employed in the tests to establish the basi formula in the paper. The form of the formula is a power funtion to desribe the relation between the ratio of the maximum DSM s due to anisotropi and isotropi onsolidations and the inrement of onsolidation ratio, max / =1+C (k -1) B. The new formula indiates that the maximum DSM is the power of k -1 instead of the nearly linear relation in Hardin and Blak s and the inreasing degree of the maximum DSM due to k >1. is signifiantly larger than that desribed by Hardin and Blak s formula. Compared with sand, the inrement of the maximum DSM for silty lay due to anisotropi onsolidation is muh larger than that of sand. KEYWORDS: onsolidation ratio, dynami shear modulus, undisturbed ohesive soil, resonant olumn test 1. INTRODUCTION The dynami shear modulus (DSM) is the most basi parameter in soil property and an be obtained through testing in the field and in the laboratory (Hardin and Blak, 1968, 1969; Yu et al, 1988; He, 1997; Chen et al, 22; Yuan et al, 25). The most advaned apparatus for testing the dynami shear modulus in small strain range in the laboratory now is the resonant olumn devie beause of its advantages in the simply mehanial priniple, lear stress ondition and onvenient operation and the small deviation of testing results. However, the most existing resonant olumn devies are only suitable for speimens under isotropi onsolidation. Considering that the onsolidation ratio, k, varies in the range of 1.4-3. in atual subsoil, some researhers and engineers tried to use Hardin and Blak s formula (1968, 1969) to predit the maximum DSM of soils under a different onsolidation ratios. The maximum DSM for k =1.5 and k =2. respetively are 8% and 15% larger than that for k =1. by the Hardin and Blak s formula. Some researhers (He, 1997) questioned the auray of Hardin and Blak s formula in prediting the maximum DSM of soil under anisotropi onsolidation in terms of the dynami triaxial tests. However, these results are only a few and the dynami triaxial tests are basially suitable for the moderate and large deformation of soils. Therefore, the effet of onsolidation ratios on the maximum DSM still needs to be studied further. 2. EQUIPMENT AND SOIL SPECIMEN 2.1. Equipment To investigate the DSM of soil under anisotropi onsolidation, a new resonant olumn devie is developed at the Institute of Engineering Mehanis, China Earthquake Administration, in 22. The devie inludes two speial designs for performing deviatori stress tests. One is a speial transmission mehanism that applies vertial stati deviatori fore to the soil speimen without eentri fore. Another is plaing a manipulator inside the pressure vessel to avoid the instability problem enountered in the proess of speimen fitting and
Otober 12-17, 28, Beijing, China applies vertial deviatori stress to the soil speimen. The devie is the fixed-free resonant olumn. The diameter and the height of the speimen are 3.91m and 8.m, respetively. The resonant olumn devie is shown in Figure 1. Figure 1 The resonant olumn devie used for tests 2.2. Soil Speimen Three types of undisturbed ohesive soil, the silty lay, silt and sludgy soil in China are tested. Fourteen speimen of three fields whih is Bridge of Taoerhe, University City of Changqing and Tunnel of Huanghe in Shan Dong, respetively, are used for silty lay test. Three speimen of one field, Whih is Bridge of Taoerhe in Shan Dong are used for silt test. Two speimen of one field, Whih is Bridge of Hangzhou in Zhe Jiang are used for sludgy soil test. The physial speifiations of undisturbed ohesive soil are listed in Table 2.1. Table 2.1 Physial speifiations of three types of undisturbed ohesive soil Speiality Serial Number Deep Density Water Content / m / g/m 3 / % SC-Tao-1 25.3-25.5 2.161 17.36 SC-Tao-2 3.7-3.9 1.989 3.83 SC-Tao-3 34.6-34.8 2.175 17.18 SC-Tao-4 36.6-36.8 2.63 23.5 SC-Chang-5 9.8-1. 2.14 19.9 SC-Chang-6 16.2-16.4 2.78 23.37 Silty Clay SC-Chang-7 2.6-2.8 1.974 27.84 SC-Chang-8 26.2-26.4 2.99 2.69 SC-Chang-9 17.6-17.8 2.57 19.73 SC-Chang-1 32.2-32.4 1.974 26.21 SC-Huang-11 16.4-16.6 2.94 21.23 SC-Huang-12 29.6-29.8 2.14 22.62 SC-Huang-13 15.4-15.6 2.135 19.25 SC-Huang-14 23.1-23.3 2.167 18.55 S-Tao-1 15.4-15.6 2.238 15. Silt S-Tao-2 19.-19.2 2.146 17.58 S-Tao-3 22.2-22.4 2.156 19.79 Sludgy Soil SS-Hang-1 29.8-3.1 1.863 33.44 SS-Hang-2 47.8-48. 1.972 34.29
