Anderson DG, Martin GR, Lam I, Wang JN. Seismic analysis and design of retaining walls, buried structures, slopes, and embankments, Transportation ...
Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska
NUMERICAL APPROACHES IN MODELING SOIL-FOUNDATION INTERACTION OF TALL BRIDGES
M. R. Falamarz-Sheikhabadi1 and A. Zerva2 ABSTRACT Inherent assumptions in the modeling of soil-foundation interaction can significantly affect the nonlinear seismic response of bridges. Pushover analyses on one of the piers of a tall bridge, the Mogollon Rim Viaduct in Arizona, are conducted herein to examine the sensitivity of the pier response to numerical modeling approaches. The investigation models the pier with three-dimensional fiber section elements using the open-source software platform OpenSees, and analyzes its response in both the weak and strong directions. The influence of bond-slip and P-∆ effects on the nonlinear response of the pier are examined. p-y, t-z and Q-z nonlinear springs are applied to model the soil-pile interaction, and equivalent nonlinear springs are derived to reproduce the soil-pile cap interaction. The numerical results of the study indicate how structural and geotechnical modeling approaches for the soil-foundation-structure interaction can affect the nonlinear response of tall bridges and lead to local or global failure. For the analyzed case, the pier embedment and foundation flexibility can dramatically modify the structural response and influence the bond-slip effect at the pier-pile cap connection.
1
Graduate Student Researcher, Dept. of Civil, Architectural & Environmental Engineering, Drexel University, Philadelphia, PA 19104 2 Professor, Dept. of Civil, Architectural & Environmental Engineering, Drexel University, Philadelphia, PA 19104 Falamarz-Sheikhabadi, MR, Zerva, A, Numerical approaches in modeling soil-foundation interaction of tall bridges, Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.
Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska
Numerical Approaches in Modeling Soil-Foundation Interaction of Tall Bridges
M. R. Falamarz-Sheikhabadi1 and A. Zerva2
ABSTRACT Inherent assumptions in the modeling of soil-foundation interaction can significantly affect the nonlinear seismic response of bridges. Pushover analyses on one of the piers of a tall bridge, the Mogollon Rim Viaduct in Arizona, are conducted herein to examine the sensitivity of the pier response to numerical modeling approaches. The investigation models the pier with three-dimensional fiber section elements using the open-source software platform OpenSees, and analyzes its response in both the weak and strong directions. The influence of bond-slip and P-∆ effects on the nonlinear response of the pier are examined. p-y, t-z and Q-z nonlinear springs are applied to model the soil-pile interaction, and equivalent nonlinear springs are derived to reproduce the soil-pile cap interaction. The numerical results of the study indicate how structural and geotechnical modeling approaches for the soil-foundation-structure interaction can affect the nonlinear response of tall bridges and lead to local or global failure. For the analyzed case, the pier embedment and foundation flexibility can dramatically modify the structural response and influence the bond-slip effect at the pier-pile cap connection.
Introduction One of the challenging problems in bridge engineering is the consideration of the soilfoundation-structure (SFS) interaction in the seismic behavior of the structures. Extensive research has been conducted on the lateral and vertical resistance of pile foundations, and different methods for pile modeling have been proposed [1] - [5]. From the earthquake engineering perspective, pile foundations may resist seismic forces with a combination of four components: (1) pile-soil-pile interaction; (2) passive earth pressure on the sides of the pile cap; (3) frictional forces at the base and sides of the pile cap, and (4) vertical resistance at the base of the pile cap. Commonly, nonlinear p-y, t-z and Q-z curves are used to approximate the resistance of single piles buried in soil [6], and pile group effects are considered by the p-multiplier method [7]. However, even though there are many studies on the seismic behavior of single piles and pile groups, e.g. [1] - [3] and [8] - [11], there are only few investigations related to the lateral and vertical behavior of the soil-pile cap system during seismic loading [12], [13]. In earthquake 1
Graduate Student Researcher, Dept. of Civil, Architectural & Environmental Engineering, Drexel University, Philadelphia, PA 19104 2 Professor, Dept. of Civil, Architectural & Environmental Engineering, Drexel University, Philadelphia, PA 19104 Falamarz-Sheikhabadi, MR, Zerva, A, Numerical approaches in modeling soil-foundation interaction of tall bridges, Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.
