THE GEOGRID STIFFNESS FROM SMALL TO LARGE STRAIN UNDER TENSILE LOADING

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1 THE GEOGRID STIFFNESS FROM SMALL TO LARGE STRAIN UNDER TENSILE LOADING Huai-Houh Hsu 1, Meng-Shan Hsieh 2, Yu-Hsien Ho 3 and Ching-Yi Lin 3 1 Department of Civil Engineering 2 Institute of Mechatronoptic Systems Chienkuo Technology University Chang-Hua, TAIWAN 3 Technical Support Department ACE Geosynthetic Enterprise Co., Ltd. Ta-Chia, TAIWAN ABSTRACT To sustain wave forces and traffic loads, some of the coastal structures are constructed with geosynthetics. Limited equilibrium analysis is widely used to analyze the stabilities of these structures. It can provide safety factor at probable failure surface but can not predict the deformation of retaining structure. The working stress analysis (WSA) has been developed and attempt to solve this problem. According to the results measured from in-situ tests and laboratory tests, WSA uses finite element method or finite difference method to estimate external deformation, distribution of internal stress and strain. The stress-strain curve for a geosynthetic material is nonlinear. In small strain level, the stiffness of geosynthetics could be varied rapidly. In order to apply WSA reasonably, the stiffness of geosynthetics at different strain level should be established. Equipped with servo motor and highly resolution measurement system, a series of tensile loading tests is performed using PET geogrids to discuss their behaviors under different strain rates. This paper introduces this equipment, presents the results, and discusses the performance of geogrids. INTRODUCTION The Mechanically Stabilized Earth Wall (MSEW) is one of the popular earth retaining structures for slope stability. The safety of MSEW generally is determined by limited equilibrium analysis (LEA). But this method will cause a conservative but less economic design. The working stress analysis (WSA) has been developed and attempts to solve this problem. By means of finite element or finite difference concepts, WSA can predict the distribution of stress and strain of MSEW. Allen and Bathurst (2003) adopted the frame of WSA to develop the K-stiffness method. There are monitoring data obtained from 64 full size MSEW to be compared with predict values of K-stiffness method. Results show that K-stiffness method can raise economical profit of constructing MSEW efficiently. To obtain well prediction values by WSA, the decision of material strength parameters are important. The stiffness of soil will decrease as strain increases (see Fig. 1). Atkison and Sallfors (1991) defined three stages of soil strain as follows: 204

2 1. very small strain: shear strain smaller than % 2. small strain: shear strain between % and 1% 3. large strain: shear strain greater than 1% Figure 1. Stiffness strain curve of soil (after Atkinson, 2000) As shown in Figure 1, the shear strain of retaining wall is between 0.01% and 0.1%. In most cases of MSEW, the peak strain was no more than 2% at the end of construction (Bathurst et al., 2002). The dynamical soil properties can be obtained from dynamic or cyclic laboratory tests. The material properties of geogrid also should be known in a small strain range at different strain levels. The stiffness of short-term tensile loading tests and creep tests are more or less different. PP and HDPE have more obvious different stiffness between these two tests, but PET is less different (Allen and Bathurst, 2002). Shinoda and Bathurst (2004) applied video-extensometer apparatus to observe the axial and lateral deformation of PET, HDPE and PP geogrids. Results show that the deformation of PET was not affected by strain rate, but the influence was clear for HDPE and PP. For reasonably predicting the behavior of MSEW by WSA, the material properties of geogrid should be known in a small strain range at different strain levels. SMALL STRAIN MEASUREMENT SYSTEM In order to establish the global load strain curve and local strain curve at different strain level, a system is capable of measuring small deformation has been developed. The small strain measurement system (SSMS) is comprised of three components: the driving system, the instrumentation system, and control system. The driving system consists of a stepper motor, a ball screw, and a ball spline. The stepper motor has a resolution of 1,228,800 steps per revolution. Its direction, step numbers, and speed can be controlled by users program. The ball screw and ball spline are used for transforming rotational 205

3 motion of stepper motor into a linear motion to generate cyclic or monotonic displacement. Every 1mm linear displacement needs 241,889 motor steps to achieve, the highly resolution is ideal for controlling a very small movement. The instrumentation system include electrical sensors and data acquisition device. Two types of load cell, 1000 and 2000 kgf, are used to measure the tensile loadings. Two linear variable differential transducer (LVDT) are separately attached at the middle part of geogrid (1/3) to the upper and bottom fixed end to read its full range deformation. Figure 2 illustrates the schematic view of SSMS. Figure 3 shows the whole assembly system. The control system controls stepper motor and data acquisition. A set of self-writing program controls the direction, speed, and steps of stepper motor to generate desire motion. A data acquisition device, which is a 22 bits analog/digital converter, is combined with self-writing program to transform sensor output readings into personal computer. Figure 2. Schematic view of SSMS 206

4 Figure 3. Photo of the SSMS DISCUSSION OF RESULTS A series of monotonic tensile loading tests were performed to verify the capability of SSMS. The properties of tested geogrid are shown in Table 1. For the sake of comparison, another tensile loading equipment (GT-AI-7000L) was used to carry out tests. Its capacity is 20,000 kgf. The deformation of grid is measured by the relative displacement of two steel wires with clips at the central of test material. Each wire connect to a roller counter at the top and bottom side of clamp. Figure 4 shows the photo of GT-AI-7000L. Two strain rates (Vs = 1%/min. and 10%/min.) were used and two strain levels (ε = 1% and 3%) were measured. Variables applied in this series of tensile loading tests are summarized in Table 2. Table 1. Basic characteristics of the tested geosynthetic Product name Type Polymer Tensile strength kn/m MD40 woven geogrid with PVC coating PET Table 2. Variables applied to the tensile loading tests Test No. Equipment Vs Sensors for measuring Strain level %/min. small strain % PET40-2 to PET40-5 SSMS 1 2 LVDTs 1, 3 PET40-6 to PET40-9 SSMS 10 2 LVDTs 1, 3 GT-1 to GT-7 GT-AI-7000L 10 none - 207

