# Cyclic Behaviour of Uniform Sand in Drained and Undrained Conditions at Low Confining Stress in Small-Scale Landslide Model

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods and Materials

#### 2.1. Small-Scale Dynamic Landslide Testing

#### 2.2. Cyclic Triaxial Equipment

#### 2.3. Soil Type and Specimen Preparation

#### 2.4. Testing Methodology

#### 2.5. Damping, Degradation, Pore Pressure Build-Up, and Volume Change

## 3. Results

#### 3.1. Undrained Cyclic Triaxial Test Results

#### 3.2. Drained Cyclic Triaxial Test Results

## 4. Discussion

## 5. Conclusions

- Low confining stress plays a significant role in the dynamic properties of sand in both drained and undrained conditions.
- In undrained tests, for axial strains up to $0.033\%$, sand first hardens and then degrades. At higher values of strain, it only degrades.
- In undrained tests, for axial strains up to $0.033\%$, sand generates up to 40% ${r}_{u}$, but it does not have a significant effect on degradation. At higher values of strain, ${r}_{u}$ rapidly rises.
- In drained tests, degradation decreases after the fourth cycle for larger values of confining stress. After the fourth cycle, soil densifies due to accumulated volumetric strain.
- In drained tests, degradation after the fourth cycle decreases and hardening takes place.
- The proposed analytical models for ${r}_{u}$ and ${\epsilon}_{v}$ are in good correlation to the tested results and can be used to evaluate the normalized pore water pressure ratio and/or accumulated volumetric strains for cycles N = 2 or N = 10 in conditions of low confining stress.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