engineering applications, it is, generally, assumed that either the pile cap behaves like an equivalent thick pile or its resistance is conservatively ignored in pile foundation modeling. This lack of consideration of the pile-cap contribution to the response may be partly due to the facts that: (1) the common bridge design codes, such as AASHTO [14] and Caltrans [15], do not recommend any specific provisions for modeling and analyzing pile caps, and (2) the pile caps are usually located on the ground surface or very close to the ground surface and surrounded with soft soil. However, recent experimental developments indicated that heavily buried pile caps may considerably contribute to the lateral resistance of pile foundations [4], [5]. In this paper, a detailed finite element analysis of one of the piers of the Mogollon Rim Viaduct in Central Arizona is performed by considering soil-foundation interaction. The pier, a tall, partially embedded, cantilever, flared column, is modeled using fiber section elements. The bond slip at the pier-pile cap connection as well as P-∆ effects are included in the structural modeling. The influence of two well-known confined concrete models, i.e., the Mander [16] and the KentScott-Park [17], [18] concrete models, on the SFS system is studied. The soil-foundation interaction is modeled using p-y, t-z and Q-z nonlinear curves. The frictional resistance and passive earth pressure effects on the embedded part of the pier and the pile cap are also considered. Model description The Mogollon Rim Viaduct (built in 1991) is located on SR 260, which is the primary roadway between the rural towns of Payson and Heber in Central Arizona. It is a three-span bridge with total length of 910 ft (with spans of 280 ft, 340 ft and 280 ft) and width of 61 ft as shown in Fig. 1 (a). The bridge superstructure is a precast, prestressed concrete, continuous girder, on a curve, with an uphill grade. The bridge has wing walls on the down-slope side of the two abutments, and extensive foundations for the two center piers. The clear height of the piers is 52.4 ft and 68.2 ft (first and second pier in Fig. 1 (a), respectively). The first pier is rigidly connected to the superstructure, whereas the second, taller pier is seismically isolated from the deck with elastomeric bearings (Fig. 1 (a)). The cross section of the piers changes with increasing height and has a flared shape. The base dimensions of the piers are 9 ft × 18 ft and their top dimensions 9 ft × 27 ft. The pile caps consist of two parts, the super cap with horizontal dimensions of 18 ft × 18 ft and depth of 7.5 ft, and the sub cap with horizontal dimensions of 30 ft × 30 ft and depth of 7.5 ft. The pile caps are supported on nine drilled shafts with diameter of 4 ft as shown, for the second pier, in Fig. 1 (b). The soil profile, also illustrated in Fig. 1 (b), is based on the existing geotechnical information. Analysis framework and finite element model The open-source software platform OpenSees [19] is used to model the SFS system. Pushover analyses are performed along the strong and (negative) weak directions of the taller pier (second pier in Fig. 1(a)). The loading pattern of the pushover analysis is proportional to the nodal masses of the pier. In order to account for the effect of the superstructure weight on the pushover analysis, an axial compression force of 7500 kips is applied at the top of the pier. This axial force is equal to the tributary dead load of the superstructure that is supported by the second pier as shown in Fig. 1(a).
Figure 1. Structural and geotechnical illustration of the model: (a) global model, (b) second pier characteristics (scales are not the same).
