Evaluation of the Modulus of Elasticity and Resilient Modulus for Highway Subgrades Elsa Eka Putri PhD student, Civil Engineering Program, School of Engineering and Information Technology, Universiti Malaysia Sabah, Kota Kinabalu, Malaysia (Lecturer of University of Andalas, Padang, Indonesia) e-mail:
[email protected],
[email protected]
N.S.V Kameswara Rao Professor in Civil Engineering Program, School of Engineering and Information Technolog; Universiti Malaysia Sabah, Kota Kinabalu, Malaysia; e-mail:
[email protected]
M. A. Mannan Assoc. Prof in Civil Engineering Program, School of Engineering and Information Technology, Universiti Malaysia Sabah, Kota Kinabalu, Malaysia; e-mail:
[email protected]
ABSTRACT The aim of this study is to evaluate the modulus of elasticity and the resilient modulus of the subgrade clayey sand soils by laboratory testing. The two tests used are California Bearing Ratio (CBR) test and Unconfined Cyclic Triaxial (UCT) test. Modulus of elasticity and resilient modulus are important material properties of subgrade soils and are the input parameters in the design of pavement. The modulus of elasticity of a soil is a soil parameter most commonly used in the estimation of settlement from static or dynamic loads. The subgrade resilient modulus (MR) is an essential engineering parameter for the mechanistic empirical pavement design. From the result of this study, the modulus of elasticity derived from CBR tests is higher than the modulus of elasticity obtained from UCT test. In addition, from the UCT test the higher the cyclic deviator stress applied to the sample the higher the modulus of elasticity, but there is no trend in the result of resilient modulus. The measured modulus of elasticity and resilient modulus of the subgrade soils from the California Bearing Ratio test and Unconfined Cyclic Triaxial test under identical moisture and density conditions were compared. In conclusion, the average values of the modulus of elasticity calculated from the California Bearing Ratio tests characterize the soil as medium clay, and then after the soil experiences the cyclic loading in the UCT test, the soil is classified as soft clay (after Das, 1994). Furthermore, the influence of amplitude of axial cyclic stress in determination of resilient modulus was also discussed.
KEYWORDS:
Modulus of Elasticity, Resilient Modulus, California Bearing Ratio (CBR), Unconfined Cyclic triaxial (UCT), Coefficient of elastic uniform compression, Cu
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INTRODUCTION Modulus of Elasticity is an important material property of subgrade soil and is an input parameter in the design of pavements. Modulus of elasticity (E) also called Young's modulus can be determined for any solid material and represents the ratio of stress and strain (stiffness). The resilient modulus (MR) is the elastic modulus based on the recoverable strain under repeated load. The resilient modulus is defined as, MR = 𝜎 /𝜀
(1)
where 𝜎 = the deviator stress and ε = axial strain. The resilient modulus is a required input for determining the stresses, strains, and deflections in pavement design. The modulus of elasticity and resilient modulus can be determined in the laboratory under specified temperature, moisture content and density of the material, using the following tests such as California Bearing Ratio tests, Triaxial test, Plate Load test etc. CBR test was developed by the California Division of Highways around 1930 and was subsequently adopted internationally. In the CBR test compares the bearing capacity of a material with that of a well-graded crushed stone thus, a high quality crushed stone material should have a CBR of 100%. It is primarily intended for, but not limited to, evaluating the strength of cohesive materials having maximum particle sizes less than 19 mm (AASHTO, 2000). Unconfined Cyclic Triaxial test (UCT) could be performed on cylindrical specimen 100 mm high and 50 mm diameter. Samples in triaxial test usually have the ratio of height to diameter (H/D) ranging between 2.0 and 2.5 (Presti, 2004). The UCT test could be conducted by applying axial cyclic stress to the specimen for 100 cycles with no confining pressure and observing the axial strain, recoverable deformation and deviator stress at various axial cyclic stress levels. It is applicable to situations where the loads are applied such that there is not enough time for the induced pore-water pressure to dissipate and for consolidation to occur during the loading period (ASTM D 2850). The strength resulting from unconfined cyclic test corresponds to a constant moisture content condition, which means that a moisture content change is not permitted prior to or during shear. This test approximates the strength for short-term condition, such as the end of construction case. Thus, this research is aimed at measuring the modulus of elasticity of clayey sand soils at the same moisture content and density, as well as the resilient modulus with a view to evaluate the influence at different levels of axial cyclic stress on resilient modulus and modulus of elasticity.
