Development of Laminar Shear Beam (LSB) Containers in Physical Modeling of Geotechnical Earthquake Problems: A Review

Document Type : Review Article

Authors

1 Ph.D. in Geotechnical Engineering, Department of Civil Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran

2 Assistant Professor, Department of Civil Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran

Abstract

Physical modelling experiments at 1 g via shaking table or augmented gravitational field (Ng) with geotechnical centrifuge are powerful tools that have been widely used to investigate the seismic behaviour of various earthquake-related problems in recent decades. It is an established method for verifying design hypothesis, realization failure mechanisms, and gaining an insight into complex geotechnical problems including liquefaction-induced phenomena and their mitigation techniques, level or inclined grounds, problematic soils, retaining walls and embankments, and soil-structure systems such as shallow or pile foundation system through the use of appropriate similitude laws. While element tests are frequently used to obtain dynamic soil parameters, they fail in providing realistic observations of how soil and structures interact in reality. Thus, physical modelling is a better approach to understanding the behaviour of a wide range of geotechnical problems where large deformations occur such as liquefaction, lateral spreading, or landslide. However, geotechnical models cannot be directly mounted on shaking tables due to the requirements of confinement. To properly model the ground in full or reduced-scale physical modelling tests, a model container is required to hold the soil in place and provide confining stresses. Replication of the semi-infinite extent of the ground in a finite dimension model soil container could raise challenging issues; the undesirable effects of the container’s artificial boundaries could affect the obtained results by altering the stress-strain field of the soils through reflected P-waves along other superfluous waves within the model.
In the current study, a comprehensive literature review on the advancement of physical modelling in geotechnics has been carried out. In this regard, a brief historical development of shaking tables and geotechnical centrifuge apparatus was outlined. Further, different types of developed model containers were explored. Additionally, vital criteria and requirements of an ideal container for carrying out seismic model tests at 1 g shaking table or Ng centrifuge experiments were thoroughly discussed. In particular, the development of laminar shear beam (LSB) containers as well as key properties in terms of detail design, construction, and particular usage in designated projects was presented in this paper. In the end, the recently fabricated LSBs were examined nationwide providing key properties and features in their design procedures.
Among all types of developed model containers, LSBs are the most common containers due to their accuracy in reproducing one-dimensional (1D) ground response in seismic conditions. The LSB allows free movement of soil column during shaking without imposing significant boundary effects and is able to maintain 1D soil column behaviour. Moreover, the use of LSBs enables the modelling of large strain modelling problems. Comparative studies by numerous researchers have confirmed that LSBs are the most advanced and efficient type of soil container in modelling soil-structure systems.

