Prediction of liquefaction potential and pore water pressure beneath machine foundations

Transcription

1 Cent. Eur. J. Eng. 4(3) DOI: /s y Central European Journal of Engineering Prediction of liquefaction potential and pore water pressure beneath machine foundations Research Article Mohammed Y. Fattah 1, Mohammed A. Al-Neami 2, Nora H. Jajjawi 3 1 Professor, Building and Construction Engineering Department University of Technology, Baghdad, Iraq. 2 Assistant Professor, Building and Construction Engineering Department University of Technology, Baghdad, Iraq. 3 Assistant Lecturer, Building and Construction Engineering Department University of Technology. Received 20 March 2013; accepted 22 March 2014 Abstract: The present research is concerned with predicting liquefaction potential and pore water pressure under the dynamic loading on fully saturated sandy soil using the finite element method by QUAKE/W computer program. As a case study, machine foundations on fully saturated sandy soil in different cases of soil densification (loose, medium and dense sand) are analyzed. Harmonic loading is used in a parametric study to investigate the effect of several parameters including: the amplitude frequency of the dynamic load. The equivalent linear elastic model is adopted to model the soil behaviour and eight node isoparametric elements are used to model the soil. Emphasis was made on zones at which liquefaction takes place, the pore water pressure and vertical displacements develop during liquefaction. The results showed that liquefaction and deformation develop fast with the increase of loading amplitude and frequency. Liquefaction zones increase with the increase of load frequency and amplitude. Tracing the propagation of liquefaction zones, one can notice that, liquefaction occurs first near the loading end and then develops faraway. The soil overburden pressure affects the soil liquefaction resistance at large depths. The liquefaction resistance and time for initial liquefaction increase with increasing depths. When the frequency changes from 5 to 10 rad/sec. (approximately from static to dynamic), the response in displacement and pore water pressure is very pronounced. This can be attributed to inertia effects. Further increase of frequency leads to smaller effect on displacement and pore water pressure. When the frequency is low; 5, 10 and 25 rad/sec., the oscillation of the displacement ends within the period of load application 60 sec., while when ω = 50 rad/sec., oscillation continues after this period. Keywords: Dynamic finite elements sand liquefaction machine foundation Versita sp. z o.o. 1. Introduction myf_1968@yahoo.com. Soil liquefaction is a major cause of damage during earthquakes. "Modern" engineering treatment of liquefaction related issues evolved initially in the wake of the two devastating earthquakes of the 1964 and 2011 Japan. 226

