Seismic response of shallow foundations over liquefiable soils improved by deep soil mixing columns

Computers and Geotechnics 110 (2019) 251–273

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Research Paper

Seismic response of shallow foundations over liquefiable soils improved by deep soil mixing columns Araz Hasheminezhad, Hadi Bahadori

T

⁎

Department of Civil Engineering, Urmia University, Urmia, Iran

A R T I C LE I N FO

A B S T R A C T

Keywords: Deep soil mixing (DSM) Soil Improvement Seismic Response Shallow Foundation

There are limited information on how an artificially non-liquefiable soil layer created by ground improvement beneath shallow foundations can help the reduction of liquefaction induced foundation settlements and the deterrence of bearing capacity failure effectively. This is addressed herein, numerically through a three-dimensional finite difference model using FLAC3D. The validity of the developed model was evaluated by comparing the results obtained from the model with the results of numerical studies and experimental centrifuge tests available in the literature. Using the validated model, the seismic response of a shallow foundation including bearing capacity and settlement was evaluated parametrically over a single DSM column in terms of its diameter and depth and also DSM group columns in terms of the diameter of columns and their center-to-center distance. Afterward, the influence of shallow foundation characteristic parameters was evaluated including thickness, width and embedded depth on the seismic response of shallow foundations over liquefiable soils improved by DSM columns. The obtained results can be used in practical engineering applications and provide new insight into the seismic performance of shallow foundations with DSM columns located over liquefiable soils.

1. Introduction It is believed that liquefaction probably happens more in loose saturated soils like silty sands or sands and gravels containing impermeable sediments exposed to sturdy ground motions in large-magnitude earthquakes. Liquefaction may result in severe loss of bearing capacity, which will extremely damage superstructures. As a result of liquefaction, extensive damage has been reported to shallow foundations in various case studies [1,30,24]. Regardless of the severity of damages, relatively few studies have been conducted regarding the seismic response of shallow foundations. Further, the extent of damage due to earthquake is strongly influenced by the quality of soil [27,24]. Liquefiable soils are found abundantly in many regions around the world, particularly in coastal areas. However, the construction of new structures such as embankments, storage tanks, and retaining walls on these types of soils is sometimes unavoidable to keep up with economic development [26,23]. In these cases, and due to the high compressibility and the lack of bearing capacity of the ground, the soil should be improved. In addition, the liquefaction vulnerability of a place should definitely be properly evaluated before any construction in that particular place to avoid any disaster in the near future [18,7]. Therefore, it is necessary to take advantage of numerous soil improvement

⁎

techniques to resist liquefaction to the maximum extent possible as a part of pre-disaster management. To this end, over the past years the topics of interest in liquefaction studies have changed and recent interests are mainly focused on advanced mitigation measures for liquefaction which are economic and useful for structures [29]. Consequently, numerous ground improvement techniques have been applied to overcome difficulties associated with the construction on liquefiable soils. Over time, further progress was observed in this particular field and many new soil improvement techniques have evolved to deal with liquefaction. The mechanisms behind most of these soil improvement techniques mainly involve densification, drainage, reinforcement and confinement [8,4,27,16,25,6]. In order to improve the bearing capacity of the soils and reduce the settlement of foundations, various soil improvement techniques have been used including stone columns (SC), dewatering, preloading and prefabricated vertical drains (PVD), and insitu mixing of admixtures such as lime and cement called deep soil mixing method. Among these methods, DSM method has attracted a great deal of attention worldwide. In DSM, to have a soil binder column to increase strength and lessen the compressibility of the weak soil, the unstable soil is mixed with cementitious and other additives. This method is chiefly dependent on increasing the stiffness of native soil reached through the addition of a strengthening admixture material like

Corresponding author. E-mail addresses: [email protected] (A. Hasheminezhad), [email protected] (H. Bahadori).

https://doi.org/10.1016/j.compgeo.2019.02.019 Received 14 November 2018; Received in revised form 27 January 2019; Accepted 17 February 2019 0266-352X/ © 2019 Elsevier Ltd. All rights reserved.

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cement, lime, gypsum and fly ash. DSM is founded on the notion of improved natural soils or brownfield ground to meet the adopted design requirements; hence, challenging excavation and replacement or more costly deep foundation methods could be circumvented. Since execution of soil mixing columns has many applications and variable patterns, it would be possible to find safe and cost-effective ground engineering solutions. Applying non-toxic binders as soil additives like industrial by-products, as well as decreased spoil volumes in comparison with jet grouting or classical drilled piles, for instance, put DSM forward as eco-friendly technology. DSM method as one of the most promising ground improvement methods has proved to be effective in stabilizing potentially liquefiable soil at several sites during earthquakes not only in controlling lateral spread but also in preventing liquefaction [20,22]. Modern seismic codes deem that shallow foundations should be used on liquefiable soils only following the appropriate ground improvement underneath and around the foundation [12]. Moreover, field case studies, as well as experimental and theoretical research reported that it is possible to reduce the destructive effects of liquefaction on the performance of shallow foundations by applying a non-liquefiable soil crust having proper dimensions and shear strength. The non-liquefiable crust can be sometimes artificially created by ground improvement. However, there are a limited number of researches on the beneficial effect of a non-liquefiable soil layer beneath shallow foundations for the reduction of liquefaction induced foundation settlements and the prevention of bearing capacity failure. Particularly, liquefaction mitigation in liquefiable soil layer improved by DSM is relatively limited, and the influence of some important design factors remains unclear. This problem is investigated herein numerically, through 3-D analyses with the FD code in FLAC3D, to simulate the seismic response of shallow foundations over liquefiable soils improved by DSMs.