Keywords

Main Subjects


  1. Fardis, M.N. and Rakicevic, Z.T. (Eds.) (2011) Role of Seismic Testing Facilities in Performance-Based Earthquake Engineering: SERIES Workshop, 22, Springer Science and Business Media. ISBN: 978-94-007-1977-4.
  2. Iai, S. (1989) Similitude for shaking table tests on soil-structure-fluid model in 1g gravitational field. Soils and Foundations, 29(1), 105-118, https://doi. org/10.3208/sandf1972.29.15.
  3. Meymand, P.J. (1998) Shaking Table Scale Model Tests of Nonlinear Soil-Pile-Super-Structure Interaction in Soft Clay. D. Dissertation, University of California Berkeley, California, USA.
  4. Iai, S., Tobita, T., and Nakahara, T. (2005) Generalised scaling relations for dynamic centrifuge tests. Géotechnique, 55(5), 355-362, https://doi.org/ 10.1680/geot.2005.55.5.355.
  5. Wartman, J. (2006) Geotechnical physical modeling for education: Learning theory approach. Journal of Professional Issues in Engineering Education and Practice132(4), 288-296, https://doi.org/10.1061/ (ASCE)1052-3928 (2006)132: 4(288).
  6. Addis B., Kurrer K.E., and Lorenz W. (2020) Physical Models: Their Historical and Current Use in Civil and Building Engineering Design. John Wiley and Sons, ISBN: 978-3-433-03257-2.
  7. Addis, B. (2020) Past, current and future use of physical models in civil engineering design. Proceedings of the Institution of Civil Engineers-Civil Engineering, 174(2), 61-70, https://doi.org/ 10.1680/jcien.20.00028.
  8. Taylor, R.E. (Ed.) (2018) Geotechnical Centrifuge Technology. CRC Press, London. ISBN: 9780367863852.
  9. Jafarian, Y., Taghavizade, H., Rouhi, S., Shojaemehr, S., and Esmaeilpour, P. (2020) Shaking table experiments to evaluate the boundary effects on seismic response of saturated and dry sands in level ground condition. International Journal of Civil Engineering, 18(7), 783-795, https://doi.org/10.1007/s40999-019-00485-4.
  10. Severn, R.T. (2011) The development of shaking tables–a historical note. Earthquake Engineering and Structural Dynamics, 40(2), 195-213, https://doi.org/10.1002/eqe.1015.
  11. Esmaeilpour, P. (2018) Seismic Behavior of Shallow Foundations on Saturated Loose Sand and Rehabilitation Using Helical Piles: 1g Physical Modeling in Laminar Shear Container. D. Dissertation, International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran (in Persian).
  12. Pokrovskii, G.I. and Fiodorov, I.S. (1936) Studies of soil pressures and deformations by means of a centrifuge. Proceeding of 1st International Conference of Soil Mechanics and Foundation Engineering, 1, p. 70.
  13. Kimura, T. (1988) Centrifuge Research Activities in Japan. Centrifuges in Soil Mechanics, Craig, W.H. James, R.G. and Schofield A.N. (Ed.) Balkema, Rotterdam, 19-28.
  14. Craig, W.H. (1989) The use of a centrifuge in geotechnical engineering education. Geotechnical Testing Journal, 12, 288-291, https://doi.org/ 10.1520/GTJ10986J.
  15. Okamoto, S. (1956) Bearing capacity of sandy soil and lateral earth pressure during earthquake. Proceeding of the 1st World Conference on Earthquake Engineering, California, USA, 1-26.
  16. Drosos, V.A., Gerolymos, N., and Gazetas, G. (2012) Constitutive model for soil amplification of ground shaking: Parameter calibration, comparisons, validation. Soil Dynamics and Earthquake Engineering, 42, 255-274, http://      org/ 10.1016/j.soildyn.2012.06.003.
  17. Giridharan, S., Gowda, S., Stolle, D.F., and Moormann, C. (2020) Comparison of UBCSAND and hypoplastic soil model predictions using the material point method. Soils and Foundations, 60(4), 989-1000, https://doi.org/10.1016/j.sandf. 2020.06.001.
  18. Kramer, S.L. (1996) Geotechnical Earthquake Engineering. Prentice Hall, Englewood Cliffs, New Jersey. ISBN-13: 978-0133749434.
  19. Jafarian, Y., Esmaeilpour, P., Shojaemehr, S., Taghavizade, H., Rouhi, S., and McCartney, J.S. (2021) Impacts of fixed-end and flexible boundary conditions on seismic response of shallow foundations on saturated sand in 1g shaking table tests. Geotechnical Testing Journal, 44(3), 637-664, https://doi.org/10.1007/s40999-019-00485-4.
  20. Zeng, X. and Schofield, A.N. (1996) Design and performance of an equivalent-shear-beam container for earthquake centrifuge modelling. Géotechnique, 46(1), 83-102, https://doi.org/10.1680/geot.1996. 46.1.83.
  21. Whitman, R.V. and Lambe, P.C. (1986) Effect of boundary conditions upon centrifuge experiments using ground motion simulation. Geotechnical Testing Journal, 9(2), 61-71, https://doi.org/10. 1520/GTJ11031J.
  22. Fishman, K.L., Mander, J.B., and Richards Jr, R. (1995) Laboratory study of seismic free-field response of sand. Soil Dynamics and Earthquake Engineering, 14(1), 33-43, https://doi.org/10.1016/ 0267-7261(94)00017-B.
