**4. Numerical results and discussion**

A series of 1g shaking table tests have been executed in order to verify the obtained numerical results. It is attempt to create almost similar conditions between laboratory model test and numerical model. The liquefiable soil is modeled by loose sand and non-liquefiable soil is modeled by very dense sand. The seismic excitation is shown in Figure 8. The numerical results are presented and compared to those of corresponding shaking table test. Figure 9(a) shows the permanent deformation pattern of the numerical model after dynamic excitation. The nodal displacement vectors are presented in Figure 9(b). As may be expected, more ground surface settlement is observed in the backfill near the wall than at far field. A rigid body rotation of the wall (tilt) to the seaward direction is also clearly seen. The deformation pattern of model test at the end of seismic loading is presented in Figure 10. The trend of deformation behind quay wall and movement of the wall are in fairly good agreement with numerical results. Comparisons between the calculated and measured results (Calculated: numerical and

> **0 5 10 15 20 TIME (s)**

(a) (b)

**Figure 9.** Computed post-earthquake (a) deformed shape, (b) nodal displacement vectors for the quay wal after the

Measured: experimental results) are made in Figure 11.

270 Engineering Seismology, Geotechnical and Structural Earthquake Engineering

**-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25**

**Figure 10.** Measured post-earthquake deformed shape after the seismic loading

**ACCELERATION (cm/s**

**Figure 8.** Input base excitation

seismic loading

**2**

**)**

Results of nonlinear effective-stress dynamic analyses are presented in this section to investi‐ gate the effects of soil properties and input excitation characteristics on liquefaction potential, deformation of quay wall and failure mechanisms of soil-wall system during seismic loading. For gravity quay walls on firm foundations, typical failure modes during earthquakes are seaward displacements and tilting. Therefore, the horizontal displacement of quay wall head is selected as a key parameter to judge about the stability of quay wall.

### **4.1. Influence of relative density of backfill soil**

Three additional sets of soil properties with different relative densities are selected for backfill material (Dr = 15%, 25% and 40%). Figure 12(a) depicts the computed lateral displacement of the quay wall's head. The horizontal deformation for all relative densities is greater than allowable value proposed by PIANC (2001) and the quay wall system goes toward failure. After the earthquake, the system reaches to equilibrium. The final permanent deformations and rate of increase for Dr=15% is much more than the others. Figure 12(b) shows cumulative vertical displacement (settlement) of the quay wall's head for the various backfill soil relative densities. As expected, the higher the relative density, the less the accumulated vertical permanent deformation. Figure 12(c) shows the excess pore water pressure ratio at far field in depth of 13 m for three different materials. It is clearly seen that the free field backfill is quickly liquefied. Figure 12(d) depicts the excess pore water pressure ratio time histories for various backfill soil relative densities behind the quay wall in depth of 13 m. It is found that the liquefaction does not occur in backfill soil behind the quay wall. This can be attributed to the movement of quay wall due to seismic loading which directly influences the pore pressure build up.

*Dr=15%*

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*Dr=25%*

*Dr=40%*

**0 5 10 15 20 Time (second)**

**02468 Time (second)**

**G=20 MPa G=35 MPa G=50 MPa**

**Figure 13.** Deformed shape of the quay wall system for various relative densities of backfill soil

allowable limits which have been mentioned in PIANC (2001).

**0 5 10 15 20 Time (second)**

**0 2 4 6 8 10 Time (second)**

Three different shear modulus values are adopted (G=20, 35 and 50 MPa) to investigate the effect of shear stiffness of the backfill soil. The other parameters are the same for all the analyses. Figures 14(a) and (b) show the permanent horizontal and vertical displacements time histories of the quay wall's head during seismic loading. It is observed that quay wall has significant movement toward the seaside. Both horizontal and vertical deformations are greater than the

(a) (b)

**ru**

**G=20 MPa G=35 MPa G=50 MPa** **0**

**0.5**

**Vertical Displacement (m)**

**1**

**1.5**

**G=20 MPa G=35 MPa G=50 MPa**

(c) (d)