2 M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi Over the nearly four decades that have followed, a significant progress has occurred. Initially, this progress was largely confined to improve the ability to assess the likelihood of initiation of liquefaction in clean, sandy soils. Additional potential problems associated with both silty and gravelly soils, and the important additional issues of post-liquefaction strength and stress deformation behaviour also began to attract increased attention [1]. 2. Liquefaction Mechanisms Liquefaction has been used to define two mainly related but different soil behaviours during earthquakes, namely flow liquefaction and cyclic softening. Since both phenomena can have quite similar consequences, it is difficult to distinguish between them. However, the mechanisms behind them are rather different. Flow liquefaction is a phenomenon in which the equilibrium is destroyed by static or dynamic loads in a soil deposit with low strength, which is defined as the strength of soils under large strain levels (critical state). Static loading, for example, can be applied by new buildings on a slope that exert additional forces on the soil beneath the foundations. Earthquakes, blasting, and pile driving are all examples of dynamic loads that could trigger flow liquefaction. Once triggered, the strength of a soil susceptible to flow liquefaction is no longer sufficient to withstand the static stresses that were acting on the soil before the disturbance. Failures caused by flow liquefaction are often characterized by large and rapid movements which can lead to disastrous consequences [2]. Cyclic softening is another phenomenon, triggered by cyclic loading, occurring in soil deposits with static shear stresses lower than the soil strength. Deformations due to cyclic softening develop incrementally because of static and dynamic stresses that exist during an earthquake. Two main engineering terms can be used to define the cyclic softening phenomenon, as follows [2]: cyclic liquefaction requires undrained cyclic loading during which shear stresses reversals occur or zero shear stress can develop; i.e. occurs when in-situ static shear stresses are low compared to cyclic shear stresses. At the point of zero effective stress, no shear stress exists. When shear stress is applied, pore water pressure drops as the material tends to dilate, but a very soft initial stress strain response can develop resulting in large deformations. Deformations during cyclic loading can accumulate to large values, but generally stabilize when cyclic loading stops. The first step in engineering assessment of the potential for initiation of soil liquefaction is the determination of whether or not soils of "potentially liquefiable nature" are present at a site. This, in turn, raises the important question regarding which types of soils are potentially vulnerable to soil liquefaction. It has long been recognized that relatively "clean" sandy soils, with few fines, are potentially vulnerable to the seismically induced liquefaction. There has, however, been significant controversy and confusion regarding the liquefaction potential of silty soils (and silty/clayey soils), and also of coarser, gravelly soils [1]. The most widely criteria used for defining potentially liquefiable soil is "Modified Chinese Criteria" [3]. According to these criteria, fine (cohesive) soils that plot above the A-line (in plasticity chart) are considered to be of potentially liquefiable type and character if: 1. There are less than 15% "clay" fines (based on the Chinese definition of "clay" sizes as less than mm), 2. A liquid limit (LL) 35%, and 3. In-situ water content greater than or equal to 90% of the liquid limit. Sitharam et al. (2004) studied methods of determining the dynamic properties as well as potential for liquefaction of soils [4]. Parameters affecting the dynamic properties and liquefaction have been brought out. A simple procedure of obtaining the dynamic properties of layered ground has been highlighted. Results of a series of cyclic triaxial tests on liquefiable sands collected from the sites close to the Sabarmati river belt have been presented. Simple method was used to obtain the equivalent modulus of layered system. Cyclic strain-controlled triaxial tests to evaluate the dynamic properties and liquefaction potential of sands have been carried out. It has been brought out that the material immediately beneath the foundation plays a dominant role in controlling the dynamic response. Material at a depth greater than twice the width of the foundation plays an insignificant role. A major reduction in the shear modulus and a corresponding increase in the damping of sand occur in the large shear strain range. As the initial densities of sand increase, the shear modulus shows clearly an increasing trend. However, more or less the same values of shear modulus occur beyond 0.5% shear strain level irrespective of their initial density. As a result of application of cyclic loads on the soils, pore water pressure builds up steadily and reaches initially applied confining pressure depending on the magnitude of cyclic shear strain as well as the density of the soil. At higher cyclic shear strain amplitudes, the pore water pressure builds up fast and there is triggering of liquefaction at lower cycles. Jin et al. (2008) tested samples of saturated loose sand under bi-directional cyclic loading to characterize liquefaction and cyclic failure, by using an advanced soil static and dynamic universal triaxial 227

3 Prediction of liquefaction potential and pore water pressure beneath machine foundations and torsional shear apparatus [5]. Tests were performed with two cyclic components involving the horizontal shear stress (torsional shear stress) and the vertical shear stress (stress difference between vertical normal stress and horizontal normal stress) to provide an approximate presentation of wave or seismic loading conditions. Samples were consolidated under various initial static horizontal shear stresses and subsequently subjected to a specified level of dynamic loading. Three stress levels of dynamic load were concerned. Results showed that the developed pore water pressure decreases linearly as initial static horizontal shear stress increases and decreases exponentially as consolidation stress ratio increases. Worthen (2009) carried out a study on the characterization of the liquefaction potential of fine-grained soils, based on plasticity characteristics using the Chinese criteria [6]. Recent research showed that such criteria are ineffective. In addition, the current liquefaction models do not account for the confining pressure of in-situ soil or the strength of the earthquake. The study used the critical state soil mechanics framework, which emphasizes that the shear strength and deformation behaviour of soil depends on changes in volume and confining stress. Lu et al. (2010) investigated the responses of saturated sand under horizontal vibration loading induced by a bucket foundation [7]. The saturated sand liquefies gradually since the vibration loading is applied on. The maximum displacement on the surface of sand layer occurs near the loading end and in this zone; the sand is compressed and moves upwards. The liquefaction zone was developed from the upper part near the loading side and stopped gradually under the vibrating loading on one side of the saturated sand; liquefaction occurs first near the loading end and then develops faraway. The deformation becomes up-heave near the loading end and degrades faraway gradually. It was found that the liquefaction and the deformation develop fast with the increase of the loading amplitude and the frequency and the decrease of the modulus. The liquefaction may occur under vibration loading on the side from the foundation side to a finite distance. It needs to be considered in the design of platform. However, the generation of pore water pressure will reduce the effective stresses and, therefore the deformation will increase. In cases near the surface, this is even more critical as the effective stresses can be reduced to almost zero and, therefore, increasing deformations. Fattah and Nsaif (2010) carried out coupled dynamic analysis on zoned earthdam subjected to earthquake excitation in which displacements and pore water pressure are calculated [8]. The finite element method is used. Al-Adhaim dam which is an earthdam is analyzed as a case study. A parametric study was carried out to investigate the effect of some parameters on the general response of the dam to earthquakes, and emphasis was made on zones at which liquefaction takes place. It was found that as the maximum horizontal component of the input acceleration increases, liquefaction zones within the dam and its foundation become larger. The maximum stresses and pore water pressure occur at a time after the earthquake shock and not on or in the vicinity of the time of the peak ground acceleration as was concluded by conventional dynamic stress analyses. Vivek and Ghosh (2012) studied dynamic interaction of two closely spaced embedded strip foundations under the action of machine vibration [9]. One of the footings was excited with a known vibration source placed on the top of the footing, called the active footing. The objective was to study the effect of dynamic excitation of active footing on the nearby passive footing through a homogeneous c-φ soil medium. The analysis was performed numerically by using finite element software, PLAXIS 2D. The soil profile was assumed to obey the Mohr-Coulomb yield criteria. The analysis was performed under two different loading conditions; sinusoidal dynamic loading with constant amplitude and varying amplitude. Under the dynamic excitation, the settlement behavior of interacting footings is studied by varying the spacing between the footings. In addition, the variation of normal and shear stress developed below the passive footing was also explored. The response of the adjoining passive structure was found to be significant up to a spacing of 2B (B is foundation width) from the actual excited structure. It was concluded from previous studies on liquefaction that most of them concentrated on earthquake induced liquefaction and that little studies talked about liquefaction caused by machine vibrations. Some equipment or heavy machines used during construction particularly on saturated sandy soil might cause some vibration and consequently, a loose soil may be susceptible to liquefaction. 3. Description of the Problem A saturated porous foundation soil 30 m wide and 20 m deep is modelled by a finite element analysis. A 2 m wide footing is placed at the middle of the top surface. The foundation will be subjected to dynamic load of harmonic excitation described by the following equation: Where: a o is the load amplitude ω is the load frequency, and t is the time F(t) = a o sin(ω, t) (1) 228

