University of Arkansas, Fayetteville ScholarWorks@UARK Graduate Theses and Dissertations 12-2018 Utilizing 3D Printed Analogue Soils to Investigate Specimen Size Effects in Triaxial Testing Claire Louise Stewart University of Arkansas, Fayetteville Follow this and additional works at: https://scholarworks.edu/etd Part of the Civil Engineering Commons, and the Geotechnical Engineering Commons Citation Stewart, C. Utilizing 3D Printed Analogue Soils to Investigate Specimen Size Effects in Triaxial Testing. Graduate Theses and Dissertations Retrieved from https://scholarworks.edu/etd/3004 This Thesis is brought to you for free and open access by ScholarWorks@UARK. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of ScholarWorks@UARK.
For more information, please contact scholar@uark. Utilizing 3D Printed Analogue Soils to Investigate Specimen Size Effects in Triaxial Testing A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering by Claire Stewart University of Arkansas Bachelor of Science in Civil Engineering, 2017 December 2018 University of Arkansas This thesis is approved for recommendation to the Graduate Council. Michelle Bernhardt-Barry, Ph. Thesis Director Richard Coffman, Ph.
Kevin Hall, Ph. Committee Member Committee Member ABSTRACT Triaxial testing is one of the fundamental laboratory tests used in geotechnical engineering to determine strength parameters, such as shear strength and friction angle. Investigating the minimum representative elementary volume (REV) can verify the independence of size effects on strength parameters and ensure that the scaled laboratory tests results are consistent, repeatable, and representative of field conditions. Although, REV has been studied for many applications, there is disagreement within geotechnical engineering of a minimum particle diameter to specimen diameter to minimize the size effects related to the REV in consolidated drained (CD) triaxial tests.
This research study compared the strength results of three different specimen diameter sizes to understand the size effects and to investigate the influence of particle shape by using 3D printed spheres and scaled Ottawa sand. 3D printed particles allows different influencing variables on strength parameters such as shape, size, gradation, and surface roughness to be controlled within the granular soil. By isolating a factor, such as shape in this case, the response of the soil can be more clearly understood and a representative REV can be determined. The scaled Ottawa sand and spheres had a greater increase in variability as the diameter decreases, implying that the REV was not met for the 7.11 cm specimen diameter.
It is recommended that a minimum specimen diameter should be at least nine times greater than the maximum particle diameter for spheres and subrounded particles in consolidated drained triaxial testing in order to minimize size effects. ACKNOWLEDGEMENTS I would like to thank my research advisor, Dr. Michelle Bernhardt-Barry, who provided me with guidance, wisdom, and knowledge throughout my research, Bachelor’s and Master’s degree. Thank you for always having your door open and never being too busy to chat even when you had a million other things to do.
I am grateful to have worked with an important role model in my life. I would also like to thank Dr. Richard Coffman and Dr. Kevin Hall for being on my research committee.
I would like to thank my mom, my dad, Natalie, Phoebe, and August. I am incredibly humbled by the constant love, encouragement, and support I received throughout this experience. Mom and Dad, thank you for always believing in my capabilities and potential. Natalie, thank you for inspiring me to achieve my goals.