**Figure 14.** Computed values of: (a) horizontal deformation, and (b) vertical deformation of quay wall's head, and (c) excess pore water pressure ratio at far field, and (d) excess pore water pressure ratio behind the quay wall for various

**0.4 0.5 0.6 0.7 0.8 0.9 1 1.1**

**4.2. Influence of shear stiffness of backfill soil**

**G=20 MPa G=35 MPa G=50 MPa**

**0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5**

**0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1**

**ru**

shear moduli of backfill soil

**Horizontal Displacement (m)**

**Figure 12.** Computed values of: (a) horizontal deformation, and (b) vertical deformation of quay wall's head, and (c) excess pore water pressure ratio at far field, and (d) excess pore water pressure ratio behind the quay wall for various relative densities of backfill soil

Figure 13 shows the deformed shape after the seismic excitation for three sets of relative densities. As may be expected, more ground surface settlement is observed in the backfill near the wall than at the far field. One may observe that there is a significant movement of quay wall for Dr=15% rather than Dr=25% and 40%. Note also that the lateral spreading of soil is clearly visible near the area influenced by the quay wall especially for Dr=15%. In addition, differential settlements between the quay wall and the apron as well as the deformation of the foundation rubble beneath the quay wall are also observed in Figure 13. This is consistent with the common mode of deformation for gravity quay walls. The analysis indicates translation and rotation mode (rocking) of the wall.

**Figure 13.** Deformed shape of the quay wall system for various relative densities of backfill soil

#### **4.2. Influence of shear stiffness of backfill soil**

and rate of increase for Dr=15% is much more than the others. Figure 12(b) shows cumulative vertical displacement (settlement) of the quay wall's head for the various backfill soil relative densities. As expected, the higher the relative density, the less the accumulated vertical permanent deformation. Figure 12(c) shows the excess pore water pressure ratio at far field in depth of 13 m for three different materials. It is clearly seen that the free field backfill is quickly liquefied. Figure 12(d) depicts the excess pore water pressure ratio time histories for various backfill soil relative densities behind the quay wall in depth of 13 m. It is found that the liquefaction does not occur in backfill soil behind the quay wall. This can be attributed to the movement of quay wall due to seismic loading which directly influences the pore pressure

(a) (b)

**ru** **Vertical Displacement (m)**

**0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1**

**Dr=15% Dr=25% Dr=40%**

**0 5 10 15 20 Time (second)**

**0 2 4 6 8 10 Time (second)**

**Dr=15% Dr=25% Dr=40%**

(c) (d)

**Figure 12.** Computed values of: (a) horizontal deformation, and (b) vertical deformation of quay wall's head, and (c) excess pore water pressure ratio at far field, and (d) excess pore water pressure ratio behind the quay wall for various

Figure 13 shows the deformed shape after the seismic excitation for three sets of relative densities. As may be expected, more ground surface settlement is observed in the backfill near the wall than at the far field. One may observe that there is a significant movement of quay wall for Dr=15% rather than Dr=25% and 40%. Note also that the lateral spreading of soil is clearly visible near the area influenced by the quay wall especially for Dr=15%. In addition, differential settlements between the quay wall and the apron as well as the deformation of the foundation rubble beneath the quay wall are also observed in Figure 13. This is consistent with the common mode of deformation for gravity quay walls. The analysis indicates translation

**0.4 0.5 0.6 0.7 0.8 0.9 1 1.1**

**Dr=15% Dr=25% Dr=40%**

build up.

**0.5 0.6 0.7 0.8 0.9 1**

**ru**

relative densities of backfill soil

and rotation mode (rocking) of the wall.