Fig. 1. Cross-sectional view of the centrifuge Test No.1 [2].

constant liquefiable layer, dense layer can mitigate the settlement by up to 50%. Dimitriadi et al. [12] investigated the performance of seismic liquefaction in strip foundations through ground improvement. In their numerical study, they studied the effect of the size of the improved area on the seismic settlement and bearing capacity of the foundation. According to the available literature, although extensive numerical and experimental studies have been made on the seismic behavior of shallow foundations, there is a lack of sufficient investigation regarding the effects of liquefiable soil improvement against liquefaction on shallow foundation seismic behavior. In particular, no studies have been conducted on the seismic response of shallow foundations over liquefiable soils improved by DSM columns as a reliable improvement method. Literature review show that previous researches had some limitations. First, lack of sufficient investigation on the effects of DSM method in single and group columns on the liquefaction mitigation of liquefiable soil beneath shallow foundations and their seismic behavior. Second, lack of sufficient investigation on the effects of parameters like DSM columns characteristics for a single DSM column regarding its diameter and depth and also DSM group columns regarding the diameter of columns and their center-to-center distance besides shallow foundation characteristics such as thickness, width and embedded depth. This study was applied using an extensive parametric numerical approach to bring these limitations to light. The present paper examines the seismic response of shallow foundations over liquefiable soils improved by DSM columns through a numerical study focusing on the effect of DSMs and shallow foundations characteristics. The main aim of this paper is to analyze the influence of soil reinforcement executed by DSM method as a non-liquefiable layer on the seismic behavior of shallow foundations. Numerical simulations were performed using of finite difference (FD) analyses in FLAC3D- in order to identify the mechanisms and the parameters guiding the seismic performance of shallow foundations. The applied numerical methodology is based on a three-dimensional finite difference (FD) model implemented in FLAC3D. The validity of the developed model was evaluated by comparing the results obtained from the model with the results of numerical studies and experimental centrifuge tests including VELACS project available in the literature. Using this well-developed model, extensive parametric analyses were conducted for the common case of a square shallow foundation overlying a liquefiable soil layer improved by a single DSM column in terms of its diameter and depth. Further, considering the diameter of columns and their centerto-center distance, DSM group columns were used to gain insight into the bearing capacity failure and mechanism of settlement. In another part of this study, the influence of shallow foundation characteristic parameters including thickness, width, and embedded depth was evaluated on the seismic response of shallow foundations over liquefiable soils improved by DSM columns.

2. Literature review Since it is a complicated issue, only relatively limited references are available in the literature on the assessment of the seismic response of shallow foundations over liquefiable soils improved by DSMs. Nevertheless, there are a number of numerical and experimental studies on the seismic behavior of shallow foundations over various types of soils like those discussed further. Dashti et al. [11] investigated the mechanisms involved in liquefaction-induced building settlement using series of centrifuge experiments. Oliveira et al. [23] in a parametric study examined the behavior of an embankment constructed on normally consolidated soft soil which was improved by deep mixing columns. Dashti and Bray [10] used UBCSAND model implemented in FLAC2D to investigate the building response on liquefiable sand using fully-coupled numerical simulations. By applying a critical state constitutive model called NTUA-SAND, into the commercial finite-difference Codes FLAC and FLAC3D, Karamitros et al. [18] evaluated shallow foundation response. Their results indicated that the presence of a non-liquefiable soil (natural or artificial) crust might efficiently mitigate the damaging effects of liquefaction and allow the installation of shallow foundations through adopting a performance-based design approach. Asgari et al. [4] parametrically investigated the effects of SCs and pile pinning on decreasing potential liquefaction effects during earthquakes. Asgari et al. [3] in a numerical parametric study evaluated the seismic response of shallow foundation on loose silt and silty sand considering the soil type, weight, and thickness of liquefiable soil layer. Rasouli et al. [24] installed sheet-pile walls around the foundation and studied the moderation of seismic settlement in light surface structures. Based on their obtained results, sheet-piling with gaps delayed initiation of settlement, but might intensify the eventual settlement of the structure. Further, through 3D dynamic fully coupled analysis, Ayoubi and Pak [5] studied the settlement of a shallow foundation on two-layered subsoil strata under earthquake loading. Their results indicated that in comparison to

3. Numerical simulations The numerical modeling involved three-dimensional dynamic finite 252

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Table 1 Characteristics of Nevada sand with a relative density of 40% [2]. Characteristics

Dry Density

Unit Values

kg/m 1500

3

Void ratio

Permeability

Poisson ratio

Shear Modulus

Friction Angle

Cohesion

(N1 )60

– 0.73

m/s 6 × 10−5

– 0.3

MPa 3.85

Degree 30

kPa 0

Blows 7

Table 2 Characteristics of DSM columns adopted in the numerical modelling [4,15]. Parameters

Dry density

shear modulus

Permeability

Friction angle

Cohesion

Bulk Modulus

Poisson ratio

Young’s modulus

Void ratio

Unit Values

kg/m3 2100

MPa 173

m/s 10−1

Degree 33

kPa 2800

MPa 375

– 0.3

MPa 450

– 0.45

in the liquefiable soils was investigated by developing a finite difference model using the FLAC3D. Then, the results of this analysis were compared with the results of model test No.1 of VELACS project as an experimental centrifuge test as well as the simulation results of Esmaeili and Hakimpoor [13]. In this way, the developed model was verified. After verification of the developed model, a three-dimensional model was developed for a square shallow foundation over a liquefiable soil improved by DSMs individually and in groups. Afterwards, extensive parametric analyses were performed considering DSMs and shallow foundation characteristics. The simulation details such as model geometry, soil, DSM columns and shallow foundation properties, dynamic loading, boundary conditions, constitutive model, damping properties, verification of the model and the analysis approach are explained further as follows.

Table 3 Characteristics of square shallow foundation adopted in the numerical modelling [3]. Parameter

Young’s Modulus of concrete, Ec

Unit Value

kPa 2.3 × 1011

3.1. Model geometry The geometry properties of the liquefiable soil were adapted from the model test No.1 of VELACS project [2]. Fig. 1 demonstrates the horizontally layered loose sand in a laminar box for the model test No.1 of VELACS project. The laminar box included horizontal layer of uniform Nevada No. 120 sand at the height of 20 cm, placed via dry pluviation at a relative density of 40%. It was completely saturated with water, spun at a centrifuge acceleration of 50g, and the seismic excitation was applied at the base. This combination was used to simulate

Fig. 2. Horizontal input motion at the bottom [2].

analyses which simulated the seismic response of shallow foundations over liquefiable soils improved by DSMs. These analyses were performed using FLAC3D. For this purpose, first occurrence of liquefaction

Fig. 3a. Comparison of EPWP values at a depth of 1.25 m with Esmaeili and Hakimpour [13] study and model test No. 1 of VELACS project. 253

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Fig. 3b. EPWP distribution at different points of the soil in the numerical model.

a 10 m soil layer in prototype. Based on the scale coefficient of 1:50 and dimensions of the test No. 1 of VELACS project, the geometry of the numerical model was selected as 12 × 16 m (12 m toward X direction and 16 m toward Y direction) at a depth of 10 m.