Phoebe, thank you for being my number one cheerleader. August, thank you for going on this journey with me and providing patience, comfort, and kind words. Words cannot express my gratitude for everything you all have done for me. TABLE OF CONTENTS INTRODUCTION …………………………………………………………………………….2 Representative Elementary Volume (REV)………………………………………………….2 REV for Granular Materials ………………………………………………………………….………11 Material …………………………………………………………………………………………11 Set Up.……………14 RESULTS AND DISCUSSION….…………………42 LIST OF TABLES Table 1: Gypsum Composite Material Properties…………………………….…………………14 Table 2: Test Schedule and Specimen Characteristics………………………………….………17 Table 3: Minimum and Maximum Void Ratio Comparison for Different Molds ……….17 Table 4: Relative Density Comparison of ASTM Mold and Triaxial Test Molds …….18 Table 5: Test Results for Spheres……………………………………………………………….29 Table 6: Test Results for Scaled Ottawa Sand………………………………………….………32 Table 7: Test Results for Large, Medium, and Small Specimen ……………………….………39 LIST OF FIGURES Figure 1: Defining REV in terms of porosity as a function of volume (Bear, 1972)…………….4 Figure 2: Reconstructed 3D tomographed volumes from 2D slices for REV statistical analysis (Ozelim and Cavalcante 2017)………………………………………………………………….…8 Figure 3: Variation of porosity with normalized radius for Silica sand specimens (Razavi et al.11 Figure 4: Projet 260C Modified Curing Protocol (Watters and Bernhardt, 2017)…………….12 Figure 5: Gypsum composite a) scaled Ottawa sand b) spheres………………….……………13 Figure 6: Gradation curve for spheres and scaled Ottawa Sand………………….16 cm scaled Ottawa sand specimen prior to shearing……………….15 Figure 8: Bladder system supplying water to triaxial test cell volume………………….20 Figure 9: Triaxial test setup schematic………………………………………………….………21 Figure 10: Comparison of pore air pressure and pore cell pressure: a) uncorrected volumetric strain b) uncorrected change in water volume c) corrected volumetric strain d) corrected change in water volume.25 Figure 11: Triaxial shear behavior of spheres with large (15.24 cm diameter), medium (10.16 cm diameter), and small (7.11 cm diameter) specimen: a) principal stress difference b) volumetric strain………………………………………….27 Figure 12: Mohr’s Circle for spheres with large (15.24 cm diameter), medium (10.16 cm diameter), and small (7.11 cm diameter) specimen with friction angle range……………….28 Figure 13: Triaxial shear behavior of scaled Ottawa sand with large (15.24 cm diameter), medium (10.16 cm diameter), and small (7.11 cm diameter) specimen: a) principal stress difference b) volumetric strain…………………………………………….30 Figure 14: Figure 13: Mohr’s Circle for scaled Ottawa sand with large (15.24 cm diameter), medium (10.16 cm diameter), and small (7.11 cm diameter) specimen with friction angle range…………………………………………………………………………………………….31 Figure 15: Triaxial shear behavior of scaled Ottawa sand and spheres with large (15.24 cm diameter): a) principal stress difference b) volumetric strain…………….34 Figure 16: Triaxial shear behavior of scaled Ottawa sand and spheres with medium (10.16 cm diameter): a) principal stress difference b) volumetric strain……………………………….35 Figure 17: Triaxial shear behavior of scaled Ottawa sand and spheres with small (7.11 cm diameter): a) principal stress difference b) volumetric strain……………………………….36 Figure 18: Mohr’s circle for scaled Ottawa sand and spheres: a) large specimen b) medium specimen c) small specimen.……………………38 INTRODUCTION Triaxial testing is one of the most common geotechnical laboratory element tests to determine strength parameters, but it can give varying results for granular materials due to size effects from failing to fulfill the representative elementary volume (REV) requirement for the test specimen.
REV has been described as the smallest material volume element of a composite for which the usual spatially constant ‘overall modulus’ macroscopic constitutive representation is a sufficiently accurate model to represent a mean constitutive response (Gitman et al. The REV is not only necessary for geotechnical engineering practice, but for many types of other granular material applications such as the necessary REV in silo flow of different types of grain, granular plant material, and chickpeas (Wiacek et al., 2012, Wiacek and Molenda, 2015). However, there is a lack of research determining size effects caused by REV for coarse-grained soils during consolidated drained (CD) triaxial testing. This research is comprised of performing CD triaxial testing to investigate the specimen size effects of different specimen diameters with the same particle size and gradation.
A gypsum composite was chosen as the 3D printed granular analogue material due to the homogeneity and consistency of the material and so that the REV of different particle shapes could be examined without any changes in material or surface properties. Inherent properties such as gradation, mineralogy, size, surface roughness, and particle shape can be controlled with additive manufacturing technology. Since it is known that particle shape affects the REV, as well as the strength parameters, spheres and scaled Ottawa sand were used to compare the influence of particle shape on the REV and overall soil behavior. Three specimen diameters were tested while the particle gradation was held constant.
