Stress-Strain Mechanism of Expanded Polystyrene ...

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/320057251

Stress-Strain Mechanism of Expanded Polystyrene Foam under Cyclic Loading Conditions within and Beyond Yield States Conference Paper · August 2017 CITATIONS

READS

0

97

3 authors, including: Sompote Youwai King Mongkut's University of Technology Thonburi 39 PUBLICATIONS   449 CITATIONS    SEE PROFILE

Some of the authors of this publication are also working on these related projects:

Geofoam View project

All content following this page was uploaded by Sompote Youwai on 27 September 2017.

The user has requested enhancement of the downloaded file.

2017 International Conference on Transportation Infrastructure and Materials (ICTIM 2017) ISBN: 978-1-60595-442-4

Stress-Strain Mechanism of Expanded Polystyrene Foam under Cyclic Loading Conditions within and Beyond Yield States Attapole Malai1, Sompote Youwai2 and Nattaporn Jaturabandit3 1

Doctoral Candidate, Civil Engineering Department, King Mongkut's University of Technology Thonburi, Thailand; [email protected] 2 Assistant Professor, Civil Engineering Department, King Mongkut's University of Technology Thonburi, Thailand; [email protected] 3 Master Degree, Civil Engineering Department, King Mongkut's University of Technology Thonburi, Thailand; [email protected]

ABSTRACT: This paper attempts to describe deformation characteristics of EPS geofoam under cyclic loading conditions within and beyond yield states. The loading pattern on geofoam specimen represented a construction sequence as well as a traffic loading of the bridge approach structure. A large size of EPS block specimens with dimensions of 30 cm high, 30 cm wide and 60 cm long were tested in laboratory with different cyclic loads pattern and wide range densities. From testing results, increase in density of EPS geofoam, yield state as well as overall deformation characteristics of EPS foam decreases. The permanent deformation was significantly observed on a low density of EPS geofoam with a low yield state. A stiffness of EPS significantly decreased with increasing of stress level beyond yield stress of material. The stress-strain mechanism of EPS was hardening without failure behaviors when the stress level being more than its yield stress. The overall cyclic behaviors of EPS can be successfully characterized with its yield state. Keywords: EPS Geofoam, Cyclic characteristics, Stress-strain mechanism

load,

Yield

states,

Deformation

INTRODUCTION Lightweight materials have been considered a technically acceptable and inexpensive solution for settlement problems highly compressible soils. The geotechnical and construction engineering have been looking for lightweight construction materials for backfill embankments on soft ground, beneath pavements and replacement material for approach bridge abutment. Due to convenience in transportation and construction, and EPS blocks have been used in projects where the time-schedule is a key issue. The utilization of EPS blocks in geotechnical structures to explicitly mitigate the intensity of loads caused by cyclic events has been constrained perhaps essentially due to the rather limited knowledge the profession has on the dynamic behavior of this material. EPS is an extremely lightweight material which is not surprisingly considering, so it is comprised of a great quantity of air about 98 percent of the total volume of EPS cellular structure. The EPS blocks are extensively used in geotechnical projects because of their lightweight properties. This material has been used as incomplete or total replacement fill in embankments on soft compressible soils to minimize settlements and escape stability problems. EPS blocks have been used by geotechnical engineers in the reduction of traffic loads on bridge abutments. Due to blocks behavior like a deformable inclusion that improve the stability of these structures by mitigating the loads imposed by the backfill, seismic forces or surcharges (Pelekis et al. 2000, Hazarika 2001,

Athanasopoulos et al. 2007, Zarnani and Bathurst 2009, Trandafir and Bartlett 2010, Trandafir and Ertugrul 2011). According to Duskov (1997), the degradation of the dynamic modulus of elasticity was carried out under cyclic unconfined stress between 3 and 6 Hz on cylindrical samples. Test results showed permanent deformations and degradation of the dynamic modulus of elasticity when the deviator stress applied surpass the elastic range. Athanasopoulos (1999) carried out cyclic unconfined compression and unconfined resonant column strain-controlled tests on EPS specimens with average densities of 12.4 and 17.1 kg/m3 to estimate damping ratios and shear moduli under varying load frequency conditions between 0.01-2 Hz. Test results indicated that the shear modulus increased with density, but the damping ratio was not influenced by this parameter. The results of cyclic test showed that there was not a significant effect of load frequency on the shear modulus. However the damping ratio increased with load frequency evidencing the viscous behavior of EPS.