BACKGROUND STUDY Modulus of elasticity is the ability of material not to deform excessively during loading. It is not the strength of the material, strength is the stress needed to break a material, where as elasticity is a measurement of how well a material returns to its original shape and size. According to Briaud (2000) the modulus of elasticity of soil depends on many factors. For instance, the loading process, soil particle organization, water content, etc, though, at the different penetration involve single specimen to determine the value of E of that soil.
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Basically there are three types of soils; frictional, cohesive and frictional cohesive soils. For cohesive soils (clay), low moisture content leads to high modulus of soil since clay shrinks and becomes very stiff when it dries. According to Briaud (2000), at low moisture content, the particle are bonded together (i.e. fine-grained soils) and effective stress increases through the suction and surface tension of water (van der Waals force). The US Army Corps Engineers (USACE) EM 1110-1-1904 tries to estimates the modulus of elasticity as, Es = KcCu
(2)
where Es is Young's soil modulus (MPa), Kc is correlation factor, Cu is undrained shear strength in MPa. Schmertmann (1970) measures the modulus of elasticity (E) estimated from the cone resistance from a static cone penetration test as, (3)
E = 2qc
On the other hand, the modulus of elasticity can be calculated based on coefficient of elastic uniform compression (Cu) or it can also be referred to as modulus of subgrade reaction, ks (Kameswara Rao, 2000). Cu is defined as the ratio of uniform pressure imposed on the soil to the elastic part of the settlement. Cu is defined as the ratio of uniform pressure imposed on the soil to the elastic part of the settlement. Cu = p/δ (kN/m3)
(4)
where p is the bearing pressure (load per unit area, kN/m2) from the CBR test. Cu is related to the soil and plunger parameter, thus E can be determined, Cu = 1.13
E (1-
1 ) √A
(5)
where E is the Modulus of Elasticity, v is the Poisson’s ratio (assumed to be 0.4 for clay soil), and A is the area of load plunger of CBR equipment. This equation [5] is applicable for uniformly distributed load acting on semi-infinite elastic soil medium. The same equation is used for displacement of soil in the CBR mould subjected to uniformly distributed load by plunger. Hence it gives on approximate value which can be used for subsequent applications for the CBR test. As Cu is calculated previously from equation [4], the modulus of elasticity for static condition can also be derived from the equation [5]. Resilient modulus, MR, is an important parameter which characterizes the subgrade’s ability to withstand repetitive stresses under traffic loadings. For testing the resilient modulus, the moving wheel loads must be simulated during the laboratory testing to represent that effect in the field. However, experience has shown that resilient modulus testing is a complex and difficult task (Ping, 2007), which is reflected by the large variation in experimental results that has been observed among different test methods and testing laboratories (Barksdale et al. 1997).
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There are several testing methods recognized for determining the resilient modulus of subgrade soils such as developed by Seed and Lee (1962), Bowles (1984), Florida testing sequence (Ho, 1989), Illinois testing sequence (Dhamrait, 1989), Washington testing sequence (Jackson, 1989) and New York testing sequence (Seim, 1989). Seed, et.al (1962) proposed that the resilient modulus could be related only to the deviator stress as follows: Mr = K (σd)n
[6]
It is based on the recoverable strains after cyclic loading. According to Bowles (1984), the resilient modulus is defined as the initial tangent modulus of a triaxial test stress-strain curve which has been cycled several times with a deviator stress and Δσ1 is the level approximating the working stress.