**Dr=15% Dr=25% Dr=40%**

272 Engineering Seismology, Geotechnical and Structural Earthquake Engineering

**Horizontal Displacement (m)**

**0 5 10 15 20 Time (second)**

**0 2 4 6 8 10 Time (second)**

Three different shear modulus values are adopted (G=20, 35 and 50 MPa) to investigate the effect of shear stiffness of the backfill soil. The other parameters are the same for all the analyses. Figures 14(a) and (b) show the permanent horizontal and vertical displacements time histories of the quay wall's head during seismic loading. It is observed that quay wall has significant movement toward the seaside. Both horizontal and vertical deformations are greater than the allowable limits which have been mentioned in PIANC (2001).

**Figure 14.** Computed values of: (a) horizontal deformation, and (b) vertical deformation of quay wall's head, and (c) excess pore water pressure ratio at far field, and (d) excess pore water pressure ratio behind the quay wall for various shear moduli of backfill soil

Figures 14(c) and (d) show the excess pore water pressure ratio time histories for the far field location and the area behind quay wall. The Figure 14(d) exhibits a significant increase in pore pressure which leads to liquefaction (ru=1) for three types of backfill soil. But for the soil behind quay wall and adjacent to it, at first, the excess pore water pressure ratio increases quickly and after 4 seconds, the excess pore water pressure is dissipated rapidly and consequently, ru decreases with time. This can be pertained to the quay wall movement during seismic loading which influences the excess pore water pressure. In addition, significant reduction is observed after 4.5 s for ru at behind quay wall.

In Figure 15, lateral spreading is clearly obvious behind the quay wall for all the analyses. Deferential settlements between the quay wall and the apron are also visible. The major failure pattern is tilting and rotation of the quay wall toward the seaside which is consistent with the actual failure mode of quay wall movement in literature.

(a) (b)

**ru**

**Vertical Displacement (m)**

**0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1**

> **Friction angle=25 degree Friction angle=30 degree Friction angle=35 degree**

**0.6 0.7 0.8 0.9 1** **0 5 10 15 20 Time (second)**

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**02468 Time (second)**

 *=25°*

 *=30°*

 *=35°*

**Friction angle=25 degree Friction angle=30 degree Friction angle=35 degree**

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**0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5**

**0.5 0.6 0.7 0.8 0.9 1 1.1**

**ru**

friction angles of backfill soil

**Horizontal Displacement (m)**

**0 5 10 15 20 Time (second)**

**0123456789 Time (second)**

**Friction angle=25 degree Friction angle=30 degree Friction angle=35 degree 0.5**

**Figure 17.** Deformed shape of the quay wall system for various friction angles of backfill soil

**4.4. Influence of maximum amplitude of seismic loading**

**Friction angle=25 degree Friction angle=30 degree Friction angle=35 degree**

(c) (d)

**Figure 16.** Computed values of: (a) horizontal deformation, and (b) vertical deformation of quay wall's head, (c) ex‐ cess pore water pressure ratio at far field, and (d) excess pore water pressure ratio behind the quay wall for various

Three different maximum amplitudes are selected for the input excitation applied to the base of the model (*a*max =0.15*g*, 0.2*g and* .25*g*) to consider the effect of input excitation intensity. All other parameters are the same for all the analyses. Figures 18(a) and (b) show the horizontal and vertical displacements time histories at the top of quay wall subjected to seismic loading with different maximum amplitudes. As expected, by increasing the maximum amplitude of seismic loading, the deformation of quay wall increases, both laterally

**Figure 15.** Deformed shape of the quay wall system for various shear moduli of backfill soil

### **4.3. Influence of friction angle of backfill soil**

Figure 16(a) shows the calculated lateral deformation of quay wall's head for three different values of backfill soil friction angle (*ϕ* =25 , 30 *and* 35 degree). As may be expected, the higher the friction angle, the less the accumulated permanent deformation. The same trend as horizontal displacement is observed for the vertical displacement of quay wall's head. Both horizontal and vertical displacements generally increase with decreasing the friction angle of backfill soil.

Figures 16(c) and (d) show the time histories of excess pore water pressure ratio at the far field and the area behind quay wall, respectively. It is seen that the excess pore water pressure ratio at the far field reaches its maximum value (ru=1) at around 2 s. At this time, liquefaction occurs. But for the region behind quay wall, liquefaction does not occur because the volume of backfill soil near the wall tends to increase during the outward movement of the wall. As previous results, Figure 17 demonstrates that the failure mode is rotation and the wall tends to rotate at the bottom.