LVDT | Linear variable differential transducers |

PID | Proportional–Integrate–Derivative |

## References

- Popescu, M.E. Landslide causal factors and landslide remediatial options. In Proceedings of the 3rd International Conference on Landslides, Slope Stability and Safety of Infra-Structures, Singapore, 11–12 July 2002; pp. 61–81. [Google Scholar]
- Wu, L.Z.; Huang, R.Q.; Xu, Q.; Zhang, L.M.; Li, H.L. Analysis of physical testing of rainfall-induced soil slope failures. Environ. Earth Sci.
**2015**, 73, 8519–8531. [Google Scholar] [CrossRef] - Kumar, S.S.; Krishna, A.M.; Dey, A. Evaluation of dynamic properties of sandy soil at high cyclic strains. Soil Dyn. Earthq. Eng.
**2017**, 99, 157–167. [Google Scholar] [CrossRef] - Icl. Instruction for World Reports on Landslides; Technical Report; Icl: New York, NY, USA, 2016. [Google Scholar]
- Yang, J.; Luo, X. Exploring the relationship between critical state and particle shape for granular materials. J. Mech. Phys. Solids
**2015**, 84, 196–213. [Google Scholar] [CrossRef] - Gabet, E.J.; Mudd, S.M. The mobilization of debris flows from shallow landslides. Geomorphology
**2006**, 74, 207–218. [Google Scholar] [CrossRef] - Iida, T. Theoretical research on the relationship between return period of rainfall and shallow landslides. Hydrol. Process.
**2004**, 18, 739–756. [Google Scholar] [CrossRef] - Saito, H.; Nakayama, D.; Matsuyama, H. Two Types of Rainfall Conditions Associated with Shallow Landslide Initiation in Japan as Revealed by Normalized Soil Water Index. SOLA
**2010**, 6, 57–60. [Google Scholar] [CrossRef][Green Version] - Matsushi, Y.; Hattanji, T.; Matsukura, Y. Mechanisms of shallow landslides on soil-mantled hillslopes with permeable and impermeable bedrocks in the Boso Peninsula, Japan. Geomorphology
**2006**, 76, 92–108. [Google Scholar] [CrossRef] - Saito, H.; Nakayama, D.; Matsuyama, H. Relationship between the initiation of a shallow landslide and rainfall intensity-duration thresholds in Japan. Geomorphology
**2010**, 118, 167–175. [Google Scholar] [CrossRef] - Gariano, S.L.; Brunetti, M.T.; Iovine, G.; Melillo, M.; Peruccacci, S.; Terranova, O.; Vennari, C.; Guzzetti, F. Calibration and validation of rainfall thresholds for shallow landslide forecasting in Sicily, southern Italy. Geomorphology
**2015**, 228, 653–665. [Google Scholar] [CrossRef] - Salciarini, D.; Godt, J.W.; Savage, W.Z.; Conversini, P.; Baum, R.L.; Michael, J.A. Modeling regional initiation of rainfall-induced shallow landslides in the eastern Umbria Region of central Italy. Landslides
**2006**, 3, 181–194. [Google Scholar] [CrossRef] - Giannecchini, R.; Galanti, Y.; D’Amato Avanzi, G. Critical rainfall thresholds for triggering shallow landslides in the Serchio River Valley (Tuscany, Italy). Nat. Hazards Earth Syst. Sci.
**2012**, 12, 829–842. [Google Scholar] [CrossRef] - Vennari, C.; Gariano, S.L.; Antronico, L.; Brunetti, M.T.; Iovine, G.; Peruccacci, S.; Terranova, O.; Guzzetti, F. Rainfall thresholds for shallow landslide occurrence in Calabria, southern Italy. Nat. Hazards Earth Syst. Sci.
**2014**, 14, 317–330. [Google Scholar] [CrossRef][Green Version] - Arbanas, Ž.; Sassa, K.; Nagai, O.; Jagodnik, V.; Vivoda, M.; Jovančevic, S.D.; Perani c, J.; Ljuti c, K. A Landslide Monitoring and Early Warning System Using Integration of GPS, TPS and Conventional Geotechnical Monitoring Methods; Springer: Berlin/Heidelberg, Germany, 2014; pp. 631–636. [Google Scholar] [CrossRef]
- Pecoraro, G.; Calvello, M.; Piciullo, L. Monitoring strategies for local landslide early warning systems. Landslides
**2019**, 16, 213–231. [Google Scholar] [CrossRef] - Guzzetti, F.; Gariano, S.L.; Peruccacci, S.; Brunetti, M.T.; Marchesini, I.; Rossi, M.; Melillo, M. Geographical landslide early warning systems. Earth-Sci. Rev.
**2020**, 200, 102973. [Google Scholar] [CrossRef] - Stark, T.D.; Choi, H.; McCone, S. Drained Shear Strength Parameters for Analysis of Landslides. J. Geotech. Geoenviron. Eng.
**2005**, 131, 575–588. [Google Scholar] [CrossRef] - Öge, İ.F. Investigation of design parameters of a failed soil slope by back analysis. Eng. Fail. Anal.
**2017**, 82, 266–279. [Google Scholar] [CrossRef] - Donati, D.; Stead, D.; Brideau, M.A.; Ghirotti, M. Using pre-failure and post-failure remote sensing data to constrain the three-dimensional numerical model of a large rock slope failure. Landslides
**2021**, 18, 827–847. [Google Scholar] [CrossRef] - Chen, X.P.; Liu, D. Residual strength of slip zone soils. Landslides
**2014**, 11, 305–314. [Google Scholar] [CrossRef] - Arbanas, Ž.; Pajalić, S.; Jagodnik, V.; Peranić, J.; Vivoda Prodan, M.; Domlija, P.; Dugonjić-Jovančević, S. Development of physical model of landslide remedial constructions’ behaviour. In Proceedings of the 4th Regional Symposium on Landslides in the Adriatic-Balkan Region, Sarajevo, Bosnia and Herzegovina, 23–25 October 2019; Uljarević, M., Zekan, S., Salković, S., Ibrahimović, D., Eds.; Društvo za Geotehniku u Bosni i Hercegovini: Sarajevo, Bosnia and Herzegovina, 2019; pp. 103–108. [Google Scholar] [CrossRef]
- Pajalić, S.; Peranić, J.; Maksimović, S.; Čeh, N.; Jagodnik, V.; Arbanas, Ž. Monitoring and data analysis in small-scale landslide physical model. Appl. Sci.
**2021**, 11, 5040. [Google Scholar] [CrossRef] - Jagodnik, V.; Turković, M.; Arbanas, Ž. Preliminary results on the undrained cyclic behavior of uniform sand at low confining stress. In Proceedings of the 5th Regional Symposium on Landslides in the Adriatic-Balkan Region, Rijeka, Croatia, 23–26 March 2022; Peranić, J., Vivoda Prodan, M., Bernat Gazibara, S., Krkač, M., Mihalič Arbanas, S., Arbanas, Ž., Eds.; Faculty of Civil Engineering, University of Rijeka and Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb: Rijeka, Croatia, 2022; pp. 201–206. [Google Scholar]
- Yang, G.; Qi, S.; Wu, F.; Zhan, Z. Seismic amplification of the anti-dip rock slope and deformation characteristics: A large-scale shaking table test. Soil Dyn. Earthq. Eng.
**2018**, 115, 907–916. [Google Scholar] [CrossRef] - Jafarzadeh, F.; Farahi-Jahromi, H.; Rajabigol, M. Applicability of rigid block based approaches in predicting sandy slope displacements by 1g shaking table tests. Soil Dyn. Earthq. Eng.
**2019**, 126, 105576. [Google Scholar] [CrossRef] - Wang, K.L.; Lin, M.L. Initiation and displacement of landslide induced by earthquake—A study of shaking table model slope test. Eng. Geol.
**2011**, 122, 106–114. [Google Scholar] [CrossRef] - Wartman, J.; Seed, R.B.; Bray, J.D. Shaking Table Modeling of Seismically Induced Deformations in Slopes. J. Geotech. Geoenviron. Eng.
**2005**, 131, 610–622. [Google Scholar] [CrossRef] - Ozkahriman, F.; Wartman, J. Investigation of 1-G Similitude Laws by “Modeling-of-Models” Exercise; American Society of Civil Engineers: Reston, VA, USA, 2007. [Google Scholar] [CrossRef]
- Grasso, S.; Lentini, V.; Sammito, M.S.V. A New Biaxial Laminar Shear Box for 1 g Shaking Table Tests on Liquefiable Soils. In Geotechnical, Geological and Earthquake Engineering; Springer: Cham, Switzerland, 2022; pp. 1499–1507. [Google Scholar] [CrossRef]
- Ling, H.; Ling, H.I. Centrifuge Model Simulations of Rainfall-Induced Slope Instability. J. Geotech. Geoenviron. Eng.
**2012**, 138, 1151–1157. [Google Scholar] [CrossRef] - Zhang, Z.; Wang, T.; Wu, S.; Tang, H.; Liang, C. Seismic performance of loess-mudstone slope by centrifuge tests. Bull. Eng. Geol. Environ.
**2017**, 76, 671–679. [Google Scholar] [CrossRef] - Zhang, Z.; Wang, T.; Wu, S.; Tang, H.; Liang, C. Investigation of dormant landslides in earthquake conditions using a physical model. Landslides
**2017**, 14, 1181–1193. [Google Scholar] [CrossRef] - Take, W.A.; Bolton, M.D.; Wong, P.C.P.; Yeung, F.J. Evaluation of landslide triggering mechanisms in model fill slopes. Landslides
**2004**, 1, 173–184. [Google Scholar] [CrossRef] - Wang, S.; Idinger, G.; Wu, W. Centrifuge modelling of rainfall-induced slope failure in variably saturated soil. Acta Geotech.
**2021**, 16, 2899–2916. [Google Scholar] [CrossRef] - Matziaris, V.; Marshall, A.M.; Yu, H.S. Centrifuge Model Tests of Rainfall-Induced Landslides. In Recent Advances in Modeling Landslides and Debris Flows; Wu, W., Ed.; Springer: Cham, Switzerland, 2015; pp. 73–83. [Google Scholar] [CrossRef]
- Madabhushi, G. Centrifuge Modelling for Civil Engineers; CRC Press: Boca Raton, FL, USA, 2017. [Google Scholar]
- Eckersley, D. Instrumented laboratory flowslides. Géotechnique
**1990**, 40, 489–502. [Google Scholar] [CrossRef] - Clough, R.W.; Pirtz, D. Earthquake Resistance of Rock-Fill Dams. J. Soil Mech. Found. Div.
**1956**, 82, 1–26. [Google Scholar] [CrossRef] - Fan, G.; Zhang, J.; Wu, J.; Yan, K. Dynamic Response and Dynamic Failure Mode of a Weak Intercalated Rock Slope Using a Shaking Table. Rock Mech. Rock Eng.
**2016**, 49, 3243–3256. [Google Scholar] [CrossRef] - Lin, M.L.; Wang, K.L. Seismic slope behavior in a large-scale shaking table model test. Eng. Geol.
**2006**, 86, 118–133. [Google Scholar] [CrossRef] - Jibson, R.W. Methods for assessing the stability of slopes during earthquakes—A retrospective. Eng. Geol.
**2011**, 122, 43–50. [Google Scholar] [CrossRef] - Iai, S.; Tobita, T.; Nakahara, T. Generalised scaling relations for dynamic centrifuge tests. Geotechnique
**2005**, 55, 355–362. [Google Scholar] [CrossRef] - White, J.R.F. A Laboratory Investigation into the Behaviour of Sand at Low Confining Stresses; University of Oxford: Oxford, UK, 2020. [Google Scholar]
- Dobry, R.; Ladd, R.; Yokel, F.Y.; Chung, R.M.; Powell, D. Prediction of Pore Water Pressure Buildup and Liquefaction of Sands during Earthquakes by the Cyclic Strain Method; National Bureau of Standards: Gaithersburg, MD, USA, 1982; Volume 138. [Google Scholar]
- Vucetic, M. Cyclic Threshold Shear Strains in Soils. J. Geotech. Eng.
**1994**, 120, 2208–2228. [Google Scholar] [CrossRef] - Tabata, K.; Vucetic, M. Threshold Shear Strain for Cyclic Degradation of Three Clays. In Proceedings of the 5th International Conferences on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, Missouri University of Science and Technology, Rolla, MO, USA, 24–29 May 2010; p. 30. [Google Scholar]
- Vucetic, M.; Mortezaie, A. Cyclic secant shear modulus versus pore water pressure in sands at small cyclic strains. Soil Dyn. Earthq. Eng.
**2015**, 70, 60–72. [Google Scholar] [CrossRef][Green Version] - Chakraborty, T.; Salgado, R. Dilatancy and Shear Strength of Sand at Low Confining Pressures. J. Geotech. Geoenviron. Eng.
**2010**, 136, 527–532. [Google Scholar] [CrossRef] - Shaoli, Y.; Sandven, R.; Grande, L. Liquefaction of sand under low confining pressure. J. Ocean Univ. Qingdao
**2003**, 2, 207–210. [Google Scholar] [CrossRef] - Sture, S.; Batiste, S.; Lankton, M.; Parisi, J. Properties of Sand under Low Effective Stresses. In Proceedings of the Ninth Biennial Conference on Engineering, Construction, and Operations in Challenging Environments, League City, Houston, TX, USA, 7–10 March 2004; Ramesh, B., Malla, R., Maji, A., Eds.; American Society of Civil Engineers: Reston, VA, USA, 2004; pp. 78–84. [Google Scholar] [CrossRef]
- NASA. What Is Microgravity? Available online: https://www.nasa.gov/audience/forstudents/5-8/features/nasa-knows/what-is-microgravity-58.html (accessed on 2 September 2022).
- Lee, C.T.; Huang, C.C.; Lee, J.F.; Pan, K.L.; Lin, M.L.; Dong, J.J. Statistical approach to earthquake-induced landslide susceptibility. Eng. Geol.
**2008**, 100, 43–58. [Google Scholar] [CrossRef] - Lee, S.; Evangelista, D.G. Earthquake-induced landslide-susceptibility mapping using an artificial neural network. Nat. Hazards Earth Syst. Sci.
**2006**, 6, 687–695. [Google Scholar] [CrossRef] - Umar, Z.; Pradhan, B.; Ahmad, A.; Jebur, M.N.; Tehrany, M.S. Earthquake induced landslide susceptibility mapping using an integrated ensemble frequency ratio and logistic regression models in West Sumatera Province, Indonesia. CATENA
**2014**, 118, 124–135. [Google Scholar] [CrossRef] - Glade, T.; Nadim, F. Early warning systems for natural hazards and risks. Nat. Hazards
**2014**, 70, 1669–1671. [Google Scholar] [CrossRef][Green Version] - Ma, J.; Xia, D.; Guo, H.; Wang, Y.; Niu, X.; Liu, Z.; Jiang, S. Metaheuristic-based support vector regression for landslide displacement prediction: A comparative study. Landslides
**2022**, 19, 2489–2511. [Google Scholar] [CrossRef] - Ma, J.; Xia, D.; Wang, Y.; Niu, X.; Jiang, S.; Liu, Z.; Guo, H. A comprehensive comparison among metaheuristics (MHs) for geohazard modeling using machine learning: Insights from a case study of landslide displacement prediction. Eng. Appl. Artif. Intell.
**2022**, 114, 105150. [Google Scholar] [CrossRef] - Miranda, E.; Brzev, S.; Bijelić, N.; Arbanas, Ž.; Bartolac, M.; Jagodnik, V.; Lazarević, D.; Arbanas, S.M.; Zlatović, S.; Acosta, A.; et al. StEER-EERI: Petrinja, Croatia December 29, 2020, Mw 6.4 Earthquake Joint Reconnaissance Report (JRR). 2021. Available online: https://www.designsafe-ci.org/data/browser/public/designsafe.storage.published/PRJ-2959/details-4541797621822058005-242ac118-0001-012 (accessed on 2 September 2022).
- Herak, D.; Sović, I.; Cecić, I.; Živčić, M.; Dasović, I.; Herak, M. Historical seismicity of the Rijeka region (northwest External Dinarides, Croatia)—Part I: Earthquakes of 1750, 1838, and 1904 in the Bakar epicentral area. Seismol. Res. Lett.
**2017**, 88, 904–915. [Google Scholar] [CrossRef] - Herak, M.; Živčić, M.; Sović, I.; Cecić, I.; Dasović, I.; Stipčević, J.; Herak, D. Historical Seismicity of the Rijeka Region (Northwest External Dinarides, Croatia)—Part II: The Klana Earthquakes of 1870. Seismol. Res. Lett.
**2018**, 89, 1524–1536. [Google Scholar] [CrossRef] - Quanser. Shake Table III XY Data Sheet; Quanser: Markham, ON, Canada, 2022. [Google Scholar]
- Han, R.; Zhao, X. Shaking Table Tests and Validation of Multi-Modal Sensing and Damage Detection Using Smartphones. Buildings
**2021**, 11, 477. [Google Scholar] [CrossRef] - Larbi, S.H.; Bourahla, N.; Benchoubane, H.; Choutri, K.; Badaoui, M. Earthquake Ground Motion Matching on a Small Electric Shaking Table Using a Combined NN-PDFF Controller. Shock Vib.
**2020**, 2020, 7260590. [Google Scholar] [CrossRef] - Bićanić, N.; Camenen, J.F.; Čeh, N.; Koziara, T. Characterisation of pattern formation in constrained multiblock assembly subjected to horizontal harmonic excitation. Int. J. Mason. Res. Innov.
**2016**, 1, 375. [Google Scholar] [CrossRef] - Dobrilla, S.; Čeh, N.; Tuhtan, M.; Jelenić, G. Experimental Analysis of Structure Response to Non-uniform Support Excitation. Zb. Rad.
**2018**, 20, 175–188. [Google Scholar] [CrossRef][Green Version] - Controls. Dynamic Triaxial System—DYNATRIAX Testing Equipment, Controls. Available online: https://www.controls-group.com/usa/dynamic-testing-systems/dynamic-triaxial-system-dynatriax-ems.php (accessed on 31 August 2020).
- ISO 14688-1:2017; Geotechnical Investigation and Testing—Identification and Classification of Soil—Part 1: Identification and Description. Technical Report; ISO: Geneva, Switzerland, 2017.
- Ladd, R.S. Preparing test specimens using under compaction. Geotech. Test. J.
**1978**, 1, 16–23. [Google Scholar] [CrossRef] - Kodicherla, S.P.K.; Gong, G.; Fan, L.; Moy, C.K.; He, J. Effects of preparation methods on inherent fabric anisotropy and packing density of reconstituted sand. Cogent Eng.
**2018**, 5, 1533363. [Google Scholar] [CrossRef] - Frost, J.D.; Park, J.Y. A critical assessment of the moist tamping technique. Geotech. Test. J.
**2003**, 26, 57–70. [Google Scholar] [CrossRef] - Raghunandan, M.E.; Juneja, A.; Hsiung, B.C.B. Preparation of reconstituted sand samples in the laboratory. Int. J. Geotech. Eng.
**2012**, 6, 125–131. [Google Scholar] [CrossRef] - da Fonseca, A.V.; Cordeiro, D.; Molina-Gómez, F. Recommended Procedures to Assess Critical State Locus from Triaxial Tests in Cohesionless Remoulded Samples. Geotechnics
**2021**, 1, 95–127. [Google Scholar] [CrossRef] - Lade, P.V. Triaxial Testing of Soils; Wiley: Hoboken, NJ, USA, 2016. [Google Scholar] [CrossRef]
- Wood, D.M. Soil Behaviour and Critical State Soil Mechanics; Cambridge University Press: Cambridge, UK, 1990. [Google Scholar]
- Duncan, J.M.; Seed, H.B. Errors in Strength Tests and Recommended Corrections; Technical Report; California University Berkeley Institute of Transportation and Traffic Engineering: Berkeley, CA, USA, 1965. [Google Scholar]
- Duncan, J.M.; Seed, H.B. Corrections for strength test data. J. Soil Mech. Found. Div.
**1967**, 93, 121–137. [Google Scholar] [CrossRef] - Silver, M.L.; Seed, H.B. Volume Changes in Sands during Cyclic Loading. J. Soil Mech. Found. Div.
**1971**, 97, 1171–1182. [Google Scholar] [CrossRef] - Thian, S.; Lee, C. Cyclic stress-controlled tests on offshore clay. J. Rock Mech. Geotech. Eng.
**2017**, 9, 376–381. [Google Scholar] [CrossRef] - Seed, H.B.; Idriss, I.M. Soil Moduli and Damping Factors for Dynamic Response Analyses; Technical Report; Earthquake Engineering Research Center, University of California: Berkeley, CA, USA, 1970. [Google Scholar]
- Darendeli, M.B. A New Family of Normalized Modulus Reduction and Material Damping Curves. Ph.D. Thesis, University of Texas, Austin, TX, USA, 2001; p. 362. [Google Scholar]
- Vucetic, M.; Thangavel, H.; Mortezaie, A. Cyclic Secant Shear Modulus and Pore Water Pressure Change in Sands at Small Cyclic Strains. J. Geotech. Geoenviron. Eng.
**2021**, 147, 04021018. [Google Scholar] [CrossRef] - Van Rossum, G.; Drake, F.L. Python 3 Reference Manual; CreateSpace: Scotts Valley, CA, USA, 2009. [Google Scholar]
- Virtanen, P.; Gommers, R.; Oliphant, T.E.; Haberland, M.; Reddy, T.; Cournapeau, D.; Burovski, E.; Peterson, P.; Weckesser, W.; Bright, J.; et al. SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nat. Methods
**2020**, 17, 261–272. [Google Scholar] [CrossRef][Green Version] - Vinet, L.; Zhedanov, A. A ‘Missing’ Family of Classical Orthogonal Polynomials. In Scientific Computation; Springer: Dordrecht, The Netherlands; New York, NY, USA, 2011; Volume 44, p. 366. [Google Scholar] [CrossRef]
- Vucetic, M.; Dobry, R. Pore Pressure Build-Up and Liquefaction at Level Sandy Sites during Earthquakes; Technical Report, CE-86-3; Rensselaer Polytechnic Institute: Troy, NY, USA, 1986. [Google Scholar]
- Panda, R.C. Introduction to PID Controllers: Theory, Tuning and Application to Frontier Areas; InTech: Rijeka, Croatia, 2012. [Google Scholar]
- Mortezaie, A.; Vucetic, M. Threshold Shear Strains for Cyclic Degradation and Cyclic Pore Water Pressure Generation in Two Clays. J. Geotech. Eng.
**2016**, 142, 1–14. [Google Scholar] [CrossRef]

**Figure 1.**Flowchart of shallow landslide examination process: (

**a**) geotechnical model input, (

**b**) type of model decision, (

**c**) numerical model, (

**d**) physical model, (

**e**) static and cyclic laboratory results, and (

**f**) verification of numerical and/or physical models.

**Figure 2.**Schematic view of slope models used in simulations: (

**a**) prototype of slope with potential for shallow landslide, and (

**b**) small-scale model used for dynamic loading test.

**Figure 3.**Small-scale landslide under dynamic loading: (

**a**) prepared test, and (

**b**) dynamically induced landslide.

**Figure 4.**Cyclic triaxial system: (

**a**) water tank, (

**b**) pneumatic actuator, (

**c**) triaxial loading frame, (

**d**) triaxial cell, (

**e**) volume controller, (

**f**) PC with data acquisition system, (

**g**) pneumatic control system for pressures and actuator, and (

**h**) water distribution panel, according to [24].

**Figure 6.**Sample preparation using undercompaction method: (

**a**) lower layers of compaction, and (

**b**) upper layers of compaction, according to [24].

**Figure 8.**Equivalent viscous damping ratio according to used frequency: (

**a**) 0.1 Hz loading frequency, (

**b**) 0.2 Hz loading frequency, and (

**c**) 0.5 Hz loading frequency.

**Figure 9.**Degradation index related to number of cycles: (

**a**) 0.1 Hz loading frequency at confining stress of 10 kPa, (

**b**) 0.1 Hz loading frequency at confining stress of 25 kPa, (

**c**) 0.1 Hz loading frequency at confining stress of 50 kPa, (

**d**) 0.2 Hz loading frequency at confining stress of 10 kPa, (

**e**) 0.2 Hz loading frequency at confining stress of 25 kPa, (

**f**) 0.2 Hz loading frequency at confining stress of 50 kPa, (

**g**) 0.5 Hz loading frequency at confining stress of 10 kPa, (

**h**) 0.5 Hz loading frequency at confining stress of 25 kPa, and (

**i**) 0.5 Hz loading frequency at confining stress of 50 kPa.

**Figure 10.**Degradation index related to normalised pore water pressure ratio: (

**a**) 0.1 Hz loading frequency at confining stress of 10 kPa, (

**b**) 0.1 Hz loading frequency at confining stress of 25 kPa, (

**c**) 0.1 Hz loading frequency at confining stress of 50 kPa, (

**d**) 0.2 Hz loading frequency at confining stress of 10 kPa, (

**e**) 0.2 Hz loading frequency at confining stress of 25 kPa, (

**f**) 0.2 Hz loading frequency at confining stress of 50 kPa, (

**g**) 0.5 Hz loading frequency at confining stress of 10 kPa, (

**h**) 0.5 Hz loading frequency at confining stress of 25 kPa, and (

**i**) 0.5 Hz loading frequency at confining stress of 50 kPa.

**Figure 11.**Normalized pore water pressure ratio for cycles N = 2 and N = 10: (

**a**) loading frequency 0.1 Hz, (

**b**) loading frequency 0.25 Hz, and (

**c**) loading frequency 0.5 Hz.

**Figure 12.**Equivalent viscous damping ratio related to relative axial strain determinated in drained tests: (

**a**) 0.1 Hz loading frequency, (

**b**) 0.2 Hz loading frequency, and (

**c**) 0.5 Hz loading frequency.

**Figure 13.**Degradation index related to number of cycles determined in drained test: (

**a**) 0.1 Hz loading frequency at confining stress of 10 kPa, (

**b**) 0.1 Hz loading frequency at confining stress of 25 kPa, (

**c**) 0.1 Hz loading frequency at confining stress of 50 kPa, (

**d**) 0.2 Hz loading frequency at confining stress of 10 kPa, (

**e**) 0.2 Hz loading frequency at confining stress of 25 kPa, (

**f**) 0.2 Hz loading frequency at confining stress of 50 kPa, (

**g**) 0.5 Hz loading frequency at confining stress of 10 kPa, (

**h**) 0.5 Hz loading frequency at confining stress of 25 kPa, and (

**i**) 0.5 Hz loading frequency at confining stress of 50 kPa.

**Figure 14.**Degradation index according to corresponding accumulated volume strain: (

**a**) 0.1 Hz loading frequency at confining stress of 10 kPa, (

**b**) 0.1 Hz loading frequency at confining stress of 25 kPa, (

**c**) 0.1 Hz loading frequency at confining stress of 50 kPa, (

**d**) 0.2 Hz loading frequency at confining stress of 10 kPa, (

**e**) 0.2 Hz loading frequency at confining stress of 25 kPa, (

**f**) 0.2 Hz loading frequency at confining stress of 50 kPa, (

**g**) 0.5 Hz loading frequency at confining stress of 10 kPa, (

**h**) 0.5 Hz loading frequency at confining stress of 25 kPa, and (

**i**) 0.5 Hz loading frequency at confining stress of 50 kPa.

**Figure 15.**Volume change according to frequency and related to axial cyclic strain: (

**a**) 0.1 Hz frequency loading, (

**b**) 0.2 Hz frequency loading, and (

**c**) 0.5 Hz frequency loading.

Quantity | Scaling Values |
---|---|

Length | 40 |

Time | 15.91 |

Frequency | 0.063 |

Strain | 6.32 |

Displacement | 252.98 |

Acceleration | 1 |

Frequency of Prototype, ${\mathit{f}}_{\mathit{p}}$ (Hz) | Frequency of Model according to Similarity Law, ${\mathit{f}}_{\mathit{m},\mathit{law}}$ (Hz) | Frequency of Model Tested on Seismic Platform, ${\mathit{f}}_{\mathit{m},\mathit{pl}}$ (Hz) |
---|---|---|