Δε vd = C1·(γ − C2·ε vd ) +

2 C3·ε vd γ + C4·ε vd

Δε vd ε = C1·exp ⎜⎛−C2· vd ⎞⎟ γ γ ⎠ ⎝

(1)

(2)

where C1, C2 , C3 , and C4 denote constants that are linked as follows: C1C2 C4 = C3 . Δε vd shows the soil volume decrease, γ denotes the size of periodic shear strains, and ε vd denotes the accumulated volumetric strain from previous cycles in percent. As explained by Byrne [9], the amount of C1 coefficient depends on the sand relative density (Dr ) by C1 = 7600(Dr )−2.5 . According to the empirical relation between Dr and (N1)60 normalized standard penetration test values, i.e. Dr = 15(N1)60−1.25 , C1 coefficient will be linked to (N1)60 by C1 = 8.7(N1)60−1.25 . C2 parameter is also a constant fraction of C1 and can 0.4 be expressed as C2 = C . Finn constitutive model is capable of con1 ducting the coupled dynamic-groundwater flow calculations and simulating the effects of liquefaction.

3.2. Soil, DSM columns and Shallow Foundation properties Table 1 indicates the characteristics of Nevada sand. Characteristics of DSM columns and square shallow foundation adopted in this study have been given in Tables 2 and 3, respectively. Terashi and Kitazume [28] presented the compressive strengths of DSM improved soils including peat, clay, and sand for different range of binder dosage. According to Terashi and Kitazume [28], binder dosage rate of 250–450 kg/m3 at different water/cement ratios could be used effectively in stabilizing sandy soils. In this study, binder dosage rate of 350 kg/m3 has been considered.

3.3. Characteristics of earthquake loading and constitutive model for liquefaction

3.4. Analysis approach and solution procedure The analysis method included static and dynamic types. Regarding static analysis in which soil was under the load of gravity, the base boundary was fixed across all directions and the side boundaries were fixed in the x and y directions. A dynamic analysis is always followed by static equilibrium calculation. Due to the 3D nature of liquefaction and DSMs, a 3D numerical model development was indispensable in this study. According to Fig. 2, in this simulation, the dynamic loading was applied as acceleration time history at the lowest point of the model with 2-Hz frequency and 0.235g acceleration. Accordingly, for interpretation and further assessment, the dynamic analyses were conducted and the results were extracted. In this regard, the static boundaries should have been applied to the model and then the static load to the base. After the equilibrium of the sample, dynamic boundaries and earthquake loading could be employed. Then, the seismic acceleration input was applied to the bottom of model. Furthermore, the dynamic boundaries should have been such that the seismic waves did not have any reflection toward the inside of soil after facing these boundaries;

The input horizontal acceleration time history at the base of the box consisted of 20 cycles of a 100-Hz sinusoidal input, with a variable amplitude and maximum peak acceleration of 11.75g. Therefore, a frequency of 2 Hz and peak acceleration of 0.235g in the prototype, and a zero vertical acceleration were considered for 50g centrifuge acceleration of the test [2]. Dynamic loading at the lower part of the model can be seen in Fig. 2. For simulation the model test No.1 of VELACS project, boundary conditions are fixed in the four sides and rigid in the bottom of model. To model a dynamic excess pore water pressure (EPWP) generation analysis, the irretrievable volume strain in the constitutive model was determined. A constitutive model named Finn [19] is formulated in FLAC3D, where Eqs. (1) and (2) are connected to plastic Mohr–Coulomb model [21] and by considering specified boundary conditions and definite coefficients, is applied to pinpoint the variations in fluid pressure by a porous medium. 254

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Fig. 4. Model geometry of a shallow foundation over a liquefiable soil improved by DSMs (a) Plan and (b) Transversal cut.

3.5. Verification of the model

otherwise, the responses will be unrealistic. In the dynamic analysis, the boundaries of the model should be considered as a free field. For soil bedrock analysis with DSMs, a square shallow foundation was used in the case of infinite boundaries as well as free boundaries on the four sides of the model. In dynamic analyses, it is necessary to determine the damping of the material; otherwise, the model analysis will not be finite. Thus, Rayleigh damping was applied in the present study. Rayleigh damping is applied for materials where damping matrix (C) is linked to the components of the toughness and mass matrixes (K, M) according to Eq. (3), using α and β factors. α stands for the damping coefficient connected to mass and β shows the damping coefficient related to stiffness.

C = αM + βK

Fig. 3a reveals the results of numerical modeling and the centrifuge test No. 1 in the VELACS project in the terms of EPWP at a depth of 1.25 m. Note that the soil characteristics, boundary conditions, and seismic acceleration input in the numerical modeling were the same as those in Esmaeili and Hakimpour [13] study. As can be seen, the results are reasonably in good agreement with the results of the model test No. 1 of VELACS project, as well as the findings of Esmaeili and Hakimpour [13]. In Fig. 3b reveals the EPWP distribution at different points of the soil in the numerical model. Figs. 4–6 illustrate the model geometry for shallow foundations over liquefied soils improved by DSMs along with the FD model of a square shallow foundation over a single and group DSMs used in the parametric study, respectively. Following the verification of the numerical methodology, the parametric investigation of the seismic response of shallow foundations over liquefiable soils improved by DSMs was performed. For this purpose, fixed and variable parameters in each numerical analysis were considered, summarized in Table 4.