METHODOLOGY For determination of modulus of elasticity as well as the resilient modulus, tests were conducted on a Clayey Sand soils which is characterized by sieve analysis (ASTM D1921 – 06) to see the particle size distribution of the soil and Atterberg limit test (ASTM D4318 – 10). In this study, the condition of the compacted subgrade for highway formations was simulated by performing tests on compacted samples. Samples were prepared by modified proctor compaction for California Bearing Ratio tests as well as for the Unconfined Cyclic Triaxial tests. Then the samples were prepared for CBR tests (compacted the sample in cylinder, diameter = 6’, height 5’), and for UCT tests (cylinder, diameter = 50 mm, height = 100 mm). To determine the value of E from the California Bearing Ratio tests the equation given by Kameswara Rao (2000) was used. The value of Cu was calculated using equation [4], where the penetration depth of the load plunger was taken as the δ, then the value of E is determined by means of equation [5]. Unconfined Cyclic Triaxial (UCT) test were performed in this study based on studies by Shahu et.al (1999) and conducted in a Geotechnical Digital System Triaxial Instruments. UCT test consists of two steps during loading. Firstly the soil subgrade was loaded in cyclic condition for 100 times at a low frequency of 1 cycle per minute in an undrained condition. Then secondly the sample was sheared in monotonic loading at a rate of strain of 0.5mm/minute until it fails. The tests were carried out at axial stress amplitude from the lower stress to the higher stress where the sample was failed before reaching the 100 cycles. Unconfined Cyclic Triaxial test is based on a constant ratio of stress and strain (stiffness) that can be calculated from the deviator stress vs. strain graph at which the recoverable strain is chosen as the straight line portion of the curve, before the sample shows the permanent strain. The slope of the graph was chosen at which the loading is still in the range of the stress recovery, and the sample has not yet failed (Brown, 1984). Resilient modulus means the ability of the material to return to its original form after being loaded at certain level of stress. In this study the axial stress in an unconfined compression test or the axial stress in excess of the confining pressure in a triaxial compression test has been applied, then the load was cycled for 100 times. The calculation of the MR was adopted from the Bowles study, who has presented the calculation of MR based on the graph produced in the cyclic triaxial testing. The slope was chosen for one cycle, from the start of the cycle until the upper point of
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that cycle. Thus, the resilient modulus (MR) is the slope of the graph that equal to q/ εa (Brown, 1984).
RESULTS AND DISCUSSIONS The result of the sieve analysis test is shown in figure 1. It illustrates the particle size distribution of the soil subgrade.
100 90 80 70 60 50 40 30 20 10 0 0.01
0.1
1
Percentage passing
Particle size distribution chart
10
Particle size (mm)
Figure 1: Particle size distribution Analysis From the Atterberg limit test, the soil has Plastic Limit equal to 56%, Liquid Limit is 33.8% and Specific gravity of soil is 2.54. From those tests as well as from particle size distribution test the soil can be classified as SC/SP based on the Unified Soil Classification System, USCS or A2-7 based on American Association of State Highway and Transportation Officials, AASHTO. From the modified proctor compaction the optimum moisture content and the maximum dry density of the sample are 13% and 1910 kg/m3 respectively as shown in Figure 2.
1930
Dry Density (kg/m3)
1910 1890 1870 1850 1830 1810 1790 1770 1750 7
9
11
13 15 Moisture Content (%)
17
19
21
Figure 2: Dry density against moisture content relationship
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The results from CBR test are presented in Table 1. The force on plunger can be determined from the reading of the force gauge at intervals of penetration of 0.5mm until 7mm penetration. This procedure is repeated for the bottom face of the sample. The result was presented for several penetrations. Commonly, the CBR value of the soil is taken at 2.5mm and 5mm penetration whichever the higher. Table 1: Results of California Bearing Ratio test Penetration (mm) Force gauge reading (div) Force on plunger (kN) TOP BOTTOM TOP BOTTOM 0 0 0 0.00 0.00 1.00 52 62 0.22 0.26 2.00 80 146 0.33 0.61 0.35 0.79 2.50 84 188 5 120 316 0.50 1.32 7 156 384 0.65 1.61
1.6
7000
1.4
6000
1.2
5000
1
4000
0.8 3000
0.6 0.4
2000
0.2
1000
0
Mod. elasticity, E (kPa)
Load (kN)
From the CBR test result, the coefficient of the elastic uniform compression, Cu was calculated using the equation [4]. Then, the modulus of elasticity values can be estimated by means of equation [5]. The value of load during the CBR test and the value of modulus of elasticity are presented in Figure 3.