4 M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi Figure 1. Typical finite element mesh. Figure 2. Shear modulus reduction function (Seed and Idriss, 1970) [16]. The duration of this dynamic load is 60 sec. with a time step t = 0.1 sec. In order to study the pore water pressure changes under such loading condition, the soil is assumed to be saturated; i.e. the water table level coincides with the ground surface. The properties of the sand are summarized in Table 1. The plane strain problem is analyzed using the QUAKE / W (2004) program which is a geotechnical finite element software product used for the dynamic analysis of earth structures subjected to earthquake shaking and other sudden impact loading. QUAKE/W is part of GeoStudio and is, consequently, the integration of QUAKE/W and other products within GeoStudio greatly expands the type and range of problems that can be analyzed beyond what can be done with other geotechnical dynamic analysis software. It is formulated for two- dimensional plane strain problems. The finite element mesh used for the analysis is shown in Figure 1. The mesh consists of 8 noded quadrilateral isoparametric elements. The side boundaries are allowed to move vertically only while the bottom boundary is restricted horizontally and vertically. The top surface is free draining while the other boundaries are impermeable. Equivalent linear elastic model is used in the analysis. The time of the analysis is taken as 100 sec with t = 0.1 sec. The analysis is repeated for three types of soils; loose, medium and dense sand. The results are presented at selected points A, B, C, D and E at different depths below the foundation in order to study the depth of soil affected by the dynamic load. The relationships used for the equivalent linear elastic model include the shear modulus reduction function of Figure 2, the relationship between the cyclic number ratio and pore pressure ratio of Figure 3 and the cyclic deviator stress with number of cycles as given in Figure 4. Figure 3. Cyclic number ratio N/NL versus pore pressure ratio ru (Seed and Booker, 1977) [17]. 4. Effect of load frequency The harmonic load is applied at the surface as shown in Figure 1. The load is changed to different values by considering different values of frequency; 5, 10, 25 and 50 rad/sec. with damping ratio equals 0.05 and the load amplitude equals 10 kn. The results are presented in figures which include; vertical displacement, pore water pressure, surface displacement and liquefaction zones, for loose, medium and dense sandy soils: Vertical displacement and pore water pressure are presented at three points A, B and C located at depths 1, 5 and 10 m, respectively. Surface displacement is drawn at different times 40, 50, 55 and 60 sec. The liquefaction zones are inspected at time 10 sec. Figures 5 to 8 show the results for loose sand with amplitude of harmonic load (a o = 10 kn) at different values 229