Otober 12-17, 28, Beijing, China 3. THE RECOMMENDED FORMULA OF MAXIMUM DSM 3.1. Results of the Silty Clay In the tests, fourteen speimens of three fields of Bridge of Taoerhe, University City of Changqing and Tunnel of Huanghe, are made for the silty lay. One onfining stresses and five onsolidation ratios, k =1., 1.2, 1.5, 1.7 and 2., are employed. For eah onfining stress, five idential samples are used respetively for the tests of five different onsolidation ratios. After finishing the onsolidation, the graded loads of the torsional moment are onduted to the soil speimen. DSM is obtained by using the free vibration tehnique. The relations of DSM and dynami shear strain, -, are onduted for different speimen of silty lay. The hyperboli equation, =1/(a+b), is used to obtain the regression urve of -. The maximum DSM is obtained from the regression equation by. Aording to the relations of the maximum DSM and the onfining stress, the inrement of the maximum DSM, max, is formed as Eqn. 3.1. max B = 1 + C ( k (3.1) where is maximum DSM for k =1. and max / is the relative inrement of the maximum DSM due to k >1.. By averaging the oeffiients of C and B from fourteen speimens, the oeffiients C and B are 1.25 and.76, respetively. The omparison between the alulation and test data is shown in Figure 2 and the average error is 8.8%. 3. max / 2.5 2. 1.5 1. 1. 1.5 2. 2.5 k Figure 2 Comparison between the presented formula and test data of silty lay 3.2. Results from The Silt In the tests, three speimens of Bridge of Taoerhe, are made for the silt. One onfining stresses and five onsolidation ratios, k =1., 1.2, 1.5, 1.7 and 2., are used for the analysis. Using the same proedure for the silty lay, the relative inrement of the maximum DSM for the silt due to k >1. is expressed in the same form, provided the oeffiients are C=1.2 and B=1.5. The omparison between the alulation and test data is illustrated in Figure 3 and the average error is only 8.7%. 3. 2.5 max / 2. 1.5 1. 1. 1.5 2. 2.5 k Figure 3 Comparison between the presented formula and test data of silt
Otober 12-17, 28, Beijing, China 3.3. Results from the Sludgy Soil In the tests, two speimen of Bridge of Hangzhou, are made for the sludgy soil. One onfining stresses and four onsolidation ratios, k =1., 1.25, 1.5 and 2., are used for the analysis. Using the same proedure for the silty lay and silt, the relative inrement of the maximum DSM for the sludgy soil due to k >1. is expressed in the same form, provided the oeffiients are C=1.85 and B=.47. The omparison between the alulation and test data is illustrated in Figure 4 and from whih it an be onluded that the errors are quite small. 3.5 3. max / 2.5 2. 1.5 1. 1. 1.5 2. 2.5 k Figure 4 Comparison between the presented formula and test data of sludgy soil 3.4. Reommended Formula in the Paper By omparing the experimental results of three types of undisturbed ohesive soil tested, three unique expression of the relative inrement of the maximum DSM under the different onsolidation ratios k for the silty lay, silt and sludgy soil, respetively, are developed as Silty lay max. 76 = 1 + 1.25 ( k Silt max 1. 5 = 1 + 1.2 ( k Sludgy soil max. 47 = 1 + 1.85 ( k (3.2) (3.3) (3.4) In Eqn. 3.2. - Eqn. 3.4., the oeffiient 1.25, 1.2 and 1.85 represents the inrement of the maximum DSM for k =2., whih is 125%, 12% and 185%, respetively, larger than that for k =1.. The results also indiate that the effet of onsolidation ratios on the maximum DSM of undisturbed ohesive soil is quite remarkable. The inreasing degree of the maximum DSM for the sludgy soil is signifiantly larger than that of the silty lay and silt. 4. COMPARISON WITH OTHER RESULTS In terms of 2 = 3 and 1 =k 3, the simplified formula for alulating max / was reommended by Hardin and Blak (1968) as shown in Eqn. 3.5. + max 3 2 k.5 = ( ) (3.5) The omparison of Eqn. 3.2 with Eqn. 3.5 proposed in this paper is illustrated in Figure 5 and it shows that the differene beomes larger and larger with the inreasing of k. Aording to Hardin and Blak s formula,
