Effects of Ground Improvement on the Seismic Stability of Sheet Pile Quay Walls
Assoc. Professor
Amirkabir University of Technology
Tehran, Iran
A. Yoosefnia Pasha
M.Sc. in Soil Mech. and Foundation Eng.
Amirkabir University of Technology
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Effects of Ground Improvement on the Seismic Stability of Sheet Pile Quay Walls
Assoc. Professor A. Yoosefnia Pasha M.Sc. in Soil Mech. and Foundation Eng.
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ABSTRACT
The importance and key role of the quay walls in the off-shore regions as a retaining structure for docks and wharves, and their vulnerabilities during earthquake loadings has caused many researchers to concentrate on the soil-structure interactions of these walls from different aspects. Although valuable results have been achieved in this respect, however, for the last decade they have suffered from extensive damages during heavy earthquakes occurred in these areas.
In this paper the influences of the two important parameters namely; the property of the improved soils (in terms of SPT numbers) and the dimensions of the improved area on the behavior of the anchored sheet pile quay walls have been numerically studied and investigated. The method of the numerical analysis, the details of the modeling, and the important results are presented and discussed.
Keywords: Quay walls- sheet pile – earthquake loading- anchored walls- liquefaction- standard penetration test (SPT) - improved soil- numerical analysis- seismic stability.
INTRODUCTION
The quay wall and in particular the sheet pile quay wall are one of the most vulnerable structures against the seismic instability and ground liquefaction. So far, different mitigation methods have been used to stable this kind of retaining structures during earthquake loadings. One of the effective methods in this respect is to do the soil stabilization. The degree of the soil improvement and the zone in which the stabilization techniques have to be applied are among the most important and effective factors in these methods. In this study a great effort has been attempted to investigate the role and influences of these two factors on the behavior of an anchored sheet pile quay wall during earthquake loading. The base and backfill soils have been selected in an initial condition that they liquefy when subjected to the ground motions. The FLAC 2D finite difference package has been used to model the soil and quay wall for numerical analyses. The properties of the modified soils such as density (?), elastic modulus (E), cohesion (C), and the angle of internal friction (f) as a function of the SPT number in practice from different soil mechanic reference books have been selected and verified.
Also, different zones by different dimensions around the sheet pile and its anchorage have been tried to get the most effective zone for mitigating the hazard risks of theses walls during earthquake loadings. In this study a numerical method was used to analyze a sheet pile quay wall. The model properties such as the model geometry, soil properties, initial and boundary conditions, and the method of applying the dynamic loadings are presented and described in the following sections. Also, according to the results of the numerical analyses, the effect of the two above mentioned parameters on the soil-quay wall interaction under dynamic loadings have been investigated and discussed.
THE ANALYSIS METHOD
In this research the non-linear dynamic analysis based on the effective stress for evaluating the pore pressure development during earthquake loadings has been used. The analyses have been carried out in the plane strain condition using the FLAC finite difference package in static and dynamic phases. For the sake of simplicity, the model has been made in one step in static condition. After getting the equilibrium condition in the static state, the dynamic phase has been applied to the model by changing the state boundary conditions to the dynamic one and imposing the earthquake loading to the system.
To model the pore pressure development, the Finn behavioral model which has been facilitated in the package has been used. To calculate the variations of the pore pressure one of the two equations suggested by Finn and Martin (1975), [3], and Byrne (1991), [2] can be used. In this study the Byrne equation, given below, has been used.
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(1) |
where
evd = the volume decrease under cyclic loading
Devd = the volume decrease increment
g = the amplitude of the cyclic shear strain
C1 and C2 are constants which vary according to the soil type and can be estimated from the following equations in case of lack of laboratory data;
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(2) |
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(3) |
Also, the variations of the soil shear modulus during dynamic loading have been modeled using the concept of the Masing criterion [5] and the Masing.fis. function in the FISH medium which is matched to the FLAC package. In this program the soil maximum shear modulus, Gmax, has been considered to be five times the static shear modulus that has been used in the static condition analyses. This value is acceptable in comparison with the values estimated from the [7] existing empirical equations. Also, the amount of tmax, has been taken to about 20000 kPa according to the stress conditions in soil from the graph suggested by Hardin & Drnevich, 1972, [6]. This figure has been given to the Masing.fis. function. A typical cyclic stress-strain curve, obtained from the application of the Masing.fis. Function and analyzing the model is shown in Figure 1.