Pier modeling The seismically isolated pier (Fig. 1(b)) is modeled as a cantilever column using threedimensional fiber section, force-based, beam-column elements; the pier is flared in its strong direction. Six different sections are introduced based on the variation of the arrangement of the longitudinal reinforcing steel. Nine nodes are used to reflect the mass distribution along the height of the pier. The pier is partially embedded in soil consisting of two different layers: loose sand with a 5 ft depth and medium sand with a 10 ft depth. A uniaxial bilinear steel material with kinematic hardening and expected material properties as given in Caltrans for steel grade 60 [15] is used to model the reinforcing steel. In practice, either the uniaxial Mander or the uniaxial Kent-Scott-Park concrete materials with degrading linear unloading/reloading stiffness and no tensile strength are used to model the pier and foundation concrete. Mander’s concrete model is applicable to all section shapes and all levels of confinement in all strain rate loading conditions, even though its use for high-strain loading appears to be unconservative. This model is commonly recommended by codes to model the confined concrete behavior for quasi-static loading conditions [15]. The Kent-Scott-Park concrete model is applicable to rectangular shaped sections and all levels of confinement for both low- and high-strain loading conditions. The consideration of the cross section of the pier (Fig. 1(b)) implies that the Kent-Scott-Park concrete model with high-strain rate may be a better choice for estimating its actual response. Both concrete models, i.e. Mander’s model at lowstrain rates and the Kent-Scott-Park model at high-strain rates, are used herein to compare the effect of the selection of the concrete constitutive modeling on the structural response. To consider bond slip in modeling, a duplicate node is placed between the pier and the pile cap to connect them with a zero-length section element [21]. The section configuration of the zerolength element is the same as the pier section, but the hysteretic behavior of its reinforcing steel is modified so as to include bond-slip effects. The torsional and two in-plane horizontal degrees of freedom of the added node are constrained to its adjacent node to prevent sliding of the beamcolumn element under lateral loading, since the torsional and shear resistance is not included in the zero-length section element. The second order P-∆ effect is also considered in the analysis of the pier via corotational transformation. Pile cap modeling The pile caps of the piers of Mogollon Rim Viaduct consist of two parts fully embedded in the soil: the super cap and the sub cap (Fig. 1). Linear beam-column elements are used to model the pile cap with the consideration of cracked concrete section, and the equivalent nonlinear p-y and t-z springs are introduced for each part as illustrated in the following. p-y springs The nonlinear p-y curves for modeling the soil-pile cap interaction are estimated using a hyperbolic equation of the form [13]: P=
y 1 k max
+ Rf
y Pult
(1)
where P is the load at deflection y, Pult is the ultimate passive force, kmax is the initial stiffness obtained herein with the approach provided in Ref [22], and Rf is the failure ratio. The ultimate passive pressure is estimated using the log spiral method [23] and the interface friction angle between concrete and soil, δ , is assumed to be two-thirds of the internal friction angle of soil, φ [24]. Using Eq. 1, nonlinear p-y curves are introduced in OpenSees in order to model the lateral resistance of the pile cap due to the passive earth pressure. t-z springs To model the frictional forces at the horizontal and vertical surfaces of the soil-pile cap interaction, the ultimate frictional capacity, tult, and the displacements at which 50% of tult is mobilized in monotonic loading, y50 or z50, should be determined. For piles buried in cohesionless soils, API recommends that y50 and z50 be equal to 0.05 in [25], and experimental results indicate that their value may be in the range of 0.1 in to 0.25 in [10]. Herein, it is conservatively assumed that the value is 0.2 in for all frictional force types because of the larger dimensions of the pile caps in comparison to the piles [3]. The ultimate surface friction forces on the horizontal surfaces of the pile cap may be obtained using the Coulomb-Mohr criterion for cohesionless soils [26]. Using this approach, the ultimate horizontal surface friction forces can be estimated by:
[
]
hor tult = (1 ± kv ) σ z Aeff + αN tan(δ )
when
⎧0 p α p 1 ⎨ ⎩α = 0
at the base of the pile cap elsewhere
(2)
where σ z = γ z is the vertical effective stress of the soil at depth z, γ the submerged unit weight of soil, Aeff the effective area of the pile cap in contact with the soil, N the axial load due to the bridge weight supported by the pile foundation, and α represents the contribution of the base of the pile cap to the vertical bearing capacity of the pile foundation. The first term on the righthand side of Eq. 2, (1 ± kv ) , represents the effect of the vertical component of the earthquake on the horizontal surface frictional forces. The ultimate friction force on the vertical surfaces of the pile cap (pile cap sides) is also obtained using the Coulomb-Mohr criterion as:
t
ver ult
z2
= b ∫ K σ z tan (δ ) dz
(3)
z1
where b is the width of the pile cap (b=30 ft for the sub cap and 18 ft for the super cap), and K is the coefficient of lateral earth pressure. The effect of the earthquake components on the vertical surface friction forces can be directly considered in the estimation of K [26], [27]. Herein, to evaluate the integration of Eq. 3, it is assumed that K = 4.62 exp[− 0.0411z ] , where z is in ft [8]. The t-z springs corresponding to the horizontal and vertical frictional forces are attached to the model with rigid links at the center of all soil-pile cap interaction surfaces.