(3)

In dynamic analyses, damping ratio of materials normally is not dependent on frequency and for geotechnical materials; damping ratio is often 2–5% of critical damping ratio. Rayleigh damping is specified in FLAC3D with the parameters fmin in Hertz (cycles per second) and ξmin . Natural frequency of model is 2 Hz in this study and damping coefficient was 5% of critical damping. 255

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Fig. 5. FD model and boundary conditions of a square shallow foundation over a single DSM.

Fig. 6. FD model and boundary conditions of a square shallow foundation over group DSMs.

4. Parametric study

improved by DSMs. The details are discussed as follows: Part A. Influence of DSM characteristics

Parametric analyses in this study were performed in two parts in terms of DSMs and shallow foundation characteristics. Part A called the influence of DSM characteristics included dynamic analysis results for EPWP and seismic response of shallow foundations for single and group DSMs. Part B called the influence of shallow foundations characteristics involved the effect of parameters of shallow foundation characteristics on the seismic response of shallow foundations over liquefiable soils

4.1. Dynamic analysis results of EPWP for a single DSM In this study, to investigate the influence of the DSM on the seismic response of shallow foundation over liquefiable soils, as well as reduction of the EPWP of liquefiable soil, a dynamic analysis was 256

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Table 4 Parameters in parametric analyses. Parametric Analyses No.

1 2 3 4 5

Fixed parameters

Variable parameters

B (m)

T (m)

z (m)

L (m)

S (m)

D (m)

D (m)

T (m)

Z (m)

B (m)

S/D

1.9 1.9 – 1.9 1.9

1.2 1.2 1.2 – 1.2

0 0 0 0 –

6 6 6 6 6

0 – 0 0 0

– – 0.9 0.9 0.9

0.9,1.2,1.5 0.9,1.2,1.5 – – –

– – – 0.8,1.2,1.6 –

– – – – 0,0.5,1,2

– – 1,1.9,2.8 – –

2,3,4,5 – – – –

Fig. 7. EPWP at the distance of 0.5 m.

Fig. 8. EPWP at the distance of 1.5 m.

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Fig. 9. EPWP at the distance of 2.5 m.

Fig. 10. EPWP at the distance of 3.5 m.

conducted using a DSM with diameters of 90, 120 and 150 cm, along with a square shallow foundation at the center of the model. Accordingly, changes of EPWP were evaluated at depths of 1.25 and 2.5 m and at distances of 0.5, 1.5, 2.5 and 3.5 m off the DSM center. The results of dynamic analysis for 1.25 m depth and distances of 0.5, 1.5, 2.5, and 3.5 m from the DSM center have been presented in Figs. 7–10, respectively. According to Figs. 7–10, with increasing the DSM diameter and the horizontal distance from the DSM, the risk of liquefaction decreases and increases, respectively. Fig. 9 demonstrates that at the distance of 2.5 m from the DSM, and at the time of about 8 s, the soil sample experienced partial liquefaction. However, according to Fig. 10, at the distance of 3.5 m from the DSM, the soil sample became completely liquefied. Therefore, through the increase in the distance from the DSM center, the effect of DSM on the liquefaction mitigation drops. In particular,

Table 5 Dynamic analysis results at the depth of 1.25 m. Distance from DSM (m)

D = 90 cm ru

D = 120 cm ru

D = 150 cm ru

0.5 1.5 2.5 3.5

0.51 0.68 0.92 1

0.32 0.38 0.89 1

0.23 0.37 0.87 1

Table 6 The efficiency of DSM at the depth of 1.25 m. Maximum reduction of liquefaction risk

D = 90 cm 49%

D = 120 cm 68%

D = 150 cm 77%

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Fig. 11. EPWP at the distance of 0.5 m.

Fig. 12. EPWP at the distance of 1.5 m.

According to Figs. 11–14, as with the depth of 1.25 m, with increase of the DSM diameter and the horizontal distance from the DSM, the risk of liquefaction decreases and increases, respectively. However, there is a significant difference among EPWPs at the depth of 2.5 m at different distances. Fig. 13 reveals that at the distance of 2.5 m from the DSM, the graphs relating to the EPWP of the DSM with a diameter of 90 cm have been partially liquefied at about 7 s. On the other hand, the EPWP diagram of the DSM with a diameter of 120 and 150 cm has not been liquefied. Fig. 14 indicates that at the depth of 2.5 m and the distance of 3.5 m from the DSM, as with the depth of 1.25 m, all soil samples became fully liquefied. Nevertheless, these graphs are closer to the stress line than the 1.25-m depth. Same as the depth of 1.25 m, with the increase of the distance from the DSM center, the effect of the existence of DSM on the liquefaction was reduced and the EPWP diagrams approached each other and almost overlapped, as illustrated in Fig. 14.

only from a certain distance off the column center, the DSM can reduce the risk of soil liquefaction. Tables 5 and 6 reveal the results of numerical simulation for a single DSM with a square shallow foundation at the depth of 1.25 m. As reported in the Table 6, with increase of the DSM diameter, the risk of liquefaction decreases. However, this decrease is not significant. Also, increasing the DSM diameter raises the radius of influence. This means that by increasing the diameter of DSM, a wider area around the liquefiable soil will be safe from the risk of liquefaction. The best performance of the single DSM to reduce the risk of liquefaction was at the depth of 1.25 m for a DSM with 150 cm diameter and at a distance of 0.5 m, reducing the risk of liquefaction by 77% (as shown in Table 6). The results of dynamic analysis for the depth of 2.5 m and distances of 0.5, 1.5, 2.5, and 3.5 m from the DSM center are presented in Figs. 11–14, respectively. 259

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Fig. 13. EPWP at the distance of 2.5 m.

Fig. 14. EPWP at the distance of 3.5 m.