5 Prediction of liquefaction potential and pore water pressure beneath machine foundations Figure 4. Cyclic test results on Sacramento River Sand (Kramer, 1996) [18]. of load frequency (ω = 5, 10, 25 and 50 rad/sec.), while Figures 9 to 12 show the results for medium sand. Figures 13 to 16 show the results for dense sand with the same amplitude of harmonic load and values of load frequency. For loose sand, it can be noticed in Figures 5 to 8 that when the frequency of dynamic load increases from (ω = 5 to 10 rad/sec.), the maximum vertical displacements at points A, B and C in the foundation soil increases by about 2101, 1393 and 1243 %, respectively. This result is in agreement with the results obtained by Lu et al. (2010) [7] who stated that the development of displacement becomes large with the increase of loading frequency. On the other hand, the increase in the frequency from ω = 5 to 10 rad/sec. leads to increase in the maximum pore water pressure at points A, B and C depending on the amplitude of load (103, 23 and 10%), respectively. When the frequency is further increased to 25 or 50 rad/sec., the pore water pressure is approximately unchanged, because that liquefaction takes place at all points under such frequencies. The pore pressure in the saturated sand increases gradually and the strength of sandy layer decreases gradually. At last, liquefaction occurs. These results are consistent with the conclusion of Seed et al. (1976) [10] who stated that during the period of earthquake shaking (or dynamic load application), there would be no significant dissipation or redistribution of pore water pressure in the soil mass. When the frequency is low; 5, 10 and 25 rad/sec., the oscillation of the displacement ends within the period of load application 60 sec., while when ω = 50 rad/sec., oscillation continues after this period. When the frequency is low; ω = 5 rad/sec., liquefaction is not taking place at points A, B and C, while when the frequency increases to 10 rad/sec. liquefaction occurs at points A and B at a short time 10 sec. and the pore water pressure continues to increase at point C. When the frequency ω = 25 and 50 rad/sec., liquefaction occurs at points A, B and C at time 10 sec. This means that liquefaction may propagate to a point at a depth of about five times the foundation width. This conclusion overrides the conclusion of Sitharam et al. (2004) [4] who stated that material at a depth greater than twice the width of the foundation plays an insignificant role. For medium sand, from Figures 9 to 12, it can be noticed that when the frequency of dynamic load increases from ω =5to10 rad/sec., the maximum vertical displacement at points A, B and C in the foundation soil increases by about 1433, 1139 and 1065 %, respectively. Further increase in the frequency to 25 and 50 rad/sec. causes increase in the maximum displacement at points A, B and C, the increase is about 36, 67 and 83 %, respectively. On the other hand, the increase in the frequency from? = 5 to 10 rad/sec. leads to increase in the maximum pore water pressure at points A and B depending on the amplitude of load; 95 and 30 %, respectively, while at point C the pore water pressure is approximately unchanged. When the frequency is further increased to 25 rad/sec., the pore water pressure is approximately unchanged, but when the frequency reached to the 50 rad/sec, the pore water pressure is slightly increased at points B and C while still constant at point A. When the frequency is low; ω = 5 rad/sec., liquefaction is not taking place at any point, while when the frequency increases to 10 rad/sec. liquefaction occurs at point A only in a short time 10 sec. and the pore water pressure continues to increase at point B slightly. When the frequency becomes 25 rad/sec., liquefaction still occurs at point A at 10 sec. and point B at time 50 sec. This means that the increase of load frequency increases the liquefaction potential and causes liquefaction at shorter times. When the frequency ω = 50 rad/sec., liquefaction occurs at points A, B at time 10 sec., liquefaction is not taking place at point C. For dense sand, Figures 13 to 16, reveal that, when the frequency of dynamic load increases from ω = 5 to 10 rad/sec., the maximum vertical displacement at points A, B and C in the foundation soil increases by about 1209, 1005 and 949 %, respectively. Further increase in the frequency to 25 and 50 rad/sec. causes increase in the maximum displacement at points A, B and C, the increase is about 15, 24 and 32 %, respectively. On the other hand, the increase in the frequency from ω = 5 to 10 rad/sec. leads to increase in the maximum pore water pressure at point A depending on the amplitude of load 95%, while the pore water pressure at points B and C is approximately unchanged. When the frequency is further increased to 25 or 50 rad/sec., the pore water pressures at points A, B and C are approximately unchanged. This conclusion agrees well with Lu et al. (2004), who stated that the rate of the liquefaction increases with the increase of the initial void ratio (or decrease of density) or amplitude and frequency of loading, 230

6 M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi Figure 5. Dynamic response of the foundation to harmonic load, a o = 10 kn, ω = 5 rad/sec., constructed over loose sand. and increases with decrease of the modulus [7]. The pore pressure increases slowly at the beginning and then increases fast up to the maximum which is equal to the sum of the initial pore pressure and the initial effective stress (after liquefaction, the fluctuating pore pressure caused by the loading is not considered). The increase rates of the pore pressure become faster and faster with increase of the loading amplitude. Also, at all values of frequency, liquefaction is not taking place at any elective points except point A, liquefaction occurs at frequency equals to 10, 25 and 50 rad/ sec. in a short time 10 sec. Similar results were found by Kumar (2008) who concluded that the dense sand has greater resistance for liquefaction [11]. It would require higher deviator cyclic stress amplitude or more 231

7 Prediction of liquefaction potential and pore water pressure beneath machine foundations Figure 6. Dynamic response of the foundation to harmonic load, a o = 10 kn, ω = 10 rad/sec., constructed over loose sand. number of cycles of deviator cyclic stress to cause initial liquefaction as compared to same soil in loose state. The deformation development becomes large with the increase of loading frequency; the deformation becomes larger and larger with time. The increase in velocity of the excess pore pressure is faster; this means that the duration developing to liquefaction is shorter. For very loose soils, as initial cyclic pore pressure induced softening leads to monotonic accumulation of shear deformations, and these, in turn, lead to further pore pressure increases. For very dense soils, the presence of non-zero initial static driving shear stresses can lead to reduction in the rate of generation of pore pressures during cyclic loading. As each cycle of loading produces an incremental increase in pore pressure, and some resultant reduction in strength and stiffness, the driving shear stresses then act to pro- 232

8 M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi Figure 7. Dynamic response of the foundation to harmonic load, a o = 10 kn, ω = 25 rad/sec., constructed over loose sand. duce shear deformations that cause dilation of the soil, in turn reducing pore pressures [1]. To simplify comparison between the results for three states of sandy soil (loose, medium and dense). It is noticed that when the frequency changes from 5 to 10 rad/sec. (approximately from static to dynamic), the response in displacement and pore water pressure is very pronounced. This can be attributed to inertia effects. Further increase of frequency leads to smaller effect on displacement and pore water pressure. 5. Effect of load amplitude The effect of load amplitude is studied by aplying the harmonic load on the foundation,. Three values of load amplitude; 20, 40 and 60 kn (where a o =10 kn is stud- 233

9 Prediction of liquefaction potential and pore water pressure beneath machine foundations Figure 8. Dynamic response of the foundation to harmonic load, a o = 10 kn, ω = 50 rad/sec., constructed over loose sand. ied in the previous section) with load frequency equals 5 rad/sec. Figures 17 to 19 show the results for medium sand with frequency of harmonic load ω = 5 rad/sec at different values of load amplitude; ao = 20, 40, 60 kn, while Figures 20 to 22 show the results for dense sand with the same frequency of harmonic load and values of load amplitude. For loose sand, it was found that when the amplitude of dynamic load increases from a o = 20 to 40 kn, the maximum vertical displacement at points A, B and C in the foundation soil increases by about 288, 248 and 212 %, respectively. Further increase in the amplitude to 40 and 60 kn causes increase in the maximum displacement at points A, B and C, the increase is about 107, 125 and 116 %, respectively. No change in the maximum pore water pressure at points A, B and C is recorded with the in- 234

10 M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi Figure 9. Dynamic response of the foundation to harmonic load, a o = 10 kn, ω = 5 rad/sec., constructed over medium sand. crease in the amplitude, because liquefaction takes place at all points under such amplitudes and the pores between the soil grains are filled with water which cannot drain sufficiently, to generate excess pore pressure. When the amplitude of dynamic load increases from a o = 20 to 40 and 60 kn, the time required for liquefaction to take place becomes 10 sec. at points A, B and C. These results are compatible with those of Sitharam et al. (2004) [4] who stated that at higher cyclic shear strain amplitudes, the pore water pressure builds up fast and there is trigging of liquefaction at lower cycles. For medium sand, Figures 17 to 19 reveal that when the amplitude of dynamic 235