  23. Jakrapiyanun, W. (2002) Physical Modeling of Dynamics Soil-Foundation- Structure-Interaction Using a Laminar Container. D. Dissertation, University of California San Diego, California, USA.
  24. Kokusho, T. and Iwatate, T. (1979) Scaled model tests and numerical analyses on nonlinear dynamic response of soft grounds. Proceedings of the Japan Society of Civil Engineers, 1979(285), 57-67, https://doi.org/10.2208/jscej1969.1979.285_57.
  25. Lambe, P.C. (1981) Dynamic Centrifuge Modeling of a Horizontal Sand Stratum. ScD thesis, Department of Civil Engineering, Massachusetts Institute of Technology (MIT), Cambridge, USA.
  26. Whitman, R.V., Lambe, P.C., and Kutter, B.L. (1981) Initial results from a stacked ring apparatus for simulation of a soil profile. Proceeding of 1st International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, S. Prakash (Ed.), University of Missouri-Rolla, Rolla, Missouri, USA, 3, 1105-1110.
  27. Arulanandan, K., Anandarajah, A., and Abghari, (1983) Centrifugal modeling of soil lique-      faction susceptibility. Journal of Geotechnical               Engineering, 109(3), 281-300, https://doi.org/10. 1061/(ASCE)0733-9410(1983)109:3(281).
  28. Hushmand, B., Scott, R.F., and Crouse, C.B. (1988) Centrifuge liquefaction tests in a laminar box. Géotechnique, 38(2), 253-262, https://doi.org/ 10.1680/geot.1988.38.2.253.
  29. Yoshikawa, M. and Arano, M. (1989) Dynamic behavior of a model pile foundation-ground systems in the liquefaction process. Proceeding of the 9th World Conference on Earthquake Engineering (9WCEE), 3, 599-604, Tokyo-Kyoto, Japan.
  30. Jafarzadeh, B. (2004) Design and evaluation concepts of laminar shear box for 1g shaking table tests. Proceeding of the 13th World Conference on Earthquake Engineering (13WCEE), Vancouver, Canada, p. 1391.
  31. Li, Y., Zheng, S., Luo, W., Cui, J., and Chen, Q. (2020) Design and performance of a laminar shear container for shaking table tests. Soil Dynamics and Earthquake Engineering, 135, 106157, https://doi.org/10.1016/j.soildyn.2020.106157.
  32. Thevanayagam, S., Kanagalingam, T., Reinhorn, A., Tharmendhira, R., Dobry, R., Abdoun, T., Zeghal, M., Ecemis, N., and El Shamy, U. (2009) Laminar box system for 1-g physical modeling of liquefaction and lateral spreading. Geotechnical Testing Journal, 32(5), 1-19, http://doi.org/10. 1520/GTJ102154.
  33. Shen, C.K., Li, X.S., Ng, C.W.W., Van Laak, P.A., Kutter, B.L., Cappel, K., and Tauscher, R.C. (1998) Development of a geotechnical centrifuge in Hong Kong. Proceeding of the International Conference Centrifuge 98, Tokyo, Japan.
  34. Endo, O. and Komanobe, K. (1995) Single and multi-directional shaking table tests of sand liquefaction. Proceeding of the 1st Conference on Earthquake Geotechnical Engineering, Tokyo, Japan, 675-681.
  35. Ueng, T.S., Wang, M.H., Chen, M.H., Chen, C.H., and Peng, L.H. (2006) A large biaxial shear box for shaking table test on saturated sand. Geotechnical Testing Journal, 29(1), 1-8, https://doi.org/10. 1520/GTJ12649.
  36. Turan, A., Hinchberger, S.D., and El Naggar, H. (2009) Design and commissioning of a laminar soil container for use on small shaking tables. Soil Dynamics and Earthquake Engineering, 29(2), 404-414, https://doi.org/10.1016/j.soildyn.2008.04. 003.
  37. Segaline, H., Sáez, E., and Ubilla, J. (2021) Continuous characterization of dynamic soil behavior by digital image correlation in a transparent shear laminar box. Acta Geotechnica, 1-20, https://doi.org/10.1007/s11440-021-01351-1.
  38. Krishna, A.M. and Latha, G.M. (2009). Container boundary effects in shaking table tests on reinforced soil wall models. International Journal of Physical Modeling in Geotechnics, 9(4), 1-14, https://doi.org/10.1680/ijpmg.2009.090401.
  39. Teymur, B. and Madabhushi, S.P.G. (2003) Experimental study of boundary effects in dynamic centrifuge modelling. Géotechnique, 53(7), 655-663, https://doi.org/10.1680/geot.2003.53.7.655.
  40. Lee, C.J., Wei, Y.C., and Kuo, Y.C. (2012) Boundary effects of a laminar container in centrifuge shaking table tests. Soil Dynamics and Earthquake Engineering, 34(1), 37-51, https://doi. org/10.1016/j.soildyn.2011.10.011.
  41. Pozo, C., Gng, Z., and Askarinejad, A. (2016) Evaluation of soft boundary effects (SBE) on the behavior of a shallow foundation. Proceeding of the 3rd European Conference on Physical Modeling in Geotechnics (Eurofuge 2016), Nantes, France, 385-390.