This means that at a depth of 2.5 m, only from a certain distance off the column center, the DSM can reduce the risk of soil liquefaction. As shown in Fig. 13, EPWP around 4 s has a sudden drop. The EPWP fluctuations around 4 s can be attributed to the reduction in the efficiency of DSM column in mitigation of liquefaction as time goes by. In fact, as time goes by, DSM column efficiency reduces and the soil leads to be liquefied. This behavior is attributed to the increase in the PWP during dynamic load that causes reduction in the inter-particle forces between solid particles of the soil skeleton, hence causing an increase in displacement response. However, the presence of DSM columns with large diameters reduced this fluctuation. Therefore, with increase of the DSM diameter, its efficiency in decreasing risk of liquefaction improves and it delays liquefaction occurrence. Tables 7 and 8 reveal the numerical simulation results of a single DSM over a square shallow foundation at the depth of 2.5 m. As shown

Table 7 Dynamic analytical results at the depth of 2.5 m. Distance from DSM (m)

D = 90 cm

D = 120 cm

D = 150 cm

0.5 1.5 2.5 3.5

ru 0.38 0.81 1 1

ru 0.26 0.69 0.94 1

ru 0.20 0.41 0.79 1

Table 8 The efficiency of DSM at the depth of 2.5 m. Maximum reduction at risk of liquefaction

D = 90 cm 62%

D = 120 cm 74%

D = 150 cm 80%

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Fig. 15. Comparison of the efficiency of the single DSM with different dimensions on the seismic response of shallow foundations.

Fig. 16. EPWP changes for group DSM with a diameter of 90 cm and a ratio of

(

s d

)

= 2, 3, 4, 5 .

shallow foundation, dynamic analysis was performed taking into account a single DSM with diameters of 90, 120 and 150 cm, along with a square shallow foundation at the center of the model with dimensions of 1.9 m. The seismic parameters included the settlement and bearing capacity of the shallow foundation. In this regard, the settlement-stress diagram for different cases is presented in Fig. 15. As revealed in Fig. 15, the static bearing capacity was first calculated by the FLAC3D. Afterwards, it was compared with the bearing capacity calculated using the Terzaghi static bearing capacity formula. It can be seen that the static bearing capacity obtained from the FLAC3D and the Terzaghi formula are close by an acceptable extent. Further, while the dimensions of the foundation were assumed to be fixed (1.9 m), through taking into account the DSMs with diameters of 90, 120 and 150 cm, the bearing capacity and settlement of shallow foundation were calculated. Also, for better comparison, the seismic response of shallow

in Table 7, at the depth of 2.5 m, with the rise of DSM diameter, the risk of liquefaction is reduced. Furthermore, increasing the DSM diameter increases the radius of influence. The best performance of the DSM to reduce the risk of liquefaction at the depth of 2.5 m for a DSM with a diameter of 150 cm was at the distance of 0.5 m, lowering the risk of liquefaction by 80% (as presented in Table 8). In general, the obtained results indicated that the performance of the DSM at the depth of 2.5 m was far better than that of the 1.25-m depth. This means that by increasing the depth, the performance of DSM increases. 4.2. Dynamic analysis results of a single DSM for seismic response of shallow foundation To evaluate the efficiency of a single DSM on the seismic response of 261

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Fig. 17. EPWP changes for group DSM with a diameter of 120 cm and a ratio of

(

s d

= 2, 3, 4, 5 .

Fig. 18. EPWP changes for group DSM with a diameter of 150 cm and a ratio of

(

s d

= 2, 3, 4, 5 .

2 3 4 5

D = 90 cm

D = 120 cm

D = 150 cm

ru

Maximum reduction of liquefaction risk

ru

Maximum reduction of liquefaction risk

ru

Maximum reduction of liquefaction risk

0.52 0.74 0.91 1

48% 26% 9% 0

0.28 0.53 0.79 1

72% 47% 21% 0

0.11 0.47 0.65 1

89% 53% 35% 0

)

foundation was also calculated in the case without any DSM. According to Fig. 15, the seismic bearing capacity is less than that of the static state. In addition, with the increase in the DSM diameter, the seismic bearing capacity has also increased. Notably, the diagram of the seismic response of the foundation, in the case of using DSM, slowly changes from elastic to plastic and then to a constant stress. However, in the absence of a DSM, the graph suddenly shifts to a constant stress. This suggests that during an earthquake, if the DSM is not applied to liquefiable soil, the foundation suffers a sudden breakdown, and therefore the presence of a DSM causes the soil to have a slow settlement. However, this effect is insignificant at higher seismic intensities. Moreover, in seismic response diagrams with DSMs, all three diagrams reach their final seismic bearing capacity after settlement of approximately 5 cm.

Table 9 Dynamic analysis results for group DSMs with diameters of 90, 120 and 150 cm at the depth of 1.25 m. S/d

)

262

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Fig. 19. Seismic response of shallow foundation for group DSM with a diameter of 90 cm and the ratio of

(

Fig. 20. Seismic response of shallow foundation for group DSM with a diameter of 120 cm and the ratio of

(

In the group DSM, the dynamic analysis was performed considering a square pattern of the DSMs. The numerical results are presented for a group DSM with diameters of 90, 120 and 150 cm, along with the square shallow foundation, based on the ratio of columns spacing to s their diameter d = 2, 3, 4, 5 . Figs. 16–18 reveal the results of dynamic analysis regarding the variations of EPWP for group DSM at the midpoint between the central column and the side column at 1.25-m depth and for the DSMs with the diameters of 90, 120, and 150 cm. In this regard, across all group DSMs with various column diameters, increasing the space between the columns leads to an increase in EPWP. s In all cases of the group DSMs, at the d = 5 ratio, all models experienced complete liquefaction. In other words, with the increase in

(

)

(

s d

)

= 2, 3, 4, 5 .

)

= 2, 3, 4, 5 .

the distance between the DSMs, each DSM column will function individually. This means that the group DSM function disappears with increase of the distance between them. According to Fig. 16, in the group DSMs, with a diameter of 90 cm at s the ratio of d = 4 , partial liquefaction was observed from the beginning of loading up to about 2 s. By increasing the DSM diameter (as indicated in Figs. 17 and 18), this partial liquefaction was eliminated. s Except for the ratio of d = 5 , where the columns acted individually and the diagram of EPWP was approximately same for the group DSM s with different diameters, at a constant d , with the rise of the DSM diameter, the EPWP diminished. Table 9 provides the numerical results for the group DSMs with diameters of 90, 120 and 150 cm along with the shallow foundation s based on d = 2, 3, 4, 5 . As shown in Table 9, in group DSMs, with

4.3. Dynamic analysis results of EPWP for group DSM

(

s d

)

(

)

()

)

(

263

)

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Fig. 21. Seismic response of shallow foundation for group DSM with a diameter of 150 cm and the ratio of

(

s d

)

= 2, 3, 4, 5 .