11 Prediction of liquefaction potential and pore water pressure beneath machine foundations Figure 10. Dynamic response of the foundation to harmonic load, a o = 10 kn, ω = 10 rad/sec., constructed over medium sand. load increases from a o = 20 to 40 kn, the maximum vertical displacement at points A, B and C in the foundation soil increases by about 248, 185 and 150 %, respectively. Further increase in the amplitude to 40 and 60 kn causes increase in the maximum displacement at points A, B and C, the increase is about 90, 70 and 58 %, respectively. Due to the increase in the amplitude from a o = 20 to 40 kn, the maximum pore water pressure is unchanged at points A and B, at time 10 sec., while at amplitude equals 20 kn, the pore water pressure at point C causes smaller increase, because the pore water pressure at this deep point is still in the development stage compared to point B which is located at shallower depth, and when a o = 40 kn, no significant change occurs at this point. When the amplitude is further increased 40 to 60 kn, the pore water pressure is approximately unchanged at points A, B and 236

12 M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi Figure 11. Dynamic response of the foundation to harmonic load, a o = 10 kn, ω = 25 rad/sec., constructed over medium sand. C because that liquefaction takes place under such amplitude. When the amplitude of dynamic load is a o = 20 kn, the time required for liquefaction to take place is 10 sec. at points A and B, while at point C, the increase in the pore water pressure continues to time 61 sec. When the amplitude of dynamic load is a o = 40 and 60 kn, the time required for liquefaction to take place is 10 sec. at points A, B and C. For dense sand, from Figures 20 to 22, it can be concluded that, when the amplitude of dynamic load increases from a o = 20 to 40 kn, the maximum vertical displacement at points A, B and C in the foundation soil increases by about 223, 156 and 132 %, respectively. Further increase in the amplitude to 40 and 60 kn causes increase in the maximum displacement at points A, B and C by about 80, 55 and 46 %, respectively. On the other hand, upon the increase in the amplitude from a o =

13 Prediction of liquefaction potential and pore water pressure beneath machine foundations Figure 12. Dynamic response of the foundation to harmonic load, a o = 10 kn, ω = 50 rad/sec., constructed over medium sand. to 40 kn, the maximum pore water pressure is unchanged at points A and C, while at point B, the increase in the amplitude leads to increase in the maximum pore water pressure depending on the amplitude of load. When the amplitude is further increased to 40 to 60 kn, the pore water pressure at points A and C is approximately unchanged, while at point B, the pore water pressure is decreased by 5%. This may be attributed to cyclic mobility which tends to stabilize the pore water pressure after liquefaction occurrence. When the amplitude is a o = 20 kn, liquefaction takes place only at point A, while when the amplitude increases to 40 and 60 kn, liquefaction occurs at points A and B in a short time 10 sec., while liquefaction is not taking place at point C, because the pore 238

14 M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi Figure 13. Dynamic response of the foundation to harmonic load, a o = 10 kn, ω = 5 rad/sec., constructed over dense sand. water pressure continues to decrease at point C till time 100 sec. In dense sand, the soil tends to dilate at failure resulting in negative pore water pressure therefore, the pore water pressure decreases as shown in Figure 22. With the increase of the sand density, the affected area and the settlement are decreased. This may be explained by the fact that, the strength of sandy layer increases with the increase of the density. This means that the ratio of the loading amplitude to the sandy layer strength decreases, therefore, the affected area decreases. When the density increases to some value, the response caused by the applied loading is elastic; therefore, the affected 239

15 Prediction of liquefaction potential and pore water pressure beneath machine foundations Figure 14. Dynamic response of the foundation to harmonic load, a o = 10 kn, ω = 10 rad/sec., constructed over dense sand. Table 1. Properties of the sandy soil used in the parametric study. Material Properties Loose sand Medium sand Dense sand Modulus of elasticity, E (kn/m 2 ) Poisson s ratio, υ Unit weight γt, (kn/m 3 ) area does not occur. This is compatible with the findings of Kumar (2008) [11] who found that the dense sand has greater resistance for liquefaction. It would require higher deviator cyclic stress amplitude or more number of cycles of deviator cyclic stress to cause initial liquefaction as compared to same soil in loose state. When the loading amplitude was small enough, there is no obvious response, 240

16 M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi Figure 15. Dynamic response of the foundation to harmonic load, a o = 10 kn, ω = 25 rad/sec., constructed over dense sand. with the increase of loading amplitude, even if no liquefaction occurred, the sandy layer surrounding the foundation settled gradually. There is no liquefaction occurring when the amplitude is smaller than a critical value [12]. Fattah et al. (2013) showed that liquefaction occurs faster at shallow depths due to low overburden pressure [13]. Also, liquefaction zones and deformation occur faster with the increase of dynamic loading amplitude. The analysis marked that increasing the amplitude pressure accelerates the occurrence of initial liquefaction and increases the pore water pressure. Based on the results obtained, it can be concluded that: " During loading, the pore pressure increases at the first stage and then decreases gradually. The reason is that, at the first stage the sand layer intents to contract, but the water is difficult to drain, the 241