5 Two types of stiffness are proposed to illustrate the variation of global and local stiffness curves. As shown in Figure 5, the global secant stiffness (J sg ) is the slope of origin to the desired strain on the curve. The local secant stiffness (J sl ) is the slope of start point of a strain level to the desired strain on the curve. Figure 4. Photo of GT-AI-7000L J sg J sl ε Figure 5. Definition of J sg and J sl Figures 6 and 7 show the load strain curve at different Vs, results indicate that the influence of Vs is not obvious. The J sg - strain curves show SSMS can make a smoother curve than GT-AI-7000L. 208

6 Load per unit width, T (kn/m) Test No. Vs, %/min. PET PET PET PET Figure 6. The global load - strain curves with different Vs Load per unit width, T (kn/m) Test No. Vs, %/min. PET PET GT-3 10 Global stiffness, J sg (kn/m) Test No. Vs, %/min. PET PET GT Figure 7. The global load - strain and J sg - strain curves with different Vs and equipments Figures 8 and 9 demonstrate local - strain curves at two strain levels. The measured local strains (ε L ) are within 0.3%, and curves obtained from readings of LVDTs indicate a clearer trend. The load strain curve becomes noisier at higher strain level. It implies that lots of PET yarns had been broken and/or slip occurs at fixed ends to release the displacement. The J sl is determined no more than ε L of 0.3%, in such a small strain range it can be considered as tangent stiffness. The J sl curve represents the variation of stiffness at certain strain level, it can provide the WSA a more precise prediction. 209

7 9 Local strain, ε L Local strain, ε L Load per unit width, T (kn/m) 8 7 Test No. PET40-9 (LVDT) GT-1 GT-2 GT-3 Local stiffness, J sl (kn/m) Test No. PET40-9 (LVDT) GT-1 GT-2 GT Figure 8. The local load - strain and J sl - strain curves at strain level of 1% 22 Local strain, ε L Local strain, ε L Load per unit width, T (kn/m) Test No. PET40-9 (LVDT) GT-1 GT-2 GT-3 Local stiffness, J sl (kn/m) Test No. PET40-9 (LVDT) GT-1 GT-2 GT Figure 9. The local load - strain and J sl - strain curves at strain level of 3% CONCLUSIONS A small strain measurement system (SSMS) has been developed, and a series of tests have been performed to verify its capability. In the light of results, the conclusions are as follows: 210

8 1. The step motor has high resolution makes it easier perform linear controlled tests. The Small Strain Measurement System (SSMS) capable of performing monotonic and cyclic tensile tests has been developed. 2. The different strain rates (1%/min. and 10%/min.) didn t show obvious difference of load strain curves. 3. The local load - strain curves (ε L = 0 to 0.3%) at different strain levels (1% and 3%) show well performance of SSMS. 4. In comparison of 2 strain levels, the local load - strain curves get more random at higher strain level. There indicates lots of PET yarns had been broken and/or slip occurs at fixed ends to release the displacement. 5. The local stiffness (J sl ), which is similar to tangent stiffness value, can actual present the variation of stiffness at the neighborhood of designated strain. While using WSA to get well predictions, the local stiffness variation curve at designating strain level should be clearly established. In the lights of test results, SSMS can achieve these requirements. REFERENCES Atkinson, J.K. and Sallfors, G Experimental Determination of Soil Properties. Proceedings, 10 th ECSMFE. Florence 3, Allen, T.M. and Bathurst, R.J Prediction of Reinforcement Loads in Reinforced Soil Walls. Department of Transportation of Washington State and in cooperation with U.S. Department of Transportation Federal Highway Administration. Report No. WA-RD Bathurst, R.J. and Cai, Z In-Isolation Cyclic Load-Extension Behavior of Two Geogrids. Geosynthetics International. 1(1): Bathurst, R.J., Allen, T.M., and Walters, D.L Short-Term Strain and Deformation Behavior of Geosynthetic Walls at Work Stress Conditions. Geosynthetics International, 9(5-6): Ling, H.I., Mohri, Y., and Kawabata, T Tensile Properties of Geogrids under Cyclic Loadings. Journal of Geotechnical and Geoenvironmental Engineering. ASCE, 124(8): Luna, R. and Jadi, H Determination of Dynamic Soil Properties Using Geophysical Methods. St. Louis, Missouri. Geophysics Dec. 15. McGown, A., Yeo, K.C. and Yogarajak, I Identification of a Dynamic Interlock Mechanism Performance of Reinfroced Soil Structure. Proceedings, International Reinforced Soil Conference Shinoda, M. and Bathurst, R. J Lateral and Axial Deformation of PP, HDPE and PET Geogrids under Tensile Load. Geotextile and Geomembrance. 22: Toki, S., Shibuya, S. and Yamashita, S Standardization of Laboratory Test Methods to Determine the Cyclic Deformation Properties of Geomaterials in Japan. Proceedings, 1st Pre-Failure Deformation of Geomaterials, Sapporo, Japan. 2: