# Liquefaction Potential of Saturated Sand Reinforced by Cement-Grouted Micropiles: An Evolutionary Approach Based on Shaking Table Tests

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

_{u}), and the number of required cycles (N

_{peak}) to liquefy the soil are obtained and modified lower and upper boundaries are suggested for the potential of liquefaction of both pure and grout-reinforced sand. Next, adopting genetic programming and the least square method in the framework of the evolutionary polynomial regression technique, high-accuracy predictive equations are developed for the estimation of r

_{umax}. Based on the results of a three-dimensional, graphical, multiple-variable parametric (MVP) analysis, and introducing the concept of the critical, boundary inclination angle, the inclination of micropiles is shown to be more effective in view of liquefaction resistivity for loose sands. Due to a lower critical boundary inclination angle, the applicability range for inclining micropiles is narrower for the medium-dense sands. MVP analyses show that the effects of a decreasing spacing ratio on decreasing r

_{umax}are amplified while micropiles are inclined.

## 1. Introduction

_{umax}. The provided computer-aided evolutionary model, which is developed based on accurate shaking table test results, enables design engineers and practitioners to mitigate the risk of liquefaction hazards by employing proper micropiles specifications and layout, and to efficiently estimate the risk of liquefaction for each of the design scenarios. Furthermore, derived evolutionary models are employed as the basis for the three-dimensional, multiple-variable, parametric studies to evaluate the effects of simultaneous changes of the number of micropiles, micropiles’ inclination angle, spacing ratio, relative density, and the scaled input loading acceleration (a/g) on the liquefaction potential of sand reinforced with the grout-injected micropiles.

## 2. Shaking Table Tests

^{2}) and a maximum frequency of 3 (Hz) [16,17].

#### 2.1. Rigid Transparent Box

#### 2.2. Instrumentation

#### 2.3. Grout-Injection Set-Up

## 3. Material Properties

## 4. Physical Model

#### 4.1. Boundary Condition

_{SA}(f) is the coherence at a given frequency of f, and P

_{SS}(f) and P

_{AA}(f), respectively, represent the power spectral density of input and output signals. Moreover, P

_{SA}(f) is the cross power spectral density of two signals. To overcome such errors, and according to suggestions of Lombardi and Bhattacharya (2012) [73], and Lombardi et al. (2015), artificial soft boundaries (foam sheets) are used as absorbing boundaries. The efficiency and the applicability of such a method was also proved throughout the shaking table study reported in Hasheminezhad et al. (2022) [22]. Moreover, to increase the accuracy of the experiment results, the minimum distance between the micropiles and lateral boundaries are considered 24 times the diameter of the micropiles. Furthermore, the distance between the bottom of the micropiles and the horizontal bottom boundary of the box is at least 24 times the diameter of the micropiles, as suggested by Lombardi et al. (2015) [64]. Figure 5 indicates the geometry of the model, the arrangement of micropiles, and distances.

#### 4.2. Scaling of Micropiles

_{L}is defined as the ratio of the model length to the prototype length [57,70]. Regarding Wood (2003) [57], the factor of α, as a parameter to correlate the stiffness and the effective stress level in the soil, is considered 0.5 for sandy soil. It should be described considering the fact that the behavior of the saturated soil is governed by the equilibrium of the pore water flow and the mass balance equations [74], and the behavior of the water during earthquake can be approximated by ignoring the viscosity of the water and the wave generated by the motion of the structure [75,76]; the viscosity of the water is not scaled.

_{u}is a dimensionless parameter, the obtained results can be directly used for a prototype with a steel micropile with a casing length of 3.2 m, thickness of 1 cm, and inner diameter of 11 cm.

#### 4.3. Model Preparation

## 5. Experimental Results

#### 5.1. Effect of Boundary Conditions on Excess Pore Water Pressure Ratio (r_{u})

_{u}) is defined in accordance with Equation (5):

_{0}′ is the initial vertical effective stress.

_{umax}) from 0.88 to 0.82 (7% reduction). Moreover, the pore water pressure was generated faster in the soil embedded in the rigid box than in the box with the absorbing boundary, while the dissipation of pore water pressure started sooner in the box with the absorbing boundary. As discussed, the development of compressive and reflective shaking-induced waves by the rigid walls generated more pressure in the soil sample compared with the absorbing boundary and consequently produced more pore water pressure. In addition, foam sheet (compared with the rigid boundary) decreased the velocity of wave propagation due to its lower impedance, which resulted in a decrease in the pore water pressure. Table 4 presents the r

_{umax}values and the number of cycles required to reach the r

_{umax}values (N

_{peak}), illustrating a slight increase in N

_{peak}in the box with the absorbing boundary. As a result, for the remaining test plan, foam sheets were used to provide better simulation conditions.

#### 5.2. Effects of Different Arrangements of Micropiles on r_{u} Values

#### 5.2.1. Effect of the Number of Micropiles

_{umax}) decreases. The results presented in Table 4 show that the reinforced sand with nine micropiles has a significant effect to reduce the liquefaction potential.

_{u}with the number of cycles at the bottom and upper PPTs during shaking.

_{peak}(about N

_{peak}= 9) than the reinforced sand with two grouted micropiles (about N

_{peak}= 11.6). Such a behavior is also shown in other reinforced samples with a different number of micropiles as presented in Table 4. Similar behavior is also observed at the shallower depths as shown in Figure 12b. Increasing the number of cycles required for the liquefaction triggering (r

_{umax}) indicates that with increasing the number of micropiles, the liquefaction resistance of the reinforced sand is increased. In addition, as presented, values of N

_{peak}obtained at the upper PPT are more than those measured using the bottom PPT. This difference can be attributed to the proximity of the upper PPT to the grouted micropiles and the grouted sand formed around the micropiles, which confines the excess pore water pressure and reduces the velocity of the pore water pressure generation. Therefore, more cycles are required to reach the maximum pore water pressure in upper PPTs.

#### 5.2.2. Effects of Micropiles Spacing Ratio (S_{mic}/d_{mic})

_{u}in the reinforced sand by 2 and 4 vertical micropiles with the spacing ratio of 4 and 7. As illustrated in this figure, a slight reduction (about 3% reduction) in the values of r

_{umax}is observed by decreasing s/d from 7 to 4 for the case of using 2 micropiles, while for the case of applying 4 micropiles, more reduction (about 10% reduction) is occurred. In addition, it is important to remark that the N

_{peak}and the maximum required time (t

_{peak}) are almost constant with the change of s/d.

#### 5.2.3. Effects of Micropiles’ Inclination

_{u}in the reinforced sand by 2 inclined and vertical micropiles with the spacing ratios of 4 and 7. As shown, the arrangement of 2 inclined micropiles with the spacing ratio of 4 has the best performance to reduce the soil liquefaction potential. This result agrees with results of the seismic performance superiority of the inclined micropiles in dry sands compared with the vertical micropiles obtained by other researchers [35,36,39,53].

#### 5.3. Effect of Different Scaled Accelerations on r_{u} Values

_{u}under two maximum accelerations of 0.2 g and 0.32 g. The results for the micropile-reinforced sand indicate that the variation of r

_{u}is highly dependent on the applied accelerations so that the maximum pore water pressure generated in pure and reinforced sands increases averagely 20% by changing the maximum acceleration applied from 0.2 g to 0.32 g. The development of soil liquefaction potential by increasing the acceleration in pure sand was also reported in previous studies [77,78].

_{u}versus the normalized number of cycles applied (i.e., N/N

_{peak}) are displayed in Figure 16.

#### 5.4. Effect of the Relative Density of Soil on r_{u} Values

_{u}with the relative density.

## 6. Data Processing and Modeling

#### 6.1. Predictive Model for the Potential of Liquefaction

_{u}obtained from the tests on the pure sand deposits with relative densities of 30% and 50% with the consideration of absorbing boundaries.

_{peak}values less than 0.5. Differences observed for N/N

_{peak}values between 0.5 to 1 can be due to the high loading acceleration induced by the shaking table. As shown in Figure 18, the results of samples reinforced by micropiles are not included in the proposed ranges for the pure sand. The results of sand samples reinforced with micropiles are separately prepared and compared with the available literature on the cemented sand [71]. Therefore, new upper and lower bounds are proposed for the micropile-reinforced sand as shown in Figure 19 and are compared with the reported results of the cemented sand in cyclic triaxial tests conducted by Porcino et al. (2015) [71].

_{u}values in the sand reinforced by cement-grout-injected micropiles, the proposed ranges can be a considerable help to engineers to assess the safety factor of foundations improved by micropiles against the liquefaction phenomenon.

#### 6.2. Evolutionary Polynomial Regression Modeling (EPR)

_{j}represents constants, F is a function constructed during the process, X shows the input variables’ matrix, f is a function defined by the user, and m stands for the maximum term numbers for the desired output. The flow diagram used as the modeling procedure in EPR is illustrated using Figure 20 [82].

_{u}values. Values of the coefficient of determination (CoD/R

^{2}) for the models at the bottom and upper PPTs are, respectively, 99.18% and 99.25%, which show their high accuracy. In addition, the values of root mean squared error (RMSE) for the bottom and upper PPTs were, respectively, 0.0002 and 0.00018.

_{u}), interactive effects of concerning parameters (N, a/g, Dr, s/d, and θ) are more important compared with the effect of each individual parameter. Hence, the following section investigates simultaneous effects of loading, geometrical, soil, and configuration parameters on the potential of liquefaction.

## 7. Multiple-Variable Parametric (MVP) Study on the Potential of Liquefaction

_{u}. The inclination angle of the micropiles as another affecting parameter does not have a known direct/reverse relationship with the liquefaction susceptibility. Such behaviors make it a complicated task to assess the liquefaction potential of micropile-reinforced sand with simultaneous changes of described, affecting parameters. Hence, the presentation of a multiple-purpose, parametric study based on the developed model for the liquefaction potential can be effective.

#### 7.1. Simultaneous Effects of a/g, Inclination Angle, and Relative Density

_{u}with the inclination in different acceleration levels shows that input ground acceleration does not have a significant effect on the variation of r

_{u}with the inclination (the whole r

_{u}-angle curve shifts as the acceleration varies). The same behavior is also observed for the effect of the inclination of micropiles on the variation of r

_{u}with the scaled input acceleration.

#### 7.2. Simultaneous Effects of Number of Micropiles, Spacing Ratio, and a/g

#### 7.3. Simultaneous Effects of Spacing Ratio, Inclination Angle, and Relative Density

## 8. Conclusions

_{umax}using the obtained experimental data, and parametric studies were performed to estimate the effects of each parameter. Three-dimensional, multiple-variable parametric studies on the developed EPR model are carried out to investigate the effects of simultaneous changes in input parameters on the liquefaction potential of the micropile-reinforced sand in the shaking table. Based on the results, the following points can be concluded:

- A more accurate response for the excess pore water pressure is obtained using foam sheets as the artificial lateral boundaries by a reduction in reflected and generated waves, in which its effect is well illustrated by a 7% decrease in r
_{umax}. - The application of only one micropile has a negligible effect on the liquefaction potential of the soil at different seismic excitations. On the other hand, 2, 4 and 9 micropiles reduce r
_{umax}values averagely by 27%, 46%, and 66%, respectively. Therefore, the results clearly show that micropile reinforcement is an effective technique to decrease the liquefaction potential of sands, especially in samples with nine micropiles. - The spacing ratio of micropiles has a small effect on r
_{umax}and N_{peak}values in the reinforced sand by two vertical micropiles, while its effect is more considerable in specimens reinforced by four vertical micropiles. - The reinforced sand by two inclined micropiles exhibits a greater resistance to liquefaction compared with vertical micropiles.
- The results indicate that specimens of reinforced sand in all micropile arrangements have more liquefaction resistance in comparison with pure sand, due to the increase in the required number of cycles (N
_{peak}) to liquefy. - With increasing the scaled input acceleration, the liquefaction potential of pure and reinforced sand increases. Moreover, the dissipation of pore water pressure occurred faster with an increase in the applied excitations due to the separation between soil and micropiles.
- The increase in relative density of the sand significantly reduces the liquefaction potential. In addition, this positive effect has a better efficiency in loose sand compared with the medium sand.
- New upper and lower bounds are suggested for the prediction of the liquefaction potential of micropile-induced sand, which can be an efficient controlling tool for design engineers.
- High-accuracy EPR models are proposed for the prediction of r
_{u}of the sand reinforced with micropiles.

- The impact of N, Dr, and a/g on r
_{u}is more significant compared with other affecting parameters. - Inclined micropiles have a better performance in the mitigation of liquefaction potential for loose sands compared with the medium-dense sand.
- The applicable range of inclination of micropiles in medium-dense sands is less than its applicable range for loose sands.
- Critical, boundary inclination angle in dense sands (33°) is lower than loose sands (67°).
- The range of (3–4) is introduced as the optimum range for the spacing ratio of micropiles (in view of both material consumption and enhancing the soil’s resistivity against the liquefaction).
- With inclining micropiles, the effect of the spacing ratio on the liquefaction potential is amplified.
- The number of micropiles plays a more important role in the liquefaction potential compared with the spacing ratio and the scaled input acceleration. With the application of at least five micropiles, the effects of s/d and a/g are shown to be negligible.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Yegian, M.K.; Nogole-Sadat, M.A.A.; Ghahraman, V.G.; Darai, H. Liquefaction Case Histories from 1990 Manjil Earthquake, Iran. In Proceedings of the Third International Conference on Case Histories in Geotechnical Engineering, Saint Louis, MO, USA, 1–4 June 1993. [Google Scholar]
- Kramer, S.L. Geotechnical Earthquake Engineering; Prentice Hall: Upper Saddle River, NJ, USA, 1996. [Google Scholar]
- Huang, Y.; Yu, M. Review of soil liquefaction characteristics during major earthquakes of the twenty-first century. Nat. Hazards
**2013**, 65, 2375–2384. [Google Scholar] [CrossRef] - Zengin, E.; Erguler, Z.A. Assessment of Liquefaction Susceptibility of Kutahya Soils Based on Recent Earthquakes in Turkey. In Proceedings of the EGU General Assembly 2014, Vienna, Austria, 27 April–2 May 2014; p. 2480. [Google Scholar]
- Ecemis, N.; Valizadeh, H.; Karaman, M. Sand-granulated rubber mixture to prevent liquefaction-induced uplift of buried pipes: A shaking table study. Bull. Earthq. Eng.
**2021**, 19, 2817–2838. [Google Scholar] [CrossRef] - Özcebe, A.G.; Giretti DBozzoni, F.; Fioravante, V.; Lai, C.G. Centrifuge and numerical modelling of earthquake-induced soil liquefaction under free-field conditions and by considering soil–structure interaction. Bull. Earthq. Eng.
**2021**, 19, 47–75. [Google Scholar] [CrossRef] - Han, Z.; Xiao, J.; Wei, Y. Spatial Distribution Characteristics of Microbial Mineralization in Saturated Sand Centrifuge Shaking Table Test. Materials
**2022**, 15, 6102. [Google Scholar] [CrossRef] [PubMed] - Sun, Y.; Zhong, X.; Lv, J.; Wang, G.; Hu, R. Experimental Study on Different Improvement Schemes of EICP-Lignin Solidified Silt. Materials
**2023**, 16, 999. [Google Scholar] [CrossRef] - Konrad, J.-M.; Watts, B.D. Undrained shear strength for liquefaction flow failure analysis. Can. Geotech. J.
**1995**, 32, 783–794. [Google Scholar] [CrossRef] - Konrad, J.-M. A methodology to evaluate the susceptibility of soils for liquefaction flow failures. In Physics and Mechanics of Soil Liquefaction; Lade, P.V., Yamamuro, J.A., Eds.; A.A. Balkema: Rotterdam, The Netherlands, 1999; p. 213. [Google Scholar]
- Baziar, M.H.; Ghorbani, A. Evaluation of lateral spreading using artificial neural networks. Soil Dyn. Earthq. Eng.
**2005**, 25, 1–9. [Google Scholar] [CrossRef] - Özener, P.T.; Özaydın, K.; Berilgen, M.M. Investigation of liquefaction and pore water pressure development in layered sands. Bull. Earthq. Eng.
**2009**, 7, 199–219. [Google Scholar] [CrossRef] - Jafarian, Y.; Abdollahi, A.S.; Vakili, R.; Baziar, M.H.; Noorzad, A. On the efficiency and predictability of strain energy for the evaluation of liquefaction potential: A numerical study. Comput. Geotech.
**2011**, 38, 800–808. [Google Scholar] [CrossRef] - El Takch, A.; Sadrekarimi, A.; El Naggar, M.H. Cyclic resistance and liquefaction behavior of silt and sandy silt soils. Soil Dyn. Earthq. Eng.
**2016**, 83, 98–109. [Google Scholar] [CrossRef] - Ghorbani, A.; Mersa, A.N.; Veiskarami, M.; Hamidzadeh, N.; Hasanzadehshooiili, H. Shaking table tests to parametrically evaluate post-shaking settlements and pore water pressure build-up in marine sands. Arab. J. Geosci.
**2021**, 14, 693. [Google Scholar] [CrossRef] - Ghorbani, A.; Eslami, A. Energy-based model for predicting liquefaction potential of sandy soils using evolutionary polynomial regression method. Comput. Geotech.
**2021**, 129, 103867. [Google Scholar] [CrossRef] - Bozzoni, F.; Bonì, R.; Conca, D.; Lai, C.G.; Zuccolo, E.; Meisina, C. Megazonation of earthquake-induced soil liquefaction hazard in continental Europe. Bull. Earthq. Eng.
**2021**, 19, 4059–4082. [Google Scholar] [CrossRef] - Bahadori, H.; Farzalizadeh, R.; Barghi, A.; Hasheminezhad, A. A comparative study between gravel and rubber drainage columns for mitigation of liquefaction hazards. J. Rock Mech. Geotech. Eng.
**2018**, 10, 924–934. [Google Scholar] [CrossRef] - Fallahzadeh, M.; Haddad, A.; Jafarian, Y.; Lee, C.J. Seismic performance of end-bearing piled raft with countermeasure strategy against liquefaction using centrifuge model tests. Bull. Earthq. Eng.
**2019**, 17, 5929–5961. [Google Scholar] [CrossRef] - Padmanabhan, G.; Shanmugam, G.K.; Berilgen, M.M. Liquefaction and reliquefaction resistance of saturated sand deposits treated with sand compaction piles. Bull. Earthq. Eng.
**2021**, 19, 4235–4259. [Google Scholar] [CrossRef] - Dou, P.; Xu, C.; Du, X.; Chen, S. Influence of structure on the aseismic stability and dynamic responses of liquefiable soil. Bull. Earthq. Eng.
**2022**, 20, 55–76. [Google Scholar] [CrossRef] - Hasheminezhad, A.; Farzalizadeh, R.; Rahimi, H.; Bahadori, H. Seismic performance assessment of wall-type gravel and rubber drains in liquefaction mitigation of sands. Bull. Earthq. Eng.
**2022**, 20, 3699–3714. [Google Scholar] [CrossRef] - FHWA NHI (Federal Highway Administration-National Highway Institute). Micropile Design and Construction—Reference Manual; FHWA NHI-05-039; U.S. Department of Transportation: McLean, VA, USA, 2005; p. 436. [Google Scholar]
- Juran, I.; Hasan, J.; Weinstein, G.M.; Sourisseau, L. FOREVER: Synthesis of the Results of the National Project on Micropiles; International Center for Ground Improvement, Polytechnic University: Southlake, TX, USA, 2003. [Google Scholar]
- Shahrour, J.I.; Juran, I. Seismic behaviour of micropile systems. Proc. Inst. Civ. Eng. Ground Improv.
**2004**, 8, 109–120. [Google Scholar] [CrossRef] - McManus, K.J.; Charton, G.; Turner, J.P. Effect of Micropiles on Seismic Shear Strain. In Proceedings of the GeoSupport Conference 2004, Orlando, FL, USA, 29–31 January 2004; Society of Civil Engineers (ASCE): Reston, VA, USA, 2004. [Google Scholar] [CrossRef]
- McManus, K.J.; Turner, J.P.; Charton, G. Inclined reinforcement to prevent soil liquefaction. In Proceedings of the Annual NZSEE Technical Conference, Wairakei, New Zealand, 11–13 March 2005; pp. 41–51. [Google Scholar]
- Tsukada, Y.; Miura, K.; Tsubokawa, Y.; Otani, Y.; You, G.L. Mechanism of bearing capacity of spread footings reinforced with micropiles. Soils Found.
**2006**, 46, 367–376. [Google Scholar] [CrossRef] [Green Version] - Esmaeili, M.; Nik, M.G.; Khayyer, F. Experimental and numerical study of micropiles to reinforce high railway embankments. Int. J. Geomech.
**2012**, 13, 729–744. [Google Scholar] [CrossRef] - Kavand, A.; Haeri, S.M.; Raisianzadeh, J.; Afzalsoltani, S. Effectiveness of a vertical micropile system for mitigation of liquefaction induced lateral spreading effects on pile foundations: 1 g large scale shake table tests. Sci. Iran.
**2021**, 29, 1038–1058. [Google Scholar] [CrossRef] - Sližytė, D. The interaction estimation of piles bored in sand. Statyba
**2001**, 7, 405–412. [Google Scholar] [CrossRef] - Juran, I.; Benslimane, A.; Hanna, S. Engineering analysis of dynamic behavior of micropile systems. Transp. Res. Rec. J. Transp. Res. Board
**2001**, 1772, 91–106. [Google Scholar] [CrossRef] - Ousta, R.; Shahrour, I. Three-dimensional analysis of the seismic behaviour of micropiles used in the reinforcement of saturated soil. Int. J. Numer. Anal. Methods Geomech.
**2001**, 25, 183–196. [Google Scholar] [CrossRef] - Mitrani, H.; Madabhushi, S.P.G. Centrifuge tests investigating inclined grout micro-piles as a method of liquefaction remediation for existing buildings. Earthq. Eng. Soil Dyn.
**2005**, 3, 245–256. [Google Scholar] - Shahrour, I.; Hassan, S.A.; Mhamed, S. 3D elastoplastic analysis of the seismic performance of inclined micropiles. Comput. Geotech.
**2012**, 39, 1–7. [Google Scholar] - Ghorbani, A.; Hasanzadehshooiili, H.; Ghamari, E. 3D finite element analysis of seismic soil-micropile-structure interaction. In Proceedings of the 2nd International Conference on Civil Engineering and Building Materials (CEBM), Hong Kong, China, 17–18 November 2012; Chang, S.-Y., Al Bahar, S.K., Zhao, J., Eds.; CRC Press: Hong Kong, China, 2012; pp. 265–269. [Google Scholar]
- Moayed, R.Z.; Naeini, S.A. Improvement of loose sandy soil deposits using micropiles. KSCE J. Civ. Eng.
**2012**, 16, 334–340. [Google Scholar] [CrossRef] - Sližytė, D.; Medzvieckas, J. Evaluation of Gravity Retaining Walls from Jet Grouting Piles Installed in Sands. Procedia Eng.
**2013**, 57, 1070–1077. [Google Scholar] [CrossRef] [Green Version] - Ghorbani, A.; Hasanzadehshooiili, H.; Ghamari, E.; Medzvieckas, J. Comprehensive three dimensional finite element analysis, parametric study and sensitivity analysis on the seismic performance of soil–micropile-superstructure interaction. Soil Dyn. Earthq. Eng.
**2014**, 58, 21–36. [Google Scholar] [CrossRef] - Abdollahi, K.; Mortezaei, A. A new expression for determining the bending stiffness of circular micropile groups. Soil Dyn. Earthq. Eng.
**2015**, 77, 58–70. [Google Scholar] [CrossRef] - Saha, R.; Dutta, S.C.; Haldar, S. Seismic response of soil-pile raft-structure system. J. Civ. Eng. Manag.
**2015**, 21, 144–164. [Google Scholar] [CrossRef] [Green Version] - Ortega, J.M.; Esteban, M.D.; Rodriguez, R.R.; Pator, J.L.; Ibanco, F.J.; Sánchez, I.; Climent, M.Á. Long-Term Behaviour of Fly Ash and Slag Cement Grouts for Micropiles Exposed to a Sulphate Aggressive Medium. Materials
**2017**, 10, 598. [Google Scholar] [CrossRef] [PubMed] - Sales, M.M.; Prezzi, M.; Salgado, R.; Choi, Y.S.; Lee, J. Load-settlement behaviour of model pile groups in sand under vertical load. J. Civ. Eng. Manag.
**2017**, 23, 1148–1163. [Google Scholar] [CrossRef] - Vali, R.; Khotbehsara, E.M.; Saberian, M.; Li, J.; Mehrinejad, M.; Jahandari, S. A three-dimensional numerical comparison of bearing capacity and settlement of tapered and under-reamed piles. Int. J. Geotech. Eng.
**2019**, 13, 236–248. [Google Scholar] [CrossRef] - Norkus, A.; Martinkus, V. Experimental study on bearing resistance of short displacement pile groups in dense sands. J. Civ. Eng. Manag.
**2019**, 25, 551–558. [Google Scholar] [CrossRef] - Mashhoud, H.J.; Yin, J.H.; Komak Panah, A.; Leung, Y.F. A 1-g shaking table investigation on response of a micropile system to earthquake excitation. Acta Geotech.
**2020**, 15, 827–846. [Google Scholar] [CrossRef] - Ghorbani, A.; Jahanpour, R.; Hasanzadehshooiili, H. Evaluation of liquefaction potential of marine sandy soil with piles considering nonlinear seismic soil–pile interaction; A simple predictive model. Mar. Georesour. Geotechnol.
**2020**, 38, 1–22. [Google Scholar] [CrossRef] - Abdlrahem, M.A.; El Naggar, M.H. Axial performance of micropile groups in cohesionless soil from full-scale tests. Can. Geotech. J.
**2020**, 57, 1006–1024. [Google Scholar] [CrossRef] - Orang, M.J.; Boushehri, R.; Motamed, R.; Prabhakaran, A.; Elgamal, A. An experimental evaluation of helical piles as a liquefaction-induced building settlement mitigation measure. Soil Dyn. Earthq. Eng.
**2021**, 151, 106994. [Google Scholar] [CrossRef] - Saadatinezhad, M.; Lakirouhani, A.; Jabin Asli, S. Seismic response of non-connected piled raft foundations. Int. J. Geotech. Eng.
**2021**, 15, 66–80. [Google Scholar] [CrossRef] - Sadeghian, F.; Jahandari, S.; Haddad, A.; Rasekh, H.; Li, J. Effects of variations of voltage and pH value on the shear strength of soil and durability of different electrodes and piles during electrokinetic phenomenon. J. Rock Mech. Geotech. Eng.
**2021**, 14, 625–636. [Google Scholar] [CrossRef] - Sabri, M.M.S.; Vatin, N.I.; Ponomarev, A.B.; Nurmukhametov, R.R.; Kostyukov, I.I. Settlement of Soil Reinforced with Vertical Fiberglass Micro-Piles. Materials
**2022**, 15, 4744. [Google Scholar] [CrossRef] [PubMed] - Komak Panah, A.; Mashhoud, H.J.; Yin, J.H.; Leung, Y.F. Shaking Table Investigation of Effects of Inclination Angle on Seismic Performance of Micropiles. Int. J. Geomech.
**2018**, 18, 04018142. [Google Scholar] [CrossRef] - Ghorbani, A.; Somti Foumani, M.A. The experimental study on the micropile effect on liquefaction potential of Anzali saturated sand. Sharif J. Civ. Eng.
**2020**, 36, 15–24. (In Farsi) [Google Scholar] - Munoz, H.; Kiyota, T. Deformation and localisation behaviours of reinforced gravelly backfill using shaking table tests. J. Rock Mech. Geotech. Eng.
**2020**, 12, 102–111. [Google Scholar] [CrossRef] - Alainachi, I.; Fall, M. Chemically induced changes in the geotechnical response of cementing paste backfill in shaking table test. J. Rock Mech. Geotech. Eng.
**2021**, 13, 513–528. [Google Scholar] [CrossRef] - Wood, D.M. Geotechnical Modelling; CRC Press: Boca Raton, FL, USA, 2003; Volume 1. [Google Scholar]
- Teymur, B.; Madabhushi, S.P.G. Experimental study of boundary effects in dynamic centrifuge modelling. Géotechnique
**2003**, 53, 655–663. [Google Scholar] [CrossRef] - Krishna, A.M.; Latha, G.M. Container boundary effects in shaking table tests on reinforced soil wall models. Int. J. Phys. Model. Geotech.
**2009**, 9, 1–14. [Google Scholar] [CrossRef] - Fishman, K.L.; Mander, J.B.; Richards, R. Laboratory study of seismic free-field response of sand. Soil Dyn. Earthq. Eng.
**1995**, 14, 33–43. [Google Scholar] [CrossRef] - Lee, C.J.; Wei, Y.C.; Kuo, Y.C. Boundary effects of a laminar container in centrifuge shaking table tests. Soil Dyn. Earthq. Eng.
**2012**, 34, 37–51. [Google Scholar] [CrossRef] - Dewoolkar, M.M.; Ko, H.Y.; Pak, R.Y.S. Experimental developments for studying static and seismic behavior of retaining walls with liquefiable backfills. Soil Dyn. Earthq. Eng.
**2000**, 19, 583–593. [Google Scholar] [CrossRef] - Soudkhah, M.; Pak, R.Y. Wave absorbing-boundary method in seismic centrifuge simulation of vertical free-field ground motion. Comput. Geotech.
**2012**, 43, 155–164. [Google Scholar] [CrossRef] - Lombardi, D.; Bhattacharya, S.; Scarpa, F.; Bianchi, M. Dynamic response of a geotechnical rigid model container with absorbing boundaries. Soil Dyn. Earthq. Eng.
**2015**, 69, 46–56. [Google Scholar] [CrossRef] - Takahashi, A.; Takemura, J. Liquefaction-induced large displacement of pile-supported wharf. Soil Dyn. Earthq. Eng.
**2005**, 25, 811–825. [Google Scholar] [CrossRef] [Green Version] - Ha, I.S.; Olson, S.M.; Seo, M.W.; Kim, M.M. Evaluation of reliquefaction resistance using shaking table tests. Soil Dyn. Earthq. Eng.
**2011**, 31, 682–691. [Google Scholar] [CrossRef] - Lee, K.L.; Albaisa, A. Earthquake induced settlements in saturated sands. J. Geotech. Eng. Div.
**1974**, 100, 387–406. [Google Scholar] [CrossRef] - De Alba, P.; Chan, C.K.; Seed, H.B. Determination of Soil Liquefaction Characteristics by Large-Scale Laboratory Tests; Springfield: Seattle, WA, USA, 1975. [Google Scholar]
- Abendroth, R.E.; Greimann, L.F. Pile behavior established from model tests. J. Geotech. Eng.
**1990**, 116, 571–587. [Google Scholar] [CrossRef] - Moccia, F. Seismic Soil Pile Interaction: Experimental Evidence. Ph.D. Thesis, University of Napoli “Federico II”, Napoli, Italy, 2009. [Google Scholar]
- Porcino, D.; Marcianò, V.; Granata, R. Cyclic liquefaction behaviour of a moderately cemented grouted sand under repeated loading. Soil Dyn. Earthq. Eng.
**2015**, 79, 36–46. [Google Scholar] [CrossRef] - Kolsky, H. Stress Waves in Solids; Dover; Courier Corporation: New York, NY, USA, 1953. [Google Scholar]
- Lombardi, D.; Bhattachaya, S. Shaking table tests on rigid soil container with absorbing boundaries. In Proceedings of the Fifthteenth World Conference on Earthquake Engineering (15 WCEE), Lisbon, Portugal, 24–28 September 2012. [Google Scholar]
- Zienkiewicz, O.C.; Chang, C.T.; Bettess, T. Drained, undrained, consolidating and dynamic behaviour assumptions in soils. Limits of validity. Geotechnique
**1980**, 30, 385–395. [Google Scholar] [CrossRef] - Lamb, H. Hydrodynamics, 6th ed.; Dover Publications: Cambridge, UK, 1932. [Google Scholar]
- Iai, S. Similitude for Shaking Table Tests on Soil-Structure-Fluid Model in 1 g Gravitational Field. Soils Found.
**1989**, 29, 105–118. [Google Scholar] [CrossRef] [Green Version] - Ueng, T.S.; Wu, C.W.; Cheng, H.W.; Chen, C.H. Settlements of saturated clean sand deposits in shaking table tests. Soil Dyn. Earthq. Eng.
**2010**, 30, 50–60. [Google Scholar] [CrossRef] - Varghese, R.M.; Latha, G.M. Shaking table tests to investigate the influence of various factors on the liquefaction resistance of sands. Nat. Hazards
**2014**, 73, 1337–1351. [Google Scholar] [CrossRef] - Maheshwari, B.K.; Singh, H.P.; Saran, S. Effects of reinforcement on liquefaction resistance of solani sand. J. Geotech. Geoenviron. Eng.
**2012**, 138, 831–840. [Google Scholar] [CrossRef] - Banerjee, R.; Konai, S.; Sengupta, A.; Deb, K. Shake Table Tests and Numerical Modeling of Liquefaction of Kasai River Sand. Geotech. Geol. Eng.
**2017**, 35, 1327–1340. [Google Scholar] [CrossRef] - Giustolisi, O.; Savic, D.A. A symbolic data-driven technique based on evolutionary polynomial regression. J. Hydroinforma.
**2006**, 8, 207–222. [Google Scholar] [CrossRef] [Green Version] - Giustolisi, O.; Savic, D.A. Advances in data-drive analyses and modelling using EPR-MOGA. J. Hydroinforma.
**2009**, 11, 225–236. [Google Scholar] [CrossRef] - Rezania, M.; Javadi, A.A.; Giustolisi, O. An evolutionary-based data mining technique for assessment of civil engineering systems. Eng. Comput.
**2008**, 25, 500–517. [Google Scholar] [CrossRef] - Ahangar-Asr, A.; Faramarzi, A.; Mottaghifard, N.; Javadi, A.A. Modeling of permeability and compaction characteristics of soils using evolutionary polynomial regression. Comput. Geosci.
**2011**, 37, 1860–1869. [Google Scholar] [CrossRef] - Ghorbani, A.; Hasanzadehshooiili, H. Prediction of UCS and CBR of microsilica-lime stabilized sulfate silty sand using ANN and EPR models; application to the deep soil mixing. Soils Found.
**2018**, 58, 34–49. [Google Scholar] [CrossRef] - Shariatmadari, N.; Karimpour-Fard, M.; Hasanzadehshooiili, H.; Hoseinzadeh, S.; Karimzadeh, Z. Effects of drainage condition on the stress-strain behavior and pore pressure buildup of sand-PET mixtures. Constr. Build. Mater.
**2020**, 233, 117295. [Google Scholar] [CrossRef] - Shariatmadari, N.; Hasanzadehshooiili, H.; Ghadir, P.; Saeidi, F.; Moharrami, F. Compressive Strength of Sandy Soils Stabilized with Alkali Activated Volcanic Ash and Slag. J. Mater. Civ. Eng.
**2021**, 33, 04021295. [Google Scholar] [CrossRef] - Ghorbani, A.; Hasanzadehshooiili, H.; Eslami, A. Parametric Evaluation of Simultaneous Effects of Damaged Zone Parameters and Rock Strength Properties on GRC. Adv. Civ. Eng.
**2021**, 2021, 2237918. [Google Scholar] [CrossRef]

**Figure 5.**Geometry of the model and the arrangement of micropiles: (

**a**) 2 vertical micropiles, s/d = 7; (

**b**) 2 inclined micropiles, s/d = 7.

**Figure 7.**Cross section of the grouted micropile in a small transparent box used to obtain the grouting pressure.

**Figure 10.**EPWP time histories subjected to 0.2 g acceleration: (

**a**) pure sand; (

**b**) 2 micropiles; (

**c**) 4 micropiles; (

**d**) 9 micropiles.

**Figure 11.**Longitudinal profile of variations of excess pore water pressure in depth for different relative densities and accelerations: (

**a**) Dr = 30% & a

_{max}= 0.2 g; (

**b**) Dr = 30% & a

_{max}= 0.32 g; (

**c**) Dr = 50% & a

_{max}= 0.32 g.

**Figure 12.**Variation of r

_{u}with the cycle number to r

_{umax}in different arrangements of micropile: (

**a**) bottom PPT; (

**b**) upper PPT.

**Figure 13.**Variation of r

_{u}relative to the applied cycles in different micropile spacing ratios: (

**a**) bottom PPT; (

**b**) upper PPT.

**Figure 14.**Effects of micropiles’ inclination on variation of r

_{u}relative to the applied cycles in different micropiles’ spacing ratios: (

**a**) bottom PPT; (

**b**) upper PPT.

**Figure 15.**Time histories of r

_{u}values at two applied accelerations: (

**a**) pure sand; (

**b**) 2 vertical micropiles; (

**c**) 4 vertical micropiles; (

**d**) 9 vertical micropiles.

**Figure 16.**Effect of the scaled loading acceleration on r

_{u}values during shaking: (

**a**) pure sand; (

**b**) 2 vertical micropile; (

**c**) 4 vertical micropiles; (

**d**) 9 vertical micropiles.

**Figure 19.**Comparison of the proposed lower and upper bounds of results obtained in the present study for the micropile-reinforced sand with the results of cemented sand under cyclic triaxial tests available in the literature [71].

**Figure 21.**Comparison between the predicted results of the EPR model and the measured r

_{u}values: (

**a**) bottom PPT; (

**b**) upper PPT.

**Figure 22.**Simultaneous effects of the micropiles’ inclination, the soil’s relative density, and the scaled loading acceleration on the liquefaction potential.

**Figure 23.**Simultaneous effects of number of micropiles, spacing ratio, and soil’s relative density on the liquefaction potential.

**Figure 24.**Simultaneous effects of the number of micropiles, scaled loading acceleration, and the soil’s relative density on the liquefaction potential.

**Figure 25.**Simultaneous effects of the micropiles’ inclination, the soil’s relative density, and the spacing ratio on the liquefaction potential.

Quantity | General | 1 g (Laboratory) | Scaling Factor (Model/Prototype) |
---|---|---|---|

Length | ${\mathrm{n}}_{\mathrm{L}}$ | $\frac{1}{\mathrm{n}}$ | $\frac{1}{15.7}$ |

Mass density | ${\mathrm{n}}_{\mathsf{\rho}}$ | $1$ | 1 |

Acceleration | ${\mathrm{n}}_{\mathrm{g}}$ | $1$ | 1 |

Stiffness | ${\mathrm{n}}_{\mathrm{G}}$ | $\frac{1}{{\mathrm{n}}^{\mathsf{\alpha}}}$ | $\frac{1}{{15.7}^{0.5}}$ |

Stress | ${\mathrm{n}}_{\mathrm{g}}{\mathrm{n}}_{\mathrm{L}}{\mathrm{n}}_{\mathsf{\rho}}$ | $\frac{1}{\mathrm{n}}$ | $\frac{1}{15.7}$ |

Strain | $\frac{{\mathrm{n}}_{\mathrm{g}}{\mathrm{n}}_{\mathrm{L}}{\mathrm{n}}_{\mathsf{\rho}}}{{\mathrm{n}}_{\mathrm{G}}}$ | $\frac{1}{{\mathrm{n}}^{1-\mathsf{\alpha}}}$ | $\frac{1}{{15.7}^{0.5}}$ |

Displacement | $\frac{{\mathrm{n}}_{\mathrm{g}}{\mathrm{n}}_{\mathrm{L}}{}^{2}{\mathrm{n}}_{\mathsf{\rho}}}{{\mathrm{n}}_{\mathrm{G}}}$ | $\frac{1}{{\mathrm{n}}^{2-\mathsf{\alpha}}}$ | $\frac{1}{{15.7}^{1.5}}$ |

Time | ${\mathrm{n}}_{\mathrm{L}}{(\frac{{\mathrm{n}}_{\mathsf{\rho}}}{{\mathrm{n}}_{\mathrm{G}}})}^{0.5}$ | $\frac{1}{{\mathrm{n}}^{1-\frac{\mathsf{\alpha}}{2}}}$ | $\frac{1}{{15.7}^{0.75}}$ |

Shear wave velocity | ${(\frac{{\mathrm{n}}_{\mathrm{G}}}{{\mathrm{n}}_{\mathsf{\rho}}})}^{0.5}$ | $\frac{1}{{\mathrm{n}}^{\frac{\mathsf{\alpha}}{2}}}$ | $\frac{1}{{15.7}^{0.25}}$ |

Frequency | $\frac{{(\frac{{\mathrm{n}}_{\mathrm{G}}}{{\mathrm{n}}_{\mathsf{\rho}}})}^{0.5}}{{\mathrm{n}}_{\mathrm{L}}}$ | ${\mathrm{n}}^{1-\frac{\mathsf{\alpha}}{2}}$ | ${15.7}^{0.75}$ |

EI | ${\mathrm{n}}_{\mathrm{G}}{\mathrm{n}}_{\mathrm{L}}{}^{4}$ | $\frac{1}{{\mathrm{n}}^{4+\alpha}}$ | $\frac{1}{{15.7}^{4.5}}$ |

Parameter | Model | Prototype |
---|---|---|

Material | Soft rubber | Steel |

Length of casing (m) | 0.2 | 3.2 |

Casing thickness (cm) | 0.06 | 1 |

Inner diameter of micropile (cm) | 0.7 | 11 |

Radius of neat grout around the micropiles (cm) | 0.1 | 2 |

Radius of grouted sand (cm) | 0.3 | 5 |

Diameter of reinforcement element (cm) | 0.12 | 1.8 |

Young’s modulus of casing (GPa) | 0.006 | 200 |

Young’s modulus of grouted sand (GPa) | 0.2 | 0.2 |

Young’s modulus of grout (GPa) | 30 | 30 |

Young’s modulus of reinforcement element (GPa) | 100 | 200 |

Test | Lateral Boundary | Duration (s) | Frequency (Hz) | Max. Acceleration (g) | Relative Density (%) | Number of Micropiles | ${\mathbf{s}}_{\mathbf{mic}}/{\mathbf{d}}_{\mathbf{mic}}$ | ${\mathbf{\theta}}_{\mathbf{mic}}$ |
---|---|---|---|---|---|---|---|---|

1 | Rigid | 12.5 | 2 | 0.2 | 30 | - | - | - |

2 | 12.5 | 2 | 2 | 7 | 90 | |||

3 | Absorbing | 12.5 | 2 | 0.2 | 30 | - | - | - |

4 | 12.5 | 2 | 1 | - | 90 | |||

5 | 12.5 | 2 | 2 | 7 | 90 | |||

6 | 12.5 | 2 | 2 | 4 | 90 | |||

7 | 12.5 | 2 | 2 | 7 | 78 | |||

8 | 12.5 | 2 | 2 | 4 | 78 | |||

9 | 12.5 | 2 | 4 | 7 | 90 | |||

10 | 12.5 | 2 | 4 | 4 | 90 | |||

11 | 12.5 | 2 | 9 | 3.5 | 90 | |||

12 | Absorbing | 9.5 | 3 | 0.32 | 30 | - | - | - |

13 | 9.5 | 3 | 1 | - | 90 | |||

14 | 9.5 | 3 | 2 | 7 | 90 | |||

15 | 9.5 | 3 | 2 | 4 | 90 | |||

16 | 9.5 | 3 | 2 | 7 | 78 | |||

17 | 9.5 | 3 | 2 | 4 | 78 | |||

18 | 9.5 | 3 | 4 | 7 | 90 | |||

19 | 9.5 | 3 | 4 | 4 | 90 | |||

20 | 9.5 | 3 | 9 | 3.5 | 90 | |||

21 | Absorbing | 9.5 | 3 | 0.32 | 50 | - | - | - |

22 | 9.5 | 3 | 1 | - | 90 | |||

23 | 9.5 | 3 | 2 | 7 | 90 | |||

24 | 9.5 | 3 | 4 | 7 | 90 |

Test | Bottom PPT | Upper PPT | ||||||
---|---|---|---|---|---|---|---|---|

${\mathbf{r}}_{{\mathbf{u}}_{\mathbf{max}}}$ | Percentage of Reduction in ${\mathbf{r}}_{{\mathbf{u}}_{\mathbf{max}}}$ Relative to the Pure Sand | ${\mathbf{N}}_{\mathbf{peak}}$ | Percentage of Increase in ${\mathbf{N}}_{\mathbf{peak}}$ Relative to the Pure Sand | ${\mathbf{r}}_{{\mathbf{u}}_{\mathbf{max}}}$ | Percentage of Reduction in ${\mathbf{r}}_{{\mathbf{u}}_{\mathbf{max}}}$ Relative to the Pure Sand | ${\mathbf{N}}_{\mathbf{peak}}$ | Percentage of Increase in ${\mathbf{N}}_{\mathbf{peak}}$ Relative to the Pure Sand | |

1 | 0.88 | - | 8.8 | - | 0.9 | - | 8.7 | - |

2 | 0.68 | 22.7 | 11.2 | 27.27 | 0.7 | 22.2 | 13.4 | 54.02 |

3 | 0.82 | - | 9 | - | 0.85 | - | 8.8 | - |

4 | 0.8 | 2.4 | 9.4 | 4.44 | 0.82 | 3.5 | 11 | 25 |

5 | 0.62 | 24.39 | 11.6 | 28.89 | 0.67 | 21.2 | 13.6 | 54.5 |

6 | 0.6 | 26.83 | 11.6 | 28.89 | 0.64 | 24.7 | 13.8 | 56.8 |

7 | 0.6 | 26.83 | 11.8 | 31.11 | 0.61 | 28.2 | 13.8 | 56.8 |

8 | 0.57 | 30.49 | 11.8 | 31.11 | 0.6 | 29.4 | 14 | 59.1 |

9 | 0.45 | 45.12 | 13.6 | 51.11 | 0.47 | 44.7 | 16 | 81.8 |

10 | 0.41 | 50 | 14 | 55.56 | 0.42 | 50.6 | 16 | 81.8 |

11 | 0.26 | 68.29 | 16 | 77.78 | 0.3 | 64.71 | 19 | 115.91 |

12 | 1 | - | 13.2 | - | 1 | - | 12.9 | - |

13 | 0.95 | 5 | 13.5 | 2.27 | 0.96 | 4 | 15.6 | 21 |

14 | 0.74 | 26 | 16.5 | 25 | 0.75 | 25 | 19.5 | 51.2 |

15 | 0.71 | 29 | 16.5 | 25 | 0.74 | 26 | 19.8 | 53.5 |

16 | 0.72 | 28 | 17.4 | 31.82 | 0.73 | 27 | 20.1 | 55.8 |

17 | 0.69 | 31 | 17.7 | 34.1 | 0.72 | 28 | 20.4 | 58.1 |

18 | 0.56 | 44 | 20.1 | 52.27 | 0.59 | 41 | 22.5 | 74.4 |

19 | 0.5 | 50 | 20.4 | 54.55 | 0.54 | 46 | 23.1 | 79 |

20 | 0.32 | 68 | 23.4 | 77.27 | 0.38 | 62 | 27 | 109.3 |

21 | 0.75 | - | 16.5 | - | 0.81 | - | 16.2 | - |

22 | 0.71 | 5.3 | 17.1 | 3.6 | 0.76 | 6.1 | 18 | 11 |

23 | 0.62 | 17.33 | 19.5 | 18.18 | 0.64 | 21 | 21.9 | 35.18 |

24 | 0.44 | 41.33 | 24 | 45.45 | 0.49 | 39.5 | 26.4 | 63 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ghorbani, A.; Hasanzadehshooiili, H.; Somti Foumani, M.A.; Medzvieckas, J.; Kliukas, R.
Liquefaction Potential of Saturated Sand Reinforced by Cement-Grouted Micropiles: An Evolutionary Approach Based on Shaking Table Tests. *Materials* **2023**, *16*, 2194.
https://doi.org/10.3390/ma16062194

**AMA Style**

Ghorbani A, Hasanzadehshooiili H, Somti Foumani MA, Medzvieckas J, Kliukas R.
Liquefaction Potential of Saturated Sand Reinforced by Cement-Grouted Micropiles: An Evolutionary Approach Based on Shaking Table Tests. *Materials*. 2023; 16(6):2194.
https://doi.org/10.3390/ma16062194

**Chicago/Turabian Style**

Ghorbani, Ali, Hadi Hasanzadehshooiili, Mohammad Ali Somti Foumani, Jurgis Medzvieckas, and Romualdas Kliukas.
2023. "Liquefaction Potential of Saturated Sand Reinforced by Cement-Grouted Micropiles: An Evolutionary Approach Based on Shaking Table Tests" *Materials* 16, no. 6: 2194.
https://doi.org/10.3390/ma16062194