0.1 | 1.59 | 1.7 |

0.2 | 3.17 | 3.2 |

0.5 | 7.93 | 8.1 |

**Table 3.**Key physical characteristics of sand used for testing, according to [23].

Physical Property | Symbol | Value | Unit |
---|---|---|---|

Specific gravity | ${G}_{s}$ | 2.7 | (-) |

Effective grain size | ${D}_{10}$ | 0.19 | (mm) |

Coefficient of uniformity | ${C}_{u}$ | 1.947 | (-) |

Coefficient of curvature | ${C}_{c}$ | 1.092 | (-) |

Minimum void ratio | ${e}_{min}$ | 0.641 | (-) |

Maximum void ratio | ${e}_{max}$ | 0.911 | (-) |

Hydraulic conductivity | ${k}_{S}$ | ${10}^{(-5)}$ | (cm/s) |

Mechanical Property | Symbol | Value | Unit |
---|---|---|---|

Initial relative density | ${D}_{r}$ | 50 | (%) |

Friction angle | ${\varphi}^{\prime}$ | 34.9 | (${}^{\circ}$) |

Cohesion | ${c}^{\prime}$ | 0.0 | (kPa) |

Specimen Height/Diameter (mm) | Initial Relative Density, ${\mathit{D}}_{\mathit{r},0}$ $(\%)$ | Effective Consolidation Stress, ${\mathit{\sigma}}_{0}^{\prime}$ (kPa) | Frequency, f (Hz) | Drainage Type |
---|---|---|---|---|

140/70 | 50 | 10, 25, 50 | 0.1, 0.2, 0.5 | Undrained/ Drained |

Testing Stage | Cyclic Axial Strain ${\mathit{\u03f5}}_{\mathit{a},\mathit{c}}$, (%) | Cyclic Shear Strain ${\mathit{\gamma}}_{\mathit{a},\mathit{c}}$, (%) |
---|---|---|

1 | 0.0033 | 0.005 |

2 | 0.005 | 0.0075 |

3 | 0.0067 | 0.01 |

4 | 0.013 | 0.02 |

5 | 0.033 | 0.05 |

6 | 0.05 | 0.075 |

7 | 0.067 | 0.1 |

8 | 0.133 | 0.2 |

9 | 0.333 | 0.5 |

10 | 0.667 | 1 |

**Table 7.**Fit parameters of Equation (17).

$\mathit{f}=0.1$ Hz | $\mathit{f}=0.2$ Hz | $\mathit{f}=0.5$ Hz | |||||||
---|---|---|---|---|---|---|---|---|---|

Cycle Number, N | m | r | s | m | r | s | m | r | s |

2 | 1.393 | 0.510 | 0.973 | 1.030 | 1.908 | 1.151 | 1.938 | 0.654 | 1.008 |

10 | 1.035 | 0.835 | 1.283 | 1.160 | 3.000 | 1.013 | 1.213 | 3.000 | 1.042 |

**Table 8.**Fitting parameters of Equation (20).

$\mathit{f}=0.1$ Hz | $\mathit{f}=0.2$ Hz | $\mathit{f}=0.5$ Hz | |||||||
---|---|---|---|---|---|---|---|---|---|

Cycle Number, N | k | l | w | k | l | w | k | l | w |

2 | 1.218 | 3.000 | 1.390 | 1.102 | 3.000 | 1.315 | 0.596 | 2.453 | 1.117 |

10 | 7.457 | 0.408 | 1.504 | 7.559 | 0.406 | 1.464 | 7.402 | 0.358 | 1.519 |

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## Share and Cite

**MDPI and ACS Style**

Jagodnik, V.; Arbanas, Ž. Cyclic Behaviour of Uniform Sand in Drained and Undrained Conditions at Low Confining Stress in Small-Scale Landslide Model. *Sustainability* **2022**, *14*, 12797.
https://doi.org/10.3390/su141912797

**AMA Style**

Jagodnik V, Arbanas Ž. Cyclic Behaviour of Uniform Sand in Drained and Undrained Conditions at Low Confining Stress in Small-Scale Landslide Model. *Sustainability*. 2022; 14(19):12797.
https://doi.org/10.3390/su141912797

**Chicago/Turabian Style**

Jagodnik, Vedran, and Željko Arbanas. 2022. "Cyclic Behaviour of Uniform Sand in Drained and Undrained Conditions at Low Confining Stress in Small-Scale Landslide Model" *Sustainability* 14, no. 19: 12797.
https://doi.org/10.3390/su141912797