**Figure 16.** Computed values of: (a) horizontal deformation, and (b) vertical deformation of quay wall's head, (c) ex‐ cess pore water pressure ratio at far field, and (d) excess pore water pressure ratio behind the quay wall for various friction angles of backfill soil

**Figure 17.** Deformed shape of the quay wall system for various friction angles of backfill soil

#### **4.4. Influence of maximum amplitude of seismic loading**

Figures 14(c) and (d) show the excess pore water pressure ratio time histories for the far field location and the area behind quay wall. The Figure 14(d) exhibits a significant increase in pore pressure which leads to liquefaction (ru=1) for three types of backfill soil. But for the soil behind quay wall and adjacent to it, at first, the excess pore water pressure ratio increases quickly and after 4 seconds, the excess pore water pressure is dissipated rapidly and consequently, ru decreases with time. This can be pertained to the quay wall movement during seismic loading which influences the excess pore water pressure. In addition, significant reduction is observed

In Figure 15, lateral spreading is clearly obvious behind the quay wall for all the analyses. Deferential settlements between the quay wall and the apron are also visible. The major failure pattern is tilting and rotation of the quay wall toward the seaside which is consistent with the

Figure 16(a) shows the calculated lateral deformation of quay wall's head for three different values of backfill soil friction angle (*ϕ* =25 , 30 *and* 35 degree). As may be expected, the higher the friction angle, the less the accumulated permanent deformation. The same trend as horizontal displacement is observed for the vertical displacement of quay wall's head. Both horizontal and vertical displacements generally increase with decreasing the friction angle of

Figures 16(c) and (d) show the time histories of excess pore water pressure ratio at the far field and the area behind quay wall, respectively. It is seen that the excess pore water pressure ratio at the far field reaches its maximum value (ru=1) at around 2 s. At this time, liquefaction occurs. But for the region behind quay wall, liquefaction does not occur because the volume of backfill soil near the wall tends to increase during the outward movement of the wall. As previous results, Figure 17 demonstrates that the failure mode is rotation and the wall tends to rotate

*G=20 MPa*

*G=35 MPa*

*G=50 MPa*

after 4.5 s for ru at behind quay wall.

actual failure mode of quay wall movement in literature.

274 Engineering Seismology, Geotechnical and Structural Earthquake Engineering

**Figure 15.** Deformed shape of the quay wall system for various shear moduli of backfill soil

**4.3. Influence of friction angle of backfill soil**

backfill soil.

at the bottom.

Three different maximum amplitudes are selected for the input excitation applied to the base of the model (*a*max =0.15*g*, 0.2*g and* .25*g*) to consider the effect of input excitation intensity. All other parameters are the same for all the analyses. Figures 18(a) and (b) show the horizontal and vertical displacements time histories at the top of quay wall subjected to seismic loading with different maximum amplitudes. As expected, by increasing the maximum amplitude of seismic loading, the deformation of quay wall increases, both laterally and vertically. It is noticed that the values of displacements are much more than the allowable values recommended by PIANC (2001). It means that in such cases, the quay wall complete‐ ly fails during loading.

*amax=0.15g*

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*amax=0.20g*

*amax=0.25g*

**0 5 10 15 20 Time (second)**

**0 5 10 15 20 Time (second)**

**Frequency=1.5 Hz Frequency=3 Hz Frequency=6 Hz**

**Figure 19.** Deformed shape of the quay wall system for various maximum amplitudes of the seismic loading

Figures 20(a) and (b) indicate the horizontal and vertical displacements time histories of the quay wall's head during seismic loading. As may be expected, by increasing the frequency of seismic loading, the displacements increase excessively and the quay wall system entirely fails. The values of displacements are so much higher than allowable values proposed by

(a) (b)