Figure 1. Road Roller compact during construction. For construction of bridge approach structure by using EPS as subgrade material, it is required a compacted backfill on top of EPS for reduction of stress from traffic and preventing floating of EPS block during flooding as shown in Fig. 1. The compaction of a first layer of backfill material might induced a stress on EPS block beyond its elastic limit. The purpose of this work is to evaluate the cyclic behavior of EPS during compacted by road roller on cover material of EPS layer. The experiment of cyclic uniaxial compression program having a wider range of densities and the influence of the cyclic stress on cyclic permanent axial strain and number of cycle. Determination of material behavior The experimental program included stress-controlled cyclic uniaxial compression tests initial on EPS with densities of 20 and 24 and 32 kg/m3, represented as EPS20 EPS24 and EPS32, respectively. Before applying a cyclic load, a preloading stress was a sand layer covered on top EPS layer applied at 65 kPa. Tested samples had a large size of EPS block specimens with dimensions of 30 cm high, 30 cm wide and 60 cm long. Apparatus in Figure 2 is load-controlled compression and extension loading. Compression and extension are provided by means of changes in the hydraulic pressure at the top of reaction frame. By using this loading apparatus, cyclic tests with specified load amplitude at a specified frequency can be performed. The monotonic loading test and cyclic loading test will tested by this instrument. An initial static deviator stress (σds) with a magnitude greater than the amplitude of applied cyclic deviator stress (Δσdc) was imposed on the specimen before starting the cyclic loading phase to maintain the cyclic stresses in the compression range. The cyclic testing phase started after the specimen had attained equilibrium under the applied static stresses 65 kPa. Tests program

were conducted at loading frequencies (f) within 5 Hz. The number of applied loading cycles was 1,000 cycles for tests of EPS geofoam. A maximum number of 1,000 cycles was considered sufficient for capturing all possible changing patterns in plastic axial strain increments during yielding of geofoam under cyclic loading. Table 1 presents the summary of test program in this study. Table 1. Summary test program of this study (Cyclic uniaxial test). Density Preloading Load Cyclic Deviator Number Number (kg/m3) Stress frequencies Stress of Cycle of (kPa) (Hz) Amplitudes (N) Sample (Δσdc), (kPa) 20 65 5 20, 25 and 30 1,000 3 24 65 5 20, 25 and 30 1,000 3 32 65 5 20, 25 and 30 1,000 3 Strain-controlled cyclic test behavior of EPS Figure 3 is an idealized hysteresis loop representation of the Young’s modulus (E) and the viscoelastic behavior of EPS geofoam. The y axis is the cyclic deviator stress (σdc) and the x axis is the axial strain (εa). The resulting damping ratio value is valid for one complete hysteresis loop. The damping ratio describes the material’s ability to dissipate energy by viscous. Where dissipated energy is per unit volume of one hysteresis loop (Wd). The Young’s modulus (E) is resolute by the secant modulus defined by the slope of the line through the origin and the initiation point of load reversal. The stored energy (Ws), as depicted in Figure 3, is the same as an elastic material resulting in the same E value for the material. Where Wd and Ws are the energy values required for the damping ratio (D) calculations. (Aurelian et al. 2012).

Figure 2. Experimental setup for the cyclic uniaxial test on EPS geofoam.

Deviator stress, σd (kPa)

Figure 3. Cyclic stress-strain hysteresis loop for a viscoelastic material.