17 Prediction of liquefaction potential and pore water pressure beneath machine foundations Figure 16. Dynamic response of the foundation to harmonic load, a o = 10 kn, ω = 50 rad/sec., constructed over dense sand. strength of the sand decreases, so the sand begins to compress and the pore pressure decreases gradually. The soil overburden pressure affects the soil liquefaction resistance at large depths. The liquefaction resistance and time for initial liquefaction increase with increasing depths. At large amplitude of dynamic load, liquefaction can occur at virtually any depth. Liquefaction occurs faster at shallow depths for all ranges of frequency and amplitude. This finding does not comply with that of (Amini and Duan, 2002) [14] who, during his numerical study on the liquefaction resistance of soil at high confining pressure, found that at a lower frequency, liquefaction occurs faster at large depths. 242

18 M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi Figure 17. Dynamic response of the foundation to harmonic load, a o = 20 kn, ω = 5 rad/sec., constructed over medium sand. Liquefaction zones increase with the increase of load frequency and amplitude. Tracing the propagation of liquefaction zones, it is noticed that, liquefaction occurs first near the loading end and then develops far away as was concluded by (Lu et al., 2010) [7]. The liquefaction and deformation develop fast when the loading amplitude and frequency increase. The liquefaction zone develops from the upper part near the loading side and stops gradually under the vibrating loading on one side of the saturated sand; liquefaction occurs first near the loading end and then develops faraway. The deformation becomes up-heave near the loading end and degrades far- 243

19 Prediction of liquefaction potential and pore water pressure beneath machine foundations Figure 18. Dynamic response of the foundation to harmonic load, a o = 40 kn, ω = 5 rad/sec., constructed over medium sand. away gradually. The maximum displacement on the surface of sandy layer occurs near loading end, after this point the soil is compressed and surface displacement is begin to decrease till reaching zero with increasing distance away from the end of vibration loading. For this reason it is important to take the effect of vibration on a finite distance from the side of reason of disturbance in foundation design. Maximum displacement increases with decrease the 244

20 M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi Figure 19. Dynamic response of the foundation to harmonic load, a o = 60 kn, ω = 5 rad/sec., constructed over medium sand. modulus of elasticity (the soil changes from dense to loose sand) this conclusion is compatible with the finding of Lu et al. (2010) [7], who found that the sand surface near the loading side becomes up-heave first and then develops to faraway, the deformation degrades from the loading side to far away and the deformation became larger when the modulus of elasticity of sandy layer is smaller The smaller the modulus is, the faster the development of the liquefaction zone is. 6. Conclusions As a result of the finite elements analysis carried out in this study and discussion presented, the following conclu- 245

21 Prediction of liquefaction potential and pore water pressure beneath machine foundations Figure 20. Dynamic response of the foundation to harmonic load, a o = 20 kn, ω = 5 rad/sec., constructed over dense sand. sions could be made: 1. At large amplitude of dynamic force, liquefaction can occur at virtually any depth, but liquefaction occurs faster at shallow depths for all cases of frequency and amplitude. Liquefaction mostly occurs within the top 10 m below the ground surface, although, it can occur up to about 20 m deep. 2. Liquefaction and deformation occur faster with the increase of loading amplitude and frequency, when the foundation is constructed over loose saturated sand. The time of initial liquefaction decreases as the frequency of dynamic load increases. 3. For loose sand, no change in pore water pressure due to increase in the load amplitude take place after the initial liquefaction has occurred but 246

22 M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi Figure 21. Dynamic response of the foundation to harmonic load, a o = 40 kn, ω = 5 rad/sec., constructed over dense sand. when the sand density increases, limited increase or (sometimes a slight decrees) occurred in pore water pressure as a result of increasing of load amplitude. 4. The soil overburden pressure affects the soil liquefaction resistance at large depths. Liquefaction resistance and time for initial liquefaction increase with increasing depth. Liquefaction may propagate to a point at depth of about five times the foundation width. 5. Liquefaction zones increase with the increase of load frequency and amplitude. Tracing the propagation of liquefaction zones, one can notice that liquefaction occurs first near the loading end and 247