Fig. 22. The effect of foundation width on EPWP at a distance of 0.5 m from DSM.

4.4. Dynamic analysis results of group DSM for the seismic response of shallow foundation

increase of the diameter of DSMs, the risk of liquefaction diminishes. s Also, at the d = 5 , all models experienced complete liquefaction. The best function of the group DSMs to reduce the risk of liquefaction at the depth of 1.25 m belonged to DSM columns with a diameter of 150 cm, lowering the risk of liquefaction by 89%. It should be noted that in the case of a single DSM, the maximum reduction of liquefaction risk was 77% and related to a column with a diameter of 150 cm. In other words, in the group mode, the DSMs will be more capable than the single mode in reducing the risk of liquefaction. Indeed, the side columns help the central columns to reduce the risk of liquefaction.

(

)

Figs. 19–21 exhibit the dynamic analysis results of the seismic response of shallow foundation for the group DSMs with 90, 120 and s 150 cm diameters and the ratio of d = 2, 3, 4, 5 , respectively. As the distance between DSMs increases, the seismic bearing capacity decreases, but the magnitude of settlement at the moment of reaching the final bearing capacity remains almost constant. With the increase of the diameter of DSMs, the seismic bearing capacity increases. Increasing the distance between the columns can change the function of columns s from group to single mode, such that at the ratio of d = 5 , the bearing capacity is almost the same under all three conditions. In addition, in the group DSMs, unlike single mode, the dynamic load does not

(

)

(

264

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Fig. 23. The effect of foundation width on EPWP at a distance of 1.5 m from DSM.

Fig. 24. The effect of foundation width on EPWP at a distance of 2.5 m from DSM.

also considered in three different dimensions with the widths of 1, 1.9 and 2.8 m. The results of dynamic analysis at the depth of 1.25 m and the distances of 0.5, 1.5, 2.5 and 3.5 m from the DSM are presented in Figs. 22–25, respectively. According to these figures, with the increase in the width of the foundation, the EPWP around the DSM sharply drops. The sharp increase in EPWP after 4 s, as shown in Figs. 24 and 25, can be attributed to the increase in the PWP during dynamic load that causes reduction in the inter-particle forces between solid particles of the soil skeleton, hence preventing solid particles from interlocking with each other to rearrange their skeleton to resist the applied dynamic loading. As a result, the EPWP is negatively influenced by the widths of 2.8 m and distances of 0.5 and 1.5 m (Figs. 22 and 23). At the distances of 2.5 m and 3.5 m from the DSM (Figs. 24 and 25), the effect of the DSM on the liquefaction diminishes, so the EPWP reduction is

significantly affect the extent of foundation settlement. As Figs. 19–21 show, the stresses in the center of stress-settlement figures decreased sharply. This can be associated with increased PWP within dynamic load leading to reduced inter-particle forces between solid particles. Part B. Influence of the characteristics of shallow foundations 4.5. Effect of shallow foundation width on EPWP In order to examine the effect of the width of shallow foundation on its seismic response and reduction of EPWP of the liquefiable soil, a dynamic analysis was conducted considering a DSM with a diameter of 90 cm along with a foundation at the center of the model. Changes in EPWP were investigated at the depths of 1.25 m and at distances of 0.5, 1.5, 2.5 and 3.5 m from the center of the column. The foundation was 265

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Fig. 25. The effect of foundation width on EPWP at a distance of 3.5 m from DSM.

Fig. 26. The effect of the width of foundation on its seismic response.

improvement of the liquefiable soil layer beneath the shallow foundation, as the foundation width increases (larger foundation), the DSM columns especially central columns beneath shallow foundations perform much for tolerating applied loads than the reducing EPWP. As a result, a large foundation generates negative EPWP. Furthermore, as shown in Figs. 22–25, the EPWP in the middle of figures after 4 s has a sharp reduction. This reduction is severe and sharper for Figs. 24 and 25 in which the distance from the DSM column is 2.5 and 3.5 m, respectively. This can be attributed to the increase in the PWP during dynamic load that causes reduction in the inter-particle forces between solid particles. In other words, as time goes by, and the distance from the DSM column increases, the efficiency of DSM columns in liquefaction mitigation decreases as discussed before. In turn, due to dynamic loading, the PWP is increased and soil becomes liquefied in the end.

also clearly evident. Thus, changes in the width of foundation can reduce EPWP. Reducing the width of the foundation from 1.9 m to 1 m has caused the soil around the DSM to experience complete liquefaction at all distances from 0.5 to 3.5 m. As shown, a large foundation generates negative EPWP. This is thought to be due to this fact that increasing the width of shallow foundation (Large shallow foundation) reduces the possibility of drainage and dissipation of PWP beneath the shallow foundation. In addition, the applied load by shallow foundation will be distributed to a larger area where a DSM column cannot drain and dissipate it effectively. As explained by Esmaeili and Khajehei [14], the weight of structure causes more than 50% of the applied load move to the DSM columns and the body of shallow foundation and sandy bed will tolerate the remainder. Besides, the central columns play more prominent role compared to the mid and side columns regarding the carrying the applied load. So, in a case of using DSM columns for 266

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Fig. 27. The effect of embedded depth of foundation on EPWP at a distance of 0.5 m from the DSM.

Fig. 28. The effect of embedded depth of foundation on EPWP at a distance of 1.5 m from the DSM.

capacity increased from approximately 75 kPa to 130 kPa, signifying 73% increase in the seismic bearing capacity. With increase of the foundation width from 1 m to 1.9 m, the settlement rate at the moment of reaching the final seismic bearing capacity (where the diagram is almost horizontal) decreased from approximately 10 cm to 4.5 cm, suggesting 55% decrease in the settlement rate. Increasing the foundation width from 1 m to 2.8 m, the settlement rate at the moment of reaching the final seismic bearing capacity (where the diagram is almost horizontal) dropped from approximately 10 cm to 2.7 cm, implying 73% decrease in the settlement rate. However, the stress vs settlement graph for the cases SD90B1.0 and SD90B2.8 has a bump in graph, which can be attributed to coincidence of shallow foundation natural frequency with earthquake loading frequency and resonance phenomenon, which has not been performed for SD90B1.9.