**ru**

**Frequency=1.5 Hz Frequency=3 Hz Frequency=6 Hz**

**Vertical Displacement (m)**

**0 0.2 0.4 0.6 0.8 1 1.2 1.4** **Frequency=1.5 Hz Frequency=3 Hz Frequency=6 Hz**

(c) (d)

**Figure 20.** Computed values of: (a) horizontal deformation, and (b) vertical deformation of quay wall's head, and (c) excess pore water pressure ratio at far field, and (d) excess pore water pressure ratio behind the quay wall for various

**0.4 0.5 0.6 0.7 0.8 0.9 1 1.1**

**4.5. Influence of frequency of seismic loading**

**Frequency=1.5 Hz Frequency=3 Hz Frequency=6 Hz**

PIANC (2001).

**0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5**

**0.5 0.6 0.7 0.8 0.9 1**

**ru**

frequencies of the seismic loading

**Horizontal Displacement (m)**

**0 5 10 15 20 Time (second)**

**0 4 8 12 Time (second)**

Figures 18(c) and (d) depict ru time histories at the far field and the area behind quay wall. As it is seen, the backfill soil liquefy at far field for all the maximum amplitude but at first liquefaction occurs for amax=0.25g. For the area behind quay wall, ru is less than 0.85 during seismic loading. Therefore, it can be concluded that liquefaction does not occur nearby (behind) the quay wall. The difference in pore pressure build up pattern between the far (free) field and near-wall field is mainly due to the fact that near the wall, soil experiences significant compression and extension alternatively during shaking (due to wall oscilla‐ tion). In the free field, soil mainly experiences shear during shaking, allowing for high ru and leading eventually to liquefaction.

Figure 19 indicates translation and rotation (rocking) of the quay wall. Lateral spreading and ground failure behind the quay wall are clearly observed. As may be expected, more ground surface settlement is noticed in the backfill near the wall than at the far field. A large tilting of the wall to the seaward is obviously observed.

**Figure 18.** Computed values of: (a) horizontal deformation, and (b) vertical deformation of quay wall's head, (c) ex‐ cess pore water pressure ratio at far field, and (d) excess pore water pressure ratio behind the quay wall for various maximum amplitudes of the seismic loading

**Figure 19.** Deformed shape of the quay wall system for various maximum amplitudes of the seismic loading

#### **4.5. Influence of frequency of seismic loading**

and vertically. It is noticed that the values of displacements are much more than the allowable values recommended by PIANC (2001). It means that in such cases, the quay wall complete‐

Figures 18(c) and (d) depict ru time histories at the far field and the area behind quay wall. As it is seen, the backfill soil liquefy at far field for all the maximum amplitude but at first liquefaction occurs for amax=0.25g. For the area behind quay wall, ru is less than 0.85 during seismic loading. Therefore, it can be concluded that liquefaction does not occur nearby (behind) the quay wall. The difference in pore pressure build up pattern between the far (free) field and near-wall field is mainly due to the fact that near the wall, soil experiences significant compression and extension alternatively during shaking (due to wall oscilla‐ tion). In the free field, soil mainly experiences shear during shaking, allowing for high ru and

Figure 19 indicates translation and rotation (rocking) of the quay wall. Lateral spreading and ground failure behind the quay wall are clearly observed. As may be expected, more ground surface settlement is noticed in the backfill near the wall than at the far field. A large tilting of

(a) (b)

**ru**

**Vetrical Displacement (m)**

**0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6**

**a(max)=0.15g a(max)=0.20g a(max)=0.25g**

**0 5 10 15 20 Time (second)**

**02468 Time (second)**

**a(max)=0.15g a(max)=0.20g a(max)=0.25g**

(c) (d)

**Figure 18.** Computed values of: (a) horizontal deformation, and (b) vertical deformation of quay wall's head, (c) ex‐ cess pore water pressure ratio at far field, and (d) excess pore water pressure ratio behind the quay wall for various

**0.4 0.5 0.6 0.7 0.8 0.9 1 1.1**

**a(max)=0.15g a(max)=0.20g a(max)=0.25g**

ly fails during loading.

leading eventually to liquefaction.