  42. Tsai, C.C., Lin, C.Y., Dashti, S., and Kirkwood, P. (2021) Influence of centrifuge container boundaries and loading characteristics on evaluation of dynamic properties in dry sand. Soil Dynamics and Earthquake Engineering, 142, 106567, https:// doi.org/10.1016/j.soildyn.2020.106567.
  43. Haeri, S.M., Rajabigol, M., Salaripour, S., Kavand, A., Sayyaf, H., Afzalsoltani, S., and Pakzad, A. (2019) Effects of liquefaction-induced lateral spreading on a 3×3 pile group using 1g shake table and laminar shear box. Earthquake Geotechnical Engineering for Protection and Development of Environment and Constructions, Silvestri F., Moraci N. (Ed.) CRC Press, London, 2764-2770.
  44. Van Laak, P.A., Taboada, V.M., Dobry, R., and Elgamal, A.W. (1994) Earthquake centrifuge modeling using a laminar box. Proceeding of Dynamic Geotechnical Testing II, ASTM International, San Francisco, California, USA, 370-384, https://doi.org/10.1520/STP13225S.
  45. Prasad, S.K. (1996) Evaluation of Deformation Characteristics of 1-g Model Ground during Shaking Using a Laminar Box. D. Dissertation, University of Tokyo, Japan.
  46. Prasad, S.K., Towhata, I., Chandradhara, G.P., and Nanjundaswamy, P. (2004) Shaking table tests in earthquake geotechnical engineering. Current Science, 87(10), 1398-1404, http://www.jstor.org/ stable/24109480.
  47. Ecemis, N. (2013) Simulation of seismic liquefaction: 1-g model testing system and shaking table tests. European Journal of Environmental and Civil Engineering, 17(10), 899-919, https:// doi.org/10.1080/19648189.2013.833140.
  48. Lei, H., Hu, Y., Han, Q., Zheng, G., Zhao, B., and Du, Y. (2020) Design and test verification of a cylindrical 3D laminar shear soil container for use on shaking tables. Soil Dynamics and Earthquake Engineering, 139, 106384. https://doi.org/10.1016/ j.soildyn.2020.106384.
  49. Gazetas, G. (1982) Vibrational characteristics of soil deposits with variable wave velocity. International Journal for Numerical and Analytical Methods in Geomechanics, 6(1), 1-20, https://doi. org/10.1002/nag.1610060103.
  50. Taylor, C.A., Dar, A.R., and Crewe, A.J. (1995) Shaking table modeling of seismic geotechnical problems. Proceeding of the 10th European Conference on Earthquake Engineers, Vienna, Austria, 441-446.
  51. Pitilakis, D., Dietz, M., Wood, D.M., Clouteau, D., and Modaressi, A. (2008) Numerical simulation of dynamic soil-structure interaction in shaking table testing. Soil Dynamics and Earthquake Engineering, 28(6), 453-467, https://doi.org/10. 1016/j.soildyn.2007.07.011.
  52. Tang, L., Ling, X., Xu, P., Gao, X., and Wang, D. (2010) Shake table test of soil-pile groups-bridge structure interaction in liquefiable ground. Earthquake Engineering and Engineering Vibration, 9(1), 39-50, https://doi.org/10.1007/ s11803-009-8131-7.
  53. Tsai, C.C., Lin, W.C., and Chiou, J.S. (2016) Identification of dynamic soil properties through shaking table tests on a large saturated sand specimen in a laminar shear box. Soil Dynamics and Earthquake Engineering, 83, 59-68, https:// doi.org/10.1016/j.soildyn.2016.01.007.
  54. Tabatabaiefar, H.R. (2016) Detail design and construction procedure of laminar soil containers for experimental shaking table tests. International Journal of Geotechnical Engineering, 10(4), 328-336, https://doi.org/10.1080/19386362.2016. 1145419.
  55. Vivek, B. and Raychowdhury, P. (2019) Design and calibration of a laminar soil box suitable for a low-capacity shake table using free-field tests on Ganga sand. Soils and Foundations, 59(5), 1602-1612, https://doi.org/10.1016/j.sandf.2019.03.010.
  56. Kim, H., Kim, D., Lee, Y., and Kim, H. (2020) Effect of soil box boundary conditions on dynamic behavior of model soil in 1g shaking table test. Applied Sciences, 10(13), 4642, https://doi.org/ 10.3390/app10134642.
  57. Esmaeilpour, P. and Jafarian, Y. (2019) Detail design and construction procedure of a large-scale aluminum laminar shear box for 1g shaking table tests. Proceeding of 8th International Conference on Seismology and Earthquake Engineering (SEE8), Tehran, Iran.
  58. Esmaeilpour, P., Shojaeemehr, S., Taghavizadeh, H., and Jafarian, Y. (2019) Detail design and performance of a small-scale laminar shear box for 1g shaking table experiments. Proceeding of 8th International Conference on Seismology and Earthquake Engineering (SEE8), Tehran, Iran.
  59. Farrin, M. and Hajialilue-Bonab, M. (2019) Experimental study of the seismic response of Tabriz subway tunnel in dry sand. Bulletin of Earthquake Science and Engineering, 6(3), 85-101.
  60. Fathi, H., Jamshidi Chenari, R., and Vafaeian, (2020) Shaking table study on PET strips-          sand mixtures using laminar box modelling. Geotechnical and Geological Engineering, 38(1), 683-694, https://doi.org/10.1007/s10706-019-01057-y.