Axial strain, εv (%) Figure 4. Lower bound total deviator stress [(σds + Δσdc) yield] and plastic yielding of EPS geofoam under cyclic loading. The strength and stress-strain behavior of EPS-geofaom show large differences based on the density of geofoam. The EPS-geofoam regularly demonstrates elasto-plastic conduct without show clear pinnacle. The yield stress is the single point on stress-strain curve at which the tangent modulus is changing at the greatest rate with respect to increasing strain. The yield strength is essential parameter to decide the performance of material and roughly design the project. Deviator stress is the difference between the major and minor principal stresses in the test which is equal to the axial load applied to the specimen divided by the cross-sectional area of the specimen. Dynamic modulus is the ratio of stress to strain under vibratory conditions. It is a property of viscoelastic materials. Figure 4 show the total deviator stress of lower bound associated with plastic yielding of EPS geofoam under cyclic loading ((σds + Δσdc) yield) is smaller than the deviator stress at yield obtained from rapid monotonic loading uniaxial tests conducted at a strain rate of 10%/min yield of monotonic loading. An evaluation of the yield strength was performed of each density using rapid monotonic loading. For the interval of investigated EPS geofoam densities between 15–25 kg/m3, the plastic yielding of EPS geofoam under cyclic loading ranged within 88-94% of yield from monotonic loading. (Aurelian et al. 2012). Table 2 is summary of yield stress and initial tangent elastic modulus of EPS specimens having different densities investigated from cyclic loading test.

Table 2. Summary of yield stress and initial tangent elastic modulus of EPS from cyclic loading test. Density Yield strength from monotonic Initial tangent elastic modulus (kg/m3) loading test, (σdm)Yield (kPa) Eo, (kPa) 20 80.0 5,353.5 24 122.9 7,554.5 32 149.7 8,771.9 1.6

0, 3

Cyclic permanent axial strain, %

2 EPS

a

0 kP

1.4 1.2 1.0 0 , 25 EPS2

0.8

EPS20

k Pa

a

, 20 k P

0.6 EPS24, 30 kPa EPS24, 25 kPa EPS24, 20 kPa

0.4

EPS32, 30 kPa EPS32, 25 kPa EPS32, 20 kPa

0.2 0.0 0

100

200

300

400

500

600

700

800

900

1000

Number of cycle Figure 5. Cyclic plastic axial strain with number of cycles at different cyclic deviator stresses and wide range densities. Plots of cyclic permanent strain versus number of cycles for various cyclic deviator stresses are shown in Figure 5 for EPS20, EPS24 and EPS32 at cyclic deviator stress amplitudes (Δσdc) of 20, 25 and 30 kPa. The permanent axial strain under cyclic loading increased with increasing cyclic deviator stresses. The total cyclic permanent strain of the EPS20 is greater than EPS24 and EPS32 because cyclic load apply on EPS20 is higher than yield stress, but there are less than yield stress of EPS24 and EPS32. The permanent strain for 1,000 cycles was about 1.6 percent for EPS20 under cyclic deviator stresses at 30 kPa. The plastic permanent axial strain of the specimens increases with incrementing the cyclic deviator stress amplitudes. In Figure 6 shows dynamic modulus of elasticity (Edyn) with the number N of cyclic load applications for different stress levels. The EPS specimens had densities of 20, 24 and 32 kg/m3, and the testing cyclic deviator stress amplitudes (Δσdc) 20, 25 and 30 kPa. EPS stiffness represented by the dynamic modulus of elasticity is not influenced by the number of loading applications when the applied stress do not reach the yield condition. However, in Figure 6 also can be seen that a significant degradation of the EPS dynamic modulus of elasticity occurs with the number of loading applications when the applied stress level is near to the yield condition. The degradation tends to be less when the numbers of loading applications reaches the 30th cycle, nor that EPS density have a significant influence on the EPS dynamic modulus of elasticity.