Figure 1. A typical stress-strain curve obtained from FLAC by using the Masing.fis function
To calibrate the numerical model used in this investigation, the results of analyses a real retaining wall using this technique, were compared with the result of the same retaining wall analyzed by Mccullough & Dickenson, 2001 [1].
PARAMETRIC STUDIES
The geometry and general dimensions of the developed model in FLAC to do the parametric studies are shown in Figure 2. The finite difference mesh selected to do the numerical analyses is shown in Figure 3 The sheet pile and the anchorage block foundation have considered to be from steel and concrete materials respectively. Both are assumed to have the linear elastic behavior. The sheet pile and the block foundation are extended along the axis perpendicular to the x-y plane. Thus, the input parameters belong to the one meter length of the wall in a plane strain condition. The earth pressures developed behind the sheet pile are transferred to the block foundation by means of anchored cables at 2.5 m. from top of the wall. The cable has been taken to behave elasto-plastic, though the induced tension forces never exceed its yielding limit (220 kN.). Since the anchored cable only transfers the wall forces to the block foundation, the soil-cable interaction has been ignored, and the values of Kbond and Sbond have been taken as small as possible. The properties of the sheet pile, block foundation and the used cable are given in table 1.
Table 1. The specifications of the sheet-pile, block foundation, and the cable.
As can be seen in Figure 2, two soil layers by an unlimited length have been considered for the model. The upper layer is a loose and liquefiable soil and the lower layer is a dense and non-liquefiable soil.
Figure 2. The geometry and general dimensions of the developed model.
The influences of the geometry and dimensions of the improved zone have been studied by selecting different zones of improved soils as are shown in Figure 6. In these analyses the SPT number of the improved soils has been taken to 30 and the sheet pile deformations along its length have been estimated. The degree of improvement has been investigated in this study as the second important factor affecting the quay wall behavior during earthquake loadings. The SPT number of the improved soil has been taken as a direct index of degree of improvement in this study. The soil parameters of the improved zones have been determined from different references based on the selected SPT number for analyses. The values of the soil unit weight (?), the elastic modulus (E), angle of internal friction (f), and also the Finn model parameters ( ff-c1, ff-c2, ff-c3), for different SPT numbers ranging from 20 to 40 have been estimated.
Figure 3. The selected finite difference mesh for numerical analysis by FLAC-2D.
In this series of analyses, the improved zone has been extended up to 14 m. in both sides of the sheet pile and down to the bottom of the quay wall. The properties of the soil layers are shown in table 2.
To model the pore pressure development and the liquefaction phenomenon, the Finn model has been used. This model has been applied to an area of upper soil layer of 60 m. length from both sides of the quay wall.
Table 2. Properties of the selected soil layers
The Mohr-Coulomb model has been applied to other zones of the soil top layer and also to the whole bottom layer (Figure 4).
Figure 4. The soil zones and the applied models in each zone.
The soil damping ratio has been taken to 5% using the local damping facilities exists in the FLAC package. The dynamic load has been applied to the bottom zone of the model in a form of sine shear stress by frequency of 3 Hz. and durations of 8 and 10 seconds. The maximum shear stress (the amplitude of the sine wave), has been calculated from the following equation for the case of having 0.2g peak ground acceleration in the surface of the model (7).
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(4) |
where
amax = peak ground acceleration,
sv = the total soil pressure at the bottom layer,
rd = reduction factor (taken as 0.5 form the relevant graph), and
g = gravitational acceleration.