4.6. Effect of the width of shallow foundation on its seismic response In this section, the dynamic analysis results are presented to investigate the effect of the width of shallow foundation on its seismic response. The seismic response of the shallow foundation is evaluated based on the seismic settlements and the bearing capacity. In this regard, Fig. 26 shows the stress-settlement graph. According to the obtained results, expectedly with an increase in the width of the foundation, the seismic bearing and settlement increased and decreased, respectively. In fact, by increasing the width of shallow foundations, the intensity of load is decreased and on the same soil more loads can be placed. Through increasing the foundation width from 1 m to 1.9 m, the seismic bearing capacity increased from approximately 75 kPa to 105 kPa, representing 40% increase in the seismic bearing capacity. Increasing the foundation width from 1 m to 2.8 m, the seismic bearing 267

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Fig. 29. The effect of embedded depth of foundation on EPWP at a distance of 2.5 m from the DSM.

Fig. 30. The effect of embedded depth of foundation on EPWP at a distance of 3.5 m from the DSM.

positive effect on the EPWP. As the embedded depth of foundation increased from 0 to 0.5 m up to 0.7 s of analysis, the EPWP was zero. Also, by increasing embedded depth to 1 m up to 1.3 s of analysis, the EPWP was negative. Unlike Fig. 27, the increase of foundation depth at 1.5 and 2.5 m from the DSM had a negative effect on the EPWP. As shown in Figs. 28 and 29, with increasing of embedded depth, the EPWP has also increased. In Fig. 29, it can be seen that at the distance of 2.5 m and embedded depth of zero, the soil still was not liquefied. However, with an increase in embedded depth to 0.5 m, the soil was partially liquefied. Consequently, with increasing the embedded depth to 1 m, the soil has fully experienced the liquefaction. According to the Fig. 30, at the distance of 3.5 m, the effect of embedded depth of foundation on EPWP has been abolished. In addition, all the graphs overlapped and the soil has undergone a fully liquefaction.

4.7. Effect of embedded depth of shallow foundation on EPWP In order to examine the effect of embedded depth of shallow foundation on its seismic response and reduction of the EPWP of liquefiable soil, a dynamic analysis was performed considering a DSM with a diameter of 90 cm, coupled with a foundation with a width of 1.9 m in the center of the model. The changes in EPWP were investigated at the depth of 1.25 m and distances of 0.5, 1.5, 2.5 and 3.5 m from the center of the column. The foundation was also considered in three different modes with embedded depths of 0, 0.5 and 1 m. The results of dynamic analysis at the depth of 1.25 m and distances of 0.5, 1.5, 2.5 and 3.5 m from the DSM are given in Figs. 27–30, respectively. According to the results obtained in Fig. 27, the increase in the depth of the foundation at the distance of 0.5 m from the DSM had a 268

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Fig. 31. The effect of the embedded depth of foundation on its seismic response.

Fig. 32. The effect of the foundation thickness on the EPWP at a distance of 0.5 m from the DSM.

foundation decreases and at a distance of 3.5 m, this increase in stress caused by shallow foundation is to the lowest amount and the soil becomes liquefied. In addition, this phenomenon is due to the change in the “influence radius” of DSM column. According to the available literature, the circular region around the DSM column is affected by radial drainage, and the diameter of this circle is four times bigger than the DSM column diameter. In fact, the shallow foundation embedded depth increase has a positive effect on EPWP in the near distances of DSM column in which DSM column influence radius is more. However, as the distance from the DSM column increases, its influence radius decreases. In this condition, increase in shallow foundation embedded depth has negative effect on EPWP. Therefore, in nearer distances of DSM column, smaller embedment depths result in slightly larger EPWP generation.

According to the obtained results, in case of using a single DSM column and at 0.5 m distance from the column, shallow foundation embedded depth increase has a positive effect on EPWP and further has a negative effect on the EPWP. As the distance from the DSM column increases, soil layer gets ready to become liquefied. This can be attributed to this fact that by increasing the shallow foundation embedded depth; much of earthquake energy is applied to the water (due to the low displacement of soil particles) and increases the PWP. However, since the effective stress is much more in the depths of soil, despite the increase in the PWP, settlement is low and the probability of liquefaction is reduced. In this regard, as the distance from the DSM column below the shallow foundation increases, the probability of liquefaction also increases, and the DSM column will not have any effect on the mitigation of liquefaction. As the distance increases (distance of 1.5 and 2.5 m in this study), the increase in stress caused by shallow 269

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Fig. 33. The effect of the foundation thickness on the EPWP at a distance of 1.5 m from the DSM.

Fig. 34. The effect of the foundation thickness on the EPWP at a distance of 2.5 m from the DSM.

of foundation from 0 to 0.5 m, the settlement at the moment of reaching the final seismic bearing capacity diminished from about 5.6 to 3.6 cm, implying 35% decrease in the settlement rates. Finally, with the increase of the embedded depth of foundation from 0 to 1 m, the settlement at the moment of reaching the final seismic bearing capacity lessened from about 5.6 to 4.2 cm, suggesting 25% decline in the settlement rates. As shown, as the embedment depth of shallow foundation increases, reduction in settlement decreases, in other words, the settlement is increased. This is due to this fact that as the embedment depth of shallow foundation increases, the PWP is less drained and dissipated, so the effective stress will be low, causing the soil particles to move and increase the settlement.