0 0
2
4 Axial Strain (mm) Load
6
8
E (mod.elasticity)
Figure 3: Coefficient of Elastic Uniform Compression, Cu and Modulus of Elasticity, E It can be seen from the Figure 3, the modulus of elasticity value increases as the axial strain is increases. However the modulus of elasticity decreases when the axial strain is beyond the 2.5 mm, even though the load is increases. From the value of modulus of elasticity, E this clay soil can be classified as medium clay (after Das, 1994). Modulus of elasticity (E) from the California Bearing Ratio tests tends to have similar value for all the data during the test even though the penetration is small or large. Perhaps the penetration is not the only parameter to determine the modulus of elasticity of the soil (Briaud, 2000).
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Deviator Stress (kPa) & Resilient Modulus (kPa)
1400
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
1200 1000 800 600 400 200 0 0
100
200
300
400
500
600
Recoverable Strain (%)
Two parameters, Resilient Modulus and Modulus of Elasticity are determined based on the UCT test, and the results are given in Figure 4 and Figure 5. The Figure 4 presents the resilient modulus result from the sample when subjected to 100 load cycles in an undrained condition in UCT test. The sample was subjected to cyclic load at the 40 kPa until 600 kPa of the amplitude of the axial stress.
700
Amplitude (kPa) Dev. stress
Resilient Modulus
Recoverable Strain
Figure 4: Resilient Modulus of the soil from UCT tests It can be seen from the Figure 4, when the soil experiences higher cyclic axial stress amplitude, it will result in the higher deviator stress as well as the recoverable strain value. However, the trend is varies with the value of resilient modulus, but when the cyclic axial stress is above 200 kPa, the value of modulus of elasticity tends to increase. The estimation of modulus of elasticity from the unconfined cyclic triaxial test is presented in Figure 5.
1400 1200 1000 800 600 400 200 0
1000 900 800 700 600 500 400 300 200 100 0 0
200
400
600
800
modulus of elasticity, E (kPa)
Deviator Stress, (kPa)
As can be seen from Figure 5, the deviator stress has similar trend as the modulus of elasticity with the increase in the amplitude of cyclic loading the modulus of the elasticity increases as well, the higher the cyclic axial stress (amplitude) the higher the modulus of elasticity.
Amplitude (kPa) deviator stress
modulus of elasticity
Figure 5: Modulus of Elasticity (E) from Unconfined Cyclic triaxial test
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CONCLUSIONS To estimate the modulus of elasticity value for clayey sand soils were. The results show, the estimation of the modulus of elasticity from UCT test is lower than the estimation from the CBR test, probably due to the effect of restriction of the sample inside the CBR mould during testing (confinement). The samples were confined inside the CBR mould, while the sample in UCT was an unconfined sample. The calculated modulus of elasticity (E) from California Bearing Ratio tests are in the range of 0.55 psi (3792 Pa) – 0.748 psi (5157 Pa), while for UCT test is 0.025 Psi (172 kPa). The calculated modulus of elasticity (E) from Unconfined Cyclic Triaxial tests are in the range of 0.007 psi (48 Pa) – 0.174 psi (1200 Pa). The higher axial stress in cyclic loading (amplitude) will result in the higher modulus of elasticity. The resilient modulus in Unconfined Cyclic Triaxial test tends to decrease with the increase of the cyclic stress amplitude.
ACKNOWLEDGMENT This project is sponsored by the FRGS (Fundamental Research Grant Scheme) Universiti Malaysia Sabah no. FRG 174-TK-2008.