Using Equation 4, the amplitude of the shear stress to be applied to the bottom of the model, has been estimated to 126.8 kPa. A typical applied dynamic load to the model is shown in Figure 5.
Figure 5. A typical applied dynamic load to the numerical model.
The boundary conditions is taken to be the free field during application of the dynamic loading. Also, the model has been analyzed for the undrained conditions for the pore pressure generation.
THE ANALYSIS RESULTS
The results of the dynamic analyses carried out on the selected sheet pile quay wall in Figure 2 are presented and discussed in the following sections.
The effect of the improved area
The results of the analyses performed on the anchored sheet pile quay wall, while different improved zones (shown in Figure 6), have been taken into account, are given in table 3. In this table the deformation of the sheet pile at points A (top of the wall), B (at the sea bed), and C (bottom of the wall), at 8 and 10 seconds of loading are presented. To compare the obtained results the amounts of the sheet pile deformations are plotted and shown in Figure 7
Table 3. Deformation of the sheet pile at points A (top), B (sea bed), and C (bottom).
Figure 6. Different zones considered for soil improvements.
Figure 7. the horizontal deformations of the wall at points A, B, and C for different soil improvement areas.
The effect of the degree of soil improvement
The degree of soil improvement can be defined in terms of soil properties. The soil properties directly can be reflected in various soil parameters such as porosity, cohesion, angle of internal friction, density, etc. Also the results of the in-situ and laboratory testings on soil, such as compressive strength or standard penetration test can be used to measure and show the soil properties. In this study the SPT number has been used to define the soil properties. To cover different degrees of soil improvement, the SPT of the modified area has been changed from 20 to 40 corresponding to a relatively well improved soil.
The results of analyses using different SPT number for the improved zone are shown in table 4. The area of improvement is shown in Figure 8. Also, the variations of the wall horizontal deformations at points A, B, and C for different degrees of soil improvement are plotted in Figure 9.
Figure 8. The area of improved soil.
Table 4. Deformations of the sheet pile at points A, B, and C.
Figure 9. Variations of the sheet pile horizontal deformations at different points.
The contours of the pore pressure ratios (Ru) at the end of the analyses for different SPT numbers are plotted in Figures 10a, b, c. It can be seen that as the SPT number increases, which means the soil becomes denser and more improved, the liquefied zone becomes smaller and the amount of the wall deformations decreases consequently.
Figure 10a. Contours of the pore pressure ratio (Ru), at the end of analyses for SPT=20.
Figure 10b. Contours of the pore pressure ratio (Ru), at the end of analyses for SPT=30.
Figure 10c. Contours of the pore pressure ratio (Ru), at the end of analyses for SPT=40.
SUMMARY AND CONCLUSIONS
In this study the influences of the degree of soil improvement and also the dimensions of the improved area on the behavior of the anchored sheet pile quay walls during dynamic loading have been investigated. The pore pressure development due to dynamic loadings within the soil around the wall has been estimated using the 2D finite difference package of FLAC. The deformations of the modeled wall have been estimated at different points under various soil improvement conditions. Taking into account the analyses results, the following remarks can be concluded:
When the soil improvement method is selected as an effective measure to stable the sheet pile quay wall against soil liquefaction during heavy earthquakes, the appropriate area to be improved is of great importance. Extending the improved area to the bottom and also in front of the wall to exceed the passive failure zone, will cause the sheet pile deformations to be reduced considerably.
The analyses results from changing the area of the improved soil proved that if the front soils are not improved, the improvement of the backfill soils can not play a major role in reducing the sheet pile deformations during dynamic loadings.
The analyses results from different degrees of soil improvements show that the stable condition for the quay wall is met when the SPT number of the improved soils increases to 25-30.
For the SPT numbers more than 30 the soil has been over improved, which means its condition is far from being liquefied. For the SPT numbers below 25 there is still the possibility of liquefaction occurrence for soils below and around the wall, which may end to overall failure of the soil-wall system.
REFERENCES
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