120

Modulus of Elasticity, Edyn (kPa)

110 100 90 80 70

EPS20@20kPa EPS20@25kPa EPS20@30kPa EPS24@20kPa EPS24@25kPa EPS24@30kPa EPS32@20kPa EPS32@25kPa EPS32@30kPa

60 50 40 30 20 1

10

100

1000

Number of cycle (N)

Figure 6. Dynamic modulus of elasticity (Edyn) versus number of load (N). CONCLUSIONS Laboratory tests on various density EPS samples have been conducted to characterize behavior under constant and cyclic loading conditions. When a unit weight of the EPS material increases, both the initial and modulus of elasticity increase. With subjected to cyclic loading, permanent deformation of EPS foam decreased when density of EPS geofoam increase. The number of cyclic load application growths, so the modulus of elasticity decreases obviously. The plastic axial strain was observed on a for EPS geofoam with low density with low yield stress. When the stress level being more than yield stress, the stressstrain mechanism of EPS was hardening without failure behaviors. ACKNOWLEDGMENTS The authors would like to thankful to the master degree member of Geotechnical Laboratory for their support in carrying out the laboratory experiments at King Mongkut's University of Technology Thonburi, Thailand. REFERENCES Abdelrahman, G.E., Kawabe, S., Tsukamoto, Y., and Tatsuoka, F., 2008a. “Small-Strain Properties of Expanded Polystyrene Geofoam” Soils and Foundations Japanese Geotechnical Society, Vol.48, No.1, pp. 61-71. Athanasopoulos, G. A., Pelekis, P. C., and Xenaki, V. C. (1999). “Dynamic properties of EPS geofoam: An experimental investigation.” Geosynth. Int., 6(3), 171-194. Aurelian C. Trandafir, Ph.D., P.E., M.ASCE and Benjamin A. Erickson (2012). “Stiffness Degradation and Yielding of EPS Geofoam under Cyclic Loading” Journal of Materials in Civil Engineering 24(1):119-124. Chun, B.S., Lim, H., Sagong, H.-S., Kim, K., 2004, “Development of a hyperbolic constitutive model for expanded polystyrene (EPS) geofoam under triaxial compression tests” Geotextiles and Geomembranes 22, p. 223-237.

Duskov, M., 1997. “Materials research on EPS-20 and EPS-15 under representative conditions in pavement structures” Geotextiles and Geomembranes, Vol.15 (1 to 3), 147-181. Hazarika, H., Okuzono, S., (2004). “On a performance enhancement of a soilstructure system with sandwiched inclusion” Proceedings of the 11th International Conference on Soil Dynamics and Earthquake Engineering and the 3rd International Conference on Earthquake Geotechnical Engineering, pp. 257-263. Berkeley California. Ossa, A., and Romo, M.P., (2008). “A model for EPS dynamic shear modulus and damping ratio” Proceedings of First Pan American Geosynthetics Conference and Exhibition, p. 894‐901. Pelekis, P. C., Xenaki, V. C., and Athanasopoulos, G. A. (2000). “Use of EPS geofoam for seismic isolation of earth retaining structures: Results of an FEM study.” In: Proceedings of Second European Geosynthetics Conference, Bologna, Italy, International Geosynthetics Society, Paris, 843-846. Romo, M.P., (1995). “Clay behavior, ground response and soil-structure interaction studies in Mexico City”. In: Proceedings: Third International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, vol. II, pp. 1039-1051. St. Louis, Missouri, USA. Trandafir, A. C., Erickson, B. A., Moyles, J. F., and Bartlett, S. F. (2011). “Confining stress effects on the stress-strain response of EPS geofoam in cyclic triaxial tests.” Proceedings, Geo-Frontiers 2011 Conf., Geo-Institute, ASCE, Reston, VA, 2084-2091. Trandafir, A. C., and Bartlett, S. F. (2010), “Seismic performance of double EPS geofoam buffer systems.” Proceedings of 5th International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics and Symp. in Honor of Professor, I. M. Idriss, San Diego, Missouri University of Science and Technology, Rolla, MO, 1-6. Trandafir, A. C., Bartlett, S. F., and Lingwall, B. N. (2010). “Behavior of EPS geofoam in stress-controlled cyclic uniaxial tests.” Geotext. Geomembr., 28(6), 514–524 Wong, H., Leo, C.J., (2006). “A simple elastoplastic hardening constitutive model for EPS geofoam”. Geotextiles and Geomembranes 24, 299-310. Zarnani, S., Bathurst, J., (2007). “Experimental investigation of EPS geofoam seismic buffers using shaking table tests” Geosynthetics International 14 (3), 165-177.

View publication stats