Pile modeling The cross section of each pile is modeled using three-dimensional fiber section, force-based, beam-column elements. Mander’s concrete model and uniaxial bilinear steel with expected properties are utilized for the fiber sections. Pile-soil-pile interaction is represented by nonlinear p-y, t-z and Q-z springs [9], [10], [25]. Pile group effects, which may reduce the bearing capacity of each pile, are considered herein by reducing the individual capacity of each shaft by a factor of 0.7 [14], because the soil surrounding the piles of the viaduct is approximately of the same type (cohesionless soil-very dense sand). Numerical results In this section, the significance of the assumptions in the numerical SFS modeling of the pier on its pushover response is compared using the six models highlighted in Table 1. The results of these comparisons are plotted in Figs. 2 to 4, which illustrate the variation of the shear force, F, at the three nodes 1 (top of pile cap), 2 (middle of second soil layer) and 3 (middle of the ground surface soil layer) along the pier (Fig. 1(b)) with the top lateral displacement of the pier, ∆. Fig. 2 compares the effect of the two concrete constitutive models on the pushover response of Model C (Table 1) along its strong and negative weak, i.e., slope effect is not considered, directions (Fig. 1(a)). Model C is structurally “complete”, as it incorporates both bond-slip and P-∆ effects, but its base is fixed, so that its response is not affected by the SFS interaction. Fig. 2 indicates that, whereas there is no significant difference between the response of the system modeled with the two concrete constitutive modeling approaches along its weak direction, a considerable difference is observed along its strong direction because of the bond-slip effect, which causes the sharp drop in the shear forces at all nodes of the system modeled with KentScott-Park material when the top lateral displacement reaches approximately 2.2 in (a pullout failure). The difference in the response behavior of the system may be attributed to the different distribution of forces across the cracked cross section of the pier caused by the two concrete models. The bundled longitudinal reinforcement (Fig. 1(b)) and low compression axial force due to the superstructure weight have amplified the bond-slip effects in both directions. However, because the effective depth of the tension steel is longer along the strong direction (Fig. 1(b)), the bond slip is more significant along this direction and is more strongly influenced by the characteristics of the concrete constitutive model. In the following, the Kent-Scott-Park model is utilized.
(a) Kent-Scott-Park concrete model Figure 2.
(b) Mander concrete model
Comparison of effect of the two concrete constitutive modeling approaches on Model C (Table 1) of the pier system along the strong (left part of each subplot) and weak (right part of each subplot) direction of the pier due to pushover.
Table 1. Description of models with different structural and geotechnical characteristics. Model characteristics Fixed base P-∆ effect Bond-slip effect Passive earth pressure effects on partially embedded pier Frictional force effects on partially embedded pier Passive earth pressure effects on pile cap resistance Frictional force effects on pile cap resistance Pile-soil-pile interaction
Model A Model B Model C Model D Model E
Model F
No Yes Yes
Yes Yes No
Yes Yes Yes
Yes Yes Yes
No Yes Yes
No Yes Yes
Yes
No
No
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Yes
No
No
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No
Yes
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No
No
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Fig. 3 presents the numerical results for the response of the pier along its strong direction considering the six different models for the SFS interaction system (Table 1). Fig. 3(a) shows the pushover results for the general Model A, which includes all SFS considerations (Table 1) and forms the basis of the comparison with the results of the other, more simplified models (Models B-F in Figs. 3(b)-(f)). Fig. 3(c) is identical to the left part of Fig. 2(a) discussed earlier. It is noted that all models that do not consider the pier embedment effect (Models B, C, E and F in the corresponding subplots of Fig. 3) result in shear forces at node 1 that are higher than those at node 2, which, in turn, are higher than those at node 3. A similar behavior of the shear forces can be observed at small displacements for Model D (Fig. 3(d)) before bond slip occurs. After bond slip occurs for this model, there is a dramatic decrease in the shear forces at node 1 relative to the forces at the other two nodes. This behavior may be attributed to the fact that, at small displacements, the fixed base condition at the support of Model D causes a shear force behavior similar to that of the fixed base of Model C (Fig. 3(c)), but, after bond slip, the pier embedment resistance picks up causing the decrease of the shear force at the lowest node. The comparison of Models B and C (Figs. 3(b) and (c)) clearly illustrates the bond-slip effect. Both models are fixed at the base, but Model C includes bond-slip and P-∆ effects, whereas Model B reflects only the P-∆ effect contribution. Clearly, bond-slip causes a localized failure (Fig. 3(c)), and neglecting its effect leads to an unrealistic distribution of shear forces along the pier (Fig. 3(b)). The comparison of Models A (Fig. 3(a)), C (Fig. 3(c)) and E (Fig. 3(e)) indicates that the consideration of the flexibility of the SFS system caused by the modeling of the pile cap and the piles dramatically reduces the bond-slip effects; local failure occurs at a larger displacement for Model A and no local failure occurs for Model E. Fig. 3(f) suggests that the pier embedment and the pile cap resistance are most important parameters, as the response of Model F (Fig. 3(f)), which does not incorporate these effects (Table 1), is not comparable with the response evaluated from the realistic Model A (Fig. 3(a)). Model F becomes unstable and a global failure or full collapse occurs at a displacement of 16.88 in, i.e. the structure cannot resist against further lateral loading and the pier will overturn. Such a behavior may be justified due to the pier height, since a small rotation at its foundation level can cause a large displacement at its top.