REFERENCES 1. Bowles, J. E (1984) Physical and Geotechnical Properties of Soils, McGraw-Hill International Edition 2. Briaud. J. Louis (2000) Introduction to soil moduli http://www.hanmicorp.net/MFG/Humboldt/GeoGauge/ GeoGauge--Reports/FHWA %20GeoGauge%20Study/Presentations/2-IntroModulus.pdf (Retrieved October 2009) 3. BS 1377-4:1990 Method of Test for Soils for Civil Engineering Purposes 4. Carmichael, R.F. III, and Stuart, E. (1985) “Predicting Resilient Modulus: A Study to Determine the Mechanical Properties of Subgrade Soils.” Transportation Research Record 1043, Transportation Research Board, Washington, D.C., pp. 145-148. 5. Dhamrait, J. S., "Illinois' Experience with Resilient Modulus," Workshop on Resilient Modulus Testing, Oregon State University, Corvallis, Oregon, March 28-30, 1989. 6. Ho, R. K. H., "Repeated Load Tests on Untreated Soils - A Florida Experience," Workshop on Resilient Modulus Testing, Oregon State University, Corvallis, Oregon, March 28-30, 1989. 7. Hudson, J.M., Drumm, E. C., and Madgett, M. (1994) “Design Handbook for the Estimation of Resilient Response of Fine Grained Subgrades.” Proc. 4th Int. Conf. on the Bearing Capacity of Roads and Airfields (BCRA), Vol. 2., pp 917-928. 8. Jackson, N. C., "Thoughts on AASHTO T-274-82, Resilient Modulus of Subgrade Soils," WSDOT Material Lad, Report NO. 200, Workshop on Resilient Modulus Testing, Oregon State University, Corvallis, Oregon, March 28-30, 1989. 9. Kameswara Rao, N.S.V., “ Dynamic Soil Tests and Applications”, A. H. Wheeler & Co. Ltd, New Delhi, First Edition 2000
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10. Kim, D. S., Kweon, G. C., and Lee, K. H. 2001. Alternative method of determining resilient modulus of subgrade soils using a static triaxial test. Can. Geotech. J. 38(1): 107–116. doi:10.1139/cgj-38-1-107 11. Ping, W. V. (2007) Enhancement Of Resilient Modulus Data for The Design Of Pavement Structures In Florida, Summary of Final Report, BD543-04 January 2007 12. Presti, L. D, Lai. Carlo and Foti, Sebastian (2004) Geophysical and Geotechnical Investigations For Ground Response Analyses, ISBN 978-1-4020-1827-5 (Print) 978-14020-2528-0 (Online) Springer Netherlands, 2004 13. Schmertmann, J.H. (1970). “Static cone to compute static settlement over sand.” J. Soil Mech. Found. Div., ASCE, 96(3), 1011-1043. 14. Seed, H.B., Chan, C.K. and Lee, C.E. (1962). “Resilience Characteristics of Subgrade Soils and Their Relation to Fatigue Failures in Asphalt Pavements.” Proc. Int. Conference on the Structural Design of Asphalt Pavements, University of Michigan, pp. 611-636. 15. Seim, D. K., (1989)"A Comprehensive Study on the Resilient Modulus of Subgrade Soils," Soil Mechanics Bureau, New York State DEpartment of Transportation, Workshop on Resilient Modulus Testing, Oregon State University, Corvallis, Oregon, March 28-30,. 16. Shahu, J.T., Yudhbir, Kameswara Rao, N.S.V. (2000) ‘A Rational Method for Design of Railroad Track Foundation,’ Soil and Foundation, Japanese Geotechnical Society, 40, No. 6, 1-10, Dec 2000. 17. Shahu, J.T., Yudhbir, Kameswara Rao, N.S.V. ‘A Simple Test Methodology for Soils Under Transportation Routes,’ Geotechnique, The Institution of Civil Engineers, London, 49, 5, October, 1999, pp.639 – 649.
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