**0.5 0.6 0.7 0.8 0.9 1**

maximum amplitudes of the seismic loading

**ru**

**Horizontal Displacement (m)**

the wall to the seaward is obviously observed.

276 Engineering Seismology, Geotechnical and Structural Earthquake Engineering

**a(max)=0.15g a(max)=0.20g a(max)=0.25g**

**0 5 10 15 20 Time (second)**

**0123456789 Time (second)**

Figures 20(a) and (b) indicate the horizontal and vertical displacements time histories of the quay wall's head during seismic loading. As may be expected, by increasing the frequency of seismic loading, the displacements increase excessively and the quay wall system entirely fails. The values of displacements are so much higher than allowable values proposed by PIANC (2001).

**Figure 20.** Computed values of: (a) horizontal deformation, and (b) vertical deformation of quay wall's head, and (c) excess pore water pressure ratio at far field, and (d) excess pore water pressure ratio behind the quay wall for various frequencies of the seismic loading

As pervious, liquefaction occurs at the far field which is not affected by the quay wall move‐ ment (Figure 20(c)) but for the area behind quay wall, liquefaction does not occur due to seaward movement of the quay wall (Figure 20(c)). As it is clear in Figure 20(d) that the excess pore pressure ratio increases till 4 seconds but after that dissipation is observed for all frequencies. The rate of dissipation for frequency of 6 Hz is higher than the others. Figure 21 depicts the deformed shape of quay wall system after seismic loading. As it is seen, the lateral spreading behind quay wall completely observed for all frequencies but it is much more severe for F=6 Hz which the quay wall has been failed entirely and the area behind quay wall has subsided excessively. The failure mode of the quay wall is translation and rotation. When the frequency of seismic loading increases, the quay wall rotates more.

alternative pumping and suction process in excess pore water pressure which are caused by wall's vibrations increase the level of damage because large amounts of backfill are forcedly leaked into the sea. The lack of backfill liquefaction near the wall is attributed to the lateral displacement of the wall. In the other words, excess pore water pressure does not attain 100% liquefaction behind the quay wall contrary to the far field. The current study states that the numerical simulation incorporated with the special numerical techniques is capable of

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School of Civil Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran

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[2] American Society of Civil Engineers, (2000). ASCE 4-98 Seismic Analysis of Safety-

[3] Byrne, P. M. (1991). A cyclic shear-volume coupling and pore pressure model for sand, *Proceeding of Second International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics*, Vol. 1, University of Missouri, Rolla, Mis‐

[4] Chen, C., Hwang, G. (1969). Preliminary analysis for quay wall movement in Tai‐ chung harbour during the September 21, 1999, Chi-Chi earthquake, *Earthquake Engi‐*

[5] Cooke, H. G. (2000). Ground improvement for liquefaction mitigation at existing highway bridges, *Ph.D. dissertation*, Department of Civil and Environmental Engi‐

[6] Dickenson, S. E., Yang, D. S. (1998). Seismically-induced deformations of caisson re‐ taining walls in improved soils, *Proceeding of Geotechnical Earthquake Engineering and Soil Dynamics III, Vol. II, Geotech. Special Pub*. No. 75., ASCE, Reston, VA, pp.

[7] Ebrahimian, B., Mostafavi Moghadam, A. A., Ghalandarzadeh, A. (2009). Numerical modeling of the seismic behavior of gravity type quay walls, *Proceeding of Perform‐*

related Nuclear Structures and Commentary. *ASCE*, Virginia, USA.

*neering and Engineering Seismology*, Vol. 2, pp. 43-54.

neering, Polytechnic Institute and State University, Virginia.

modeling the seismic response of gravity-type quay walls.

**Author details**

Babak Ebrahimian\*

**References**

28-30.

souri, pp. 47-55.

1071-1082.

**Figure 21.** Deformed shape of the quay wall system for various frequencies of the seismic loading