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Figure 3. Pushover analyses results along the strong direction of the pier for Models A-F described in Table 1. Fig. 4 presents the numerical results corresponding to those of Fig. 3 but for the (negative) weak direction of the pier. It is noted, however, that the scale of the force and displacement axes in the two figures (Figs. 3 and 4) differ. Fig. 4(c) is identical to the right part of Fig. 2(a) discussed earlier. The same trend regarding the value of the shear force at node 1 relative to the shear forces at nodes 2 and 3 as a consequence of the pier embedment effects can be observed for Models B, C, E and F in both Figs. 3 and 4. Similarly, for Model D (Fig. 4(d)), the forces at all nodes are similar at small displacements, but pier embedment effects start picking up with increasing displacements causing a reduction of the shear force at node 1 compared to those at the other nodes. From a different perspective, the response of the pier in this direction relative to its response in the strong direction clearly indicates that bond-slip effects are not significant in the negative weak direction of the pier. This may be attributed to the shorter distance of the extreme row of the tension steel from the neutral axis in the shorter, weak cross section of the pier relative to that in its strong one (Fig. 1(b)). Furthermore, the comparison of the response of Models C and E shows that the foundation flexibility does not dramatically change the ultimate capacity of the system. A similar trend in the structural response of the pier along both its strong and weak directions when the pier embedment and the pile cap resistance are neglected can also be observed (Figs. 3(a) and (f), and 4(a) and (f)). It is noted, however, that the global failure (full collapse) of Model F due to the pushover along the weak direction (Fig. 4 (f)) occurs at a larger displacement (17.93 in) in comparison to the pushover of this model along the strong direction (Fig. 3 (f)). The reason of the failure of Model F in both directions is the plastic behavior of the soil surrounding the piles, i.e. the pier behaves rigidly in comparison to the soil during pushover.
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Figure 4. Pushover analyses results along the weak (negative) direction of the pier for Models A-F described in Table 1.
Conclusions In this paper, a detailed pushover analysis is performed to estimate the effects of the numerical modeling approaches on the structural response of a flared tall pier with the consideration of SFS interaction. The numerical results indicate that the modeling assumptions of the SFS interaction can significantly influence the nonlinear response of tall bridges. For the system analyzed herein, the modeling of the pier embedment and pile cap resistance can be very significant, and ignoring either one of them can detrimentally affect its behavior. From a structural viewpoint, the appropriate selection of the concrete model may considerably modify the effect of the bond slip on the structural response; however, the foundation flexibility may delay and even reduce this effect. Acknowledgments This study was supported by the National Science Foundation under Grant No. CMMI-0900179. References 1.
Boulanger RW, Curras CJ, Kutter BL, Wilson DW, Abghari A. Seismic soil-pile-structure interaction experiments and analyses, Journal of Geotechnical and Geoenvironmental Engineering 1999, 125 (9): 750-759.
2.
Curras CJ, Boulanger RW, Kutter BL, Wilson DW. Dynamic experiments and analyses of a pile-groundsupported structure, Journal of Geotechnical and Geoenvironmental Engineering 2001, 127 (7): 585-596.