The specimen size effects were then investigated according to the stress-strain and volumetric responses. Following this introduction, additional 1 background on REV and specimen size effects is given. Then the methodology for this study is presented, followed by the results, discussion, and conclusions. BACKGROUND Since its advent in the 1930’s by Dr.
Casagrande, triaxial testing has become one of the most prominent geotechnical laboratory element tests for measuring soil shear strength. Its popularity is mainly due to the ease of testing (i. setup, controlled drainage, and analysis of the results), and the fact that there are significantly less stress concentrations within the specimen, and unlimited locations of the failure plane (Holtz et al. Depending on the in situ state of the soil, there are many methods of triaxial tests that can be performed to mimic the actual field conditions.
CD triaxial testing was used in this research to replicate a condition of a previously consolidated granular soil with a high permeability, allowing for the drainage of water in the cell volume when an axial load is applied to the soil. Standards have been set which outline the proper testing setup and procedures for CD triaxial testing, so that a soil’s shear strength can be accurately predicted; however, the correct particle size to specimen diameter ratios have been a topic of disagreement amongst researchers. Results of CD triaxial testing can be skewed or inconsistent if the largest particle diameter is too large compared to the specimen diameter. Therefore, the REV in CD triaxial testing of granular materials needs to be further investigated.
Representative Element Volume (REV) All engineering materials that are tested to further understand engineering properties have one important question that needs to be answered before testing begins: what is the volume of material needed (known as REV) which will eliminate size effects? Obtaining the REV when 2 performing laboratory material tests at a reduced scale is crucial to replicate equivalent results that would be observed in the field. The REV verifies the independence of scaling for the physical and mechanical properties of any type of engineering material. Bear introduced the concept of REV in 1972 with a mathematical concept as presented in Equation 1: 𝑛𝑖 ≡ 𝑛𝑖 (∆𝑈𝑖 ) = (∆𝑈𝑣 )𝑖 /∆𝑈𝑖 (Equation 1) where 𝑛𝑖 = porosity; ∆𝑈𝑖 = total volume; and ∆𝑈𝑣 𝑖 = the volume of void space. The porosity at a volume much larger than a single grain must be equal to the porosity when gradually reducing the volume: ∆𝑈1 > ∆𝑈2 > ∆𝑈3 … > 𝛥𝑈𝑖.
Porosity is chosen in this instance as the variable to define the concept of REV, but Bear (1972) also stated that REVs of the medium may need to be defined on the basis of parameters other than porosity, such as stress tensor (Masson and Martinez, 2000), permeability (Ozelim and Cavalcante, 2017), moisture saturation and interfacial area (Costanza-Robinson et al., 2011), and average coordination number (Wiacek and Molenda, 2015.; Masson and Martinez, 2000). Figure 1 represents the scaling effects on porosity as the total volume increases as presented by Bear (1972). The fluctuation of porosity can be seen when a volume is between 0 and ∆𝑈𝑜 due to microscopic effects, when the volume becomes on the order of magnitude of the average distance between the molecules. From ∆𝑈0 to ∆𝑈1 , the REV is sufficiently captured for homogeneous materials due to the constant porosity value of 𝑛.
Once the volume reaches ∆𝑈1 the medium shifts from a homogeneous to inhomogeneous medium, the soil layers are assumed to change. 3 Figure 1: Defining REV in terms of porosity as a function of volume (Bear, 1972). REV has also been described as the smallest volume of a soil sample where the macroscopic mechanical behavior of the soil can be determined in terms of averages (Wiacek and Molenda, 2015). REV must be determined in order to accurately predict the behavior of materials at different scales (i., micro-scale in laboratory testing and macro-scale in the field).
Choosing the appropriate test size will dictate the reliability and representation of collected laboratory data.