Otober 12-17, 28, Beijing, China max / -k, there is a nearly linearly inreases in the maximum DSM, while the formula proposed in this paper, max / -k -1, inreases in exponential form in the interval of k =1. to 2.. It also an be seen from Figure 5 that the effet of onsolidation ratios on the maximum DSM of soil is quite remarkable. The inreasing degree of the maximum DSM from the formula proposed in the paper is signifiantly larger than that Hardin and Blak s formula. For k =1.5 and k =2. in Figure 5, the estimated values of max / from Eqn. 3.2 are 1.85 and 2.25 respetively, however, the values estimated from Hardin and Blak s formula are only 1.8 and 1.15. It means the max / will be underestimated by the Hardin and Blak s formula. 2.8 max / 2.4 2. 1.6 Silty lay Sand 1.2 Hardin and Blak 1. 1.5 2. 2.5 k Figure 5 Comparison of max / k for three formulas The effet of the onsolidation ratios on the maximum DSM for two types of sand had been investigated by the author (Sun, 26) and an inremental formula for alulating the maximum DSM under the anisotropi onsolidation had been reommended as shown in Eqn. 3.6. max.54 = 1 +.66 ( k (3.6) The omparison between Eqn. 3.2 and Eqn. 3.6 proposed in the paper is also illustrated in Figure 5. By omparing with the formula of sand, it shows that the inreasing degree of the maximum DSM for the silty lay proposed is signifiantly larger than that of sand. For instane, in ase of k =2. in Figure 5, the value of max / is around 2.25 aording to the Eqn.3.2 but only 1.66 estimated from the formula of sand. He (1997) onduted dynami triaxial tests for disturbed the silty lay under the deviatori stresses. It an be dedued that max / for the ases of k =2. are about 1.4 and 2. whih is ompatible with the result obtained in the paper. 5. CONCLUSIONS The onlusions of the paper are summarized as follows: 1. The effet of the anisotropi onsolidation on the maximum DSM of soil is quite remarkable and the reommended inremental formula for alulating the effet is developed. 2. For silty lay, silt and sludgy soil, respetively, the reommended formula are max / =1+1.25 (k -1).76, max / =1+1.2 (k -1) 1.5 and max / =1+1.85 (k -1).47, respetively. The results also indiate that the inreasing degree of the maximum DSM for the sludgy soil is signifiantly larger than that of the silty lay and silt. 3. The inreasing in the maximum DSM due to k >1. is signifiantly larger than that predited by Hardin and Blak s formula, e.g., the inreasing of k from 1. to 2. aording to the silty lay is about 125%, while it is only 15% aording to Hardin and Blak s formula. 4. By omparing to the formula of sand, the inreasing degree of the maximum DSM for silty lay is
Otober 12-17, 28, Beijing, China signifiantly larger than that of sand. ACKNOWLEDEMENTS The work is supported by Youth Foundation of Heilongjiang University under rant No. QL2635 and Dotoral Start-up Foundation of Heilongjiang University. The supports are gratefully aknowledged. REFERENCES Hardin, B.O., and Blak, W.L. (1968). Vibration modulus of normally onsolidated lay. Journal of the Soil Mehanis and Foundations Division. ASCE 94:2, 353-369. Hardin, B.O., and Blak, W.L. (1969). Vibration modulus of normally onsolidated lay (losure). Journal of the Soil Mehanis and Foundations Division. ASCE 95:6, 1531-1537. He, C.R. (1997). Dynami triaxial test on dynami modulus and damping ratio. Chinese Journal eotehnial Engineering, 19:2, 39-48 (in Chinese). Yu, P.J., and Rihart, F.E. (1984). Stress ratio effets on shear modulus of dry sands. Journal of the Soil Mehanis and Foundations Division. ASCE, 11:3, 331-345. Yu, P.J., Liang,Y.X., and Qin, W.Q. (1988). Dynami modulus and damping ratio of disturbed sands. Chinese Journal eotehnial Engineering, 1:4, 57-63 (in Chinese). Chen C.L., Hu Z.Q., Xie D.Y. and Feng Z.Y. (22), Researh on dynami harateristi of sand in foundation of Xiabandi Dam. Pro. 6th Chinese National Conferene on Soil Dynamis, Nanjing, China, 698-74. (in Chinese) Xiaoming Yuan, Jing Sun and Sun Rui (25). Effet of Consolidation Ratios on Maximum Dynami Shear Modulus of Sands. Earthquake Engineering and Engineering Vibration 4:1, 59-68. (in Chinese) Jing Sun and Xiaoming Yuan (26). The Effet of the Consolidation Ratio of Sands on Dynami Shear Modulus and Response Spetrum of Soil layer. eotehnial Speial Publiation, ASCE, 437-443.