23 Prediction of liquefaction potential and pore water pressure beneath machine foundations Figure 22. Dynamic response of the foundation to harmonic load, a o = 60 kn, ω = 5 rad/sec., constructed over dense sand. then develops faraway. 6. When the frequency changes from 5 to 10 rad/sec. (approximately from static to dynamic), the response in displacement and pore water pressure is very pronounced. This can be attributed to inertia effects. Further increase of frequency leads to smaller effect on displacement and pore water pressure. When the frequency is low; 5, 10 and 25 rad/sec., the oscillation of the displacement ends within the period of load application 60 sec., while when ω = 50 rad/sec., oscillation continues after this period. 7. The deformation development becomes large with the increase of loading frequency; the deformation becomes larger and larger with time. The increase in velocity of the excess pore pressure is faster; this 248

24 M.Y. Fattah, M.A. Al-Neami, N.H. Jajjawi means that the duration developing to liquefaction is shorter. For very loose soils, as initial cyclic pore pressure induced softening leads to monotonic accumulation of shear deformations, and these, in turn, lead to further pore pressure increases. References [1] Seed H. B., Cetin K.O., Moss R.E.S., Kammerer A.M., et al. Recent Advances in Soil Liquefaction Engineering, A Unified and Consistent Framework, 26th Annual ASCE, Los Angeles Geotechnical Spring Seminar, Keynote Presentation, H.M.S. Queen Mary, 2003 [2] Youd T.L., and Idriss I.M., Liquefaction Resistance of Soils, Report from the NCEER, National Center for Earthquake Engineering, Workshops on Evaluation of Liquefaction Resistance of Soils", Journal of Geotechnical and Geo-environmental Engineering, ASCE, April 2001, pp [3] Wang W., Some Findings in Soil Liquefaction, Research Report, Water Conservancy, and Hydroelectric Power Scientific Research Institute, Beijing, August 1979 [4] Sitharam T.G., Govinda Raju L. and Sridharan A., Dynamic Properties and Liquefaction Potential of Soils, Journal of Current Science, Vol. 87, No. 10, 25, November 2004 [5] Jin D., Luan M., Li C., Liquefaction and Cyclic Loading, EJGE, Vol.13, Bund, G [6] Worthen D., Critical State Framework and Liquefaction of Fine-Grained Soils, M.Sc. Thesis, Department of Civil and Environmental Engineering, University of Washington State, 2009 [7] Lu X., Zhang X. and Shi Z., Responses of Saturated Sand Surrounding a bucket Foundation under Horizontal Vibration Loading, The Open Ocean Engineering Journal, Vol. 3, 2010, pp [8] Fattah M.Y., Nsaif M. H., Propagation of Liquefaction Zones Due to Earthquake Excitation in a Zoned Earthdam, the 2nd Regional Conference for Engineering Sciences. /College. of Eng. / Al-Nahrain University /1-2/12/2010, 2010, pp [9] Vivek P., and Gosh P., Dynamic Interaction of Two nearby Machine Foundation on Homogeneous Soil", GeoCongress 2012, ASCE, 2012, pp [10] Seed H.B., Martin P.P. and Lysmer J., Pore-Water Pressure Changes during Soil Liquefaction", Journal of the Geo-technical Engineering Division, ASCE, GT4, 1976, pp [11] Kumar K., Basic Geotechnical Earthquake Engineering, New Age International, 2008 [12] Wang Y., Lu X., Wang S. and Shi Z., The Response of Bucket Foundation under Horizontal Dynamic Loading, The Open Ocean Engineering Journal, Vol.33, 2006, pp [13] Fattah M.Y., Al-Neami M. A., Jajjawi N. H., Implementation of Finite Element Method for Prediction of Soil Liquefaction around Underground Structure, Engineering and Technology Journal, University of Technology, Vol. 31, No. 4, 2013, pp [14] Amini F., Duan Z., Centrifuge and Numerical Modeling of Soil Liquefaction at Very large Depths, 15th ASCE Engineering Mechanics Conference, Columbia University New York, NY, [15] Manual of Dynamic Modeling with QUAKE/W, 2007 (2009). An Engineering Methodology, 4th Edition, Geo-Slope International, Ltd. [16] Seed H.B., Idress I.M., Soil Moduli and Damping Factors for Dynamic Analysis, EERC Report No , University of California, 1970 [17] Seed H.B., and Booker J.R., Stabilization of Potentially Liquefiable Sand Deposits Using Giravel Drains, Journal of Geotechnical Engineering Division, ASCE, Vol. 103, No., GT7, 1977, pp [18] Kramer S.L., Geotechnical Earthquake Engineering, Prentice Hall,