4.8. Effect of embedded depth of shallow foundation on its seismic response In this section, the dynamic analysis results are presented to investigate the effect of embedded depth of shallow foundation on its seismic response. The seismic parameters included the settlement and bearing capacity of the shallow foundation. According to Fig. 31, expectedly, with of the increase in the embedded depth of shallow foundation, the seismic bearing capacity and settlement increased and decreased, respectively. With increase of the embedded depth of foundation from 0 to 0.5 m, the seismic bearing capacity rose from approximately 104 kPa to 111 kPa, showing 7% increase in the seismic bearing capacity. With the increase of embedded depth of foundation from 0 to 1 m, the seismic bearing capacity was augmented from approximately 104 kPa to 122 kPa, signifying 17% increase in the seismic bearing capacity. Also, with of the development of the embedded depth 270

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Fig. 35. The effect of the foundation thickness on the EPWP at a distance of 3.5 m from the DSM.

Fig. 36. The effect of foundation thickness on its seismic response.

liquefaction. At 2.5 m (Fig. 34), with a reduction in the foundation thickness from 120 to 80 cm, approximately from 5 to 8 s, the soil underwent partial liquefaction. At 3.5 m (Fig. 35), the effect of the foundation thickness totally faded and the diagrams overlapped.

4.9. Effect of shallow foundation thickness on EPWP In order to examine the effect of shallow foundation thickness on its seismic response and to decrease EPWP of the liquefiable soil, a dynamic analysis was conducted using a DSM with a diameter of 90 cm, a foundation of 1.9 m, and an embedded depth of 0 in the center of the model. Changes in EPWP at the depth of 1.25 m and at distances of 0.5, 1.5, 2.5 and 3.5 m from the center of the DSM column were also studied. The foundation was also considered in three different modes with the thicknesses of 80, 120 and 160 cm. Figs. 32–35 display the dynamic analysis results at the depth of 1.25 m and distances of 0.5, 1.5, 2.5 and 3.5 m from the DSM. According to these figures, the increase in the thickness of the foundation reduces the EPWP. As the distance from the DSM increases, the effect of the foundation thickness diminishes and the soil tends to experience

4.10. Effect of shallow foundation thickness on seismic response of shallow foundation In this section, the results of dynamic analysis are presented to investigate the effect of foundation thickness on its seismic response. The seismic parameters were shallow foundation settlement and bearing capacity. As expected and according to Fig. 36, the change in the thickness of the foundation has had little effect on the bearing capacity, since increasing the thickness of the foundation further increases the shear strength of the concrete foundation. In addition, such a condition 271

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and the soil tended to undergo liquefaction. The change in the thickness of the foundation had little effect on the bearing capacity, since increasing the thickness of the foundation further increases the shear strength of the concrete foundation.

has a limited use because with increase in thickness of the foundation, the weight and cost of foundation also increases. 5. Conclusions

Overall, considering low settlements and acceptable seismic bearing capacity and in the presence of DSMs, it is possible to ensure adequate seismic shallow foundation performance in liquefiable soils. At the end, it should be noted that the results obtained from present study can be used in practical engineering applications as well as in investigating the seismic performance of shallow foundations with DSM columns located over liquefiable soils. Further experimental investigation on the seismic performance of shallow foundations over liquefiable soil improved by DSMs is required which is in progress by the authors.

Through an extensive parametric study, the present paper described the numerical aspects of seismic response of shallow foundations over liquefiable soils improved by DSMs as implemented in the finite difference code, FLAC3D. The developed model displayed reasonably good agreement with the results of numerical studies and experimental centrifuge tests available in the literature. The focus of the conducted parametric studies was on variables including the characteristics of DSMs and shallow foundations. Accordingly, it was observed that an artificially created non-liquefiable soil layer employing DSM columns may effectively mitigate the damaging effects of liquefaction on shallow foundations and allow for a seismic performance design of shallow foundations. The major findings of this research are summarized below, involving the basic aspects of seismic response of shallow foundation performance related to DSMs:

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▪ Shallow foundation over a single DSM in a liquefiable soil: By increasing the diameter of a single DSM and the horizontal distance from the DSM, the risk of liquefaction decreased and increased, respectively. As the distance from the center of the single DSM increases, the effect of the DSM on the liquefaction decreased. Particularly, the DSMs could reduce the risk of soil liquefaction only from a certain distance off the center of the column. The best performance of the DSM to reduce the risk of liquefaction at a depth of 1.25 m for a column with a diameter of 150 cm was at the distance of 0.5 m, which reduced the risk of liquefaction by 77%. With the increase of depth, the performance of the single DSM was improved. With the increase in the diameter of the single DSM, the seismic bearing capacity also increased. ▪ Shallow foundation over DSM group in a liquefiable soil: Across all group DSMs with different column diameters, through increasing the distance between columns, the extent of EPWP also increased. By increasing the distance between the DSMs, each DSM column functioned individually. Any increase in the distance between the columns eliminated their group function. Increasing the distance between the columns caused the columns to change their function from group to single mode. In group DSMs, by increasing the diameter of DSM, the risk of liquefaction diminished. The best group performance of DSMs to reduce the risk of liquefaction was obtained at the depth of 1.25 m for a column with a diameter of 150 cm, lowering the risk of liquefaction by 89%. In the group mode, the side columns helped the central column in reducing the risk of liquefaction; therefore, group DSM would be more capable of reducing the risk of liquefaction than single mode. By increasing the distance between the DSMs, the seismic bearing capacity dropped, but the extent of settlement at the moment of reaching the final bearing capacity remained almost constant. In the group mode, with increase of the diameter of DSM, the seismic bearing capacity increased, to such an extent that the seismic bearing capacity with columns 150 cm in diameter was greater than the static bearing capacity. In the group mode of DSMs unlike single-mode, dynamic load did not significantly affect the extent of foundation settlement. ▪ Shallow foundation characteristics: With the increase in the width of the foundation, the EPWP around the DSM decreased dramatically. With an increase in the width of the foundation, the seismic bearing and settlement increased and decreased, respectively. The increase in the depth of the foundation at the distance of 0.5 m from the DSM had a positive effect on the EPWP. With the growth of the embedded depth of shallow foundation, the seismic bearing capacity and settlement increased and decreased, respectively. The increase in the thickness of the foundation reduced the EPWP. As the distance from the DSM increased, the effect of the foundation thickness diminished 272

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