3. 4. 5.
Kornkasem W. Seismic behavior of pile-supported bridges, PhD thesis, University of Illinois at UrbanaChampaign, 2001. Rollins KM, Cole RT. Cyclic lateral load behavior of a pile cap and backfill, Journal of Geotechnical and Geoenvironmental Engineering 2006, 132 (9): 1143-1153. Rollins KM, Sparks A. Lateral resistance of full-scale pile cap with gravel backfill, Journal of Geotechnical and Geoenvironmental Engineering 2002, 128 (9): 711-723.
6.
Anderson DG, Martin GR, Lam I, Wang JN. Seismic analysis and design of retaining walls, buried structures, slopes, and embankments, Transportation Research Board, NCHRP Report 611, 2008.
7.
Comodromos EM, Papadopoulou MC. Explicit extension of the p-y method to pile groups in cohesive soils, Computers and Geotechnics 2013, 47 (1): 28-41. Rollins KM, Clayton RJ, Mikesell RC, Blaise BC. Drilled shaft side friction in gravelly soils, Journal of Geotechnical and Geoenvironmental Engineering 2005, 131 (8): 987-1003.
8. 9.
Mosher RL. Load transfer criteria for numerical analysis of axially loaded piles in sand, US Army Engineering Waterways Experimental Station, Automatic Data Processing Center, Vicksburg, Mississippi, 1984. 10. Vijayvergiya VN. Load-movement characteristics of piles, Proceedings, Ports 77 Conference, American Society of Civil Engineers 1977, Long Beach, CA, II: 269-286. 11. Wang MC, Liao WP. Active length of laterally loaded piles, Journal of Geotechnical Engineering 1987, 113 (9): 1044-1048. 12. Cole RT, Rollins KM. Passive earth pressure mobilization during cyclic loading, Journal of Geotechnical and Geoenvironmental Engineering 2006, 132 (9): 1154-1164. 13. Duncan JM, Mokwa RL. Passive earth pressures: theories and tests, Journal of Geotechnical and Geoenvironmental Engineering 2001, 127 (3): 248-257. 14. AASHTO LRFD Bridge Design Specifications, American Association of State Highway and Transportation Officials, 2005 Interim Revisions. 15. Caltrans Seismic Design Criteria Version 1.7, California Department of Transportation Division of Engineering Services, 2013. 16. Mander JB, Priestley MJN, Park R. Theoretical stress-strain model for confined concrete, Journal of Structural Engineering 1988, 114 (8): 1804-1825. 17. Kent DC, Park R. Flexural members with confined concrete, Journal of the Structural Division 1971, 97 (7): 51-93. 18. Scott BD, Park R, Priestley MJN. Stress-strain behavior of concrete confined by overlapping hoops at low and high strain rates, Journal of the American Concrete Institute 1982, 79 (1): 13-27. 19. Mazzoni S, McKenna F, Scott MH, Fenves GL, et al. OpenSees Command Language Manual, University of California at Berkeley, 2006. 20. Karsan ID, Jirsa JO. Behavior of concrete under compressive loading, Journal of Structural Division 1969, 95: ST12. 21. Zhao J, Sritharan S. Modeling of strain penetration effects in fiber-based analysis of reinforced concrete structures, ACI Structural Journal 2007, 104 (2): 133-141. 22. Douglas DJ, Davis EH. The movements of buried footings due to moment and horizontal load and the movement of anchor plates, Geotechnique 1964, 14 (2): 115-132. 23. Caquot A, Kerisel J. Tables for the calculation of passive pressure, active pressure and bearing capacity of foundations, translated by Bec MA. London, Gauthier-Villars, Paris, 1948. 24. Matsuzawa H, Ishibashi I, Kawamura M. Dynamic soil and water pressures of submerged soils, Journal of Geotechnical Engineering 1985, 111 (10): 1161-1176. 25. API recommended practice 2Z-WSD, Recommended practice for planning, design and constructing fixed offshore platforms-working stress design, 2005. 26. Kulhawy FH. Drilled shaft foundation, Foundation engineering handbook, Second edition, H. Y. Fang, ed., Van Nostrand-Reinhold, New York, 1991. 27. Bowles EJ. Foundation analysis and design, Fifth edition, McGraw-Hill, New York, 1996.
