Failure Envelope of Embedded Wall in Clay

Proceedings of the 6th ACEC and the 6th AEEC 21-22 November 2013, Bangkok, Thailand

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FAILURE ENVELOPE OF EMBEDDED WALLS IN CLAY SUBJECTED TO COMBINED HORIZONTAL

LOAD AND MOMENT Suraparb Keawsawasvong1, Boonchai Ukritchon2

1Graduate Student, Department of Civil Engineering, Chulalongkorn University, Bangkok 10330, Thailand, [email protected]

2Associate Professor, Department of Civil Engineering, Chulalongkorn University, Bangkok 10330, Thailand, [email protected]

Abstract At present, design processes of structures have become complicated such as those in offshore engineering or large bridge structures, etc. Generally, piles used in supporting those structures carry loads not only the vertical load direction, but also the horizontal direction arising from wave forces in the sea, wind loading or forces of earthquake actions. Those forces may result in damages and failures of structures if considering only the vertical direction. This research presents a study of undrained stability of embedded wall in clay subjected to combined horizontal load and moment. The 2D plane strain condition is considered in this analysis. The objective of this research is to determine the failure envelope of embedded wall subjected to horizontal load and moment. The studied parameters include untrained shear strength of the clay layer, the thickness of the wall (D), and wall embedded length (L). The results of analyses are presented in terms of dimensionless graph between normalized horizontal load, moment, and ratio of wall length to thickness (L/D). Finite element software, PLAXIS was used in this analysis. The embedded wall is set to have property of linear elastic material without failure consideration, while the clay is modeled as the Mohr-Coulomb material. The analyses consider ratio of wall length to thickness, ranging from 5-80 for wide practical applications. Series of failure envelopes were determined for each value of L/D. Results of this research can be applied in design and analysis of embedded walls, where their results are more accurate. In addition, they provide preliminary calculations for the similar loading cases of single pile in 3D problems.

Keywords: Numerical analysis, Combined loading, Plane strain, Finite element

Introduction In designing pile foundations of complex structures such as foundations of offshore structures or large structures such as bridges or high-rise buildings, it is not valid to consider loading of pile foundations of those structures to exist only the vertical load direction. Instead, loading considerations should include horizontal load direction as well as overturning moment in order to model the most realistic state. This is because in reality forces acting on those structures may include wave forces, wind loadings, or dynamics forces from earthquake actions. Such forces can cause horizontal load and moment acting on the top of individual pile. In the past, several research works presented calculations of ultimate lateral pile resistance, where comparisons of those methods were made in terms of advantages and disadvantages by Ruigrok (2010) [10] and Reese (2007) [11].

One of the most popular methods for analyzing ultimate lateral load on the pile is the method proposed by Blum (1932) [3] and Broms (1964, 1965) [1], [2]. Even though those two methods can be used to determine ultimate lateral resistance of pile, they are different in theoretical background in modeling lateral resistance of soil using simple geometrical earth pressure distribution. As a result, results of calculations may be incorrect and not


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accurate enough. In addition, Blum's method does not use input parameter of undrained shear strength in the calculation such that its modeling does not follow the actual situation when applying for the analysis case of cohesive soils.

At present, the analytical tools are more advanced that those in the past. The finite element method has become popular in analyzing ultimate load resistance of pile. Research works by Chaudry (1994) [8], Klar (2008) [4], and Zhang (2011) [5] were based on the finite element analyses in calculations of pile under lateral load. However, their results were not presented in terms of dimensionless chart between ultimate load and length or the graph of failure envelope. One of examples of failure envelope studies include the works by Ukritchon et al. (1998) [7] involving with limit state of strip footing, not pile.

The above mentioned works did not consider the combined loading of horizontal force and moment. In contrast, Ukritchon (1998) [9] and Huang (2007) [6] applied finite element limit analyses in determining the curve of failure envelope for the lateral force and moment of embedded wall. The characteristics of failure envelope for different types of loadings are shown in Figure 1b. Their results were based on the modeling of wall as plate element and did not consider the effect of wall thickness. However, the embedded wall structures have the finite thickness in actual conditions. Thus, the effect of wall thickness should be incorporated into the study and it is the objective of this paper.

This research presents the dimensionless graph between ultimate lateral load and length of embedded wall when subjected to horizontal force and moment. In addition, the results of this research also include the failure envelope for the general case of embedded wall acted by horizontal force and moment. The two dimensional finite element analyses, PLAXIS (Brinkgreve, 2002) [12], are used in this study. In particular, the embedded walls are modeled with solid elements with its finite thickness dimension as shown in Figure 1a, not using plate element like previous research works. As a result, its modeling corresponds to a more realistic case of embedded wall in the field. The next section explains important modeling issues and analysis details of this research.

(a) (b)

Figure 1. (a) Problem geometry of combined lateral load and moment, (b) Loading conditions


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Method of analysis

Model for analysis This research uses the commercial finite element software, PLAXIS 2D (Brinkgreve, 2002) [12]. The two dimensional plane strain geometry is used to model the embedded wall in the clay layer. The clay model is the Mohr-Coulomb material, where the undrained shear strength profile is homogeneous and isotropic. The undrained condition of the clay is modeled by the undrained type B, where state of stresses is effective stress, the stiffness and Poisson's ratio are effective types. But, the undrained shear strength, su is total stress, where the friction angle, = 0 and the dilatancy angle, = 0 in the analysis. The soil has the total unit weight of , and the effective Young's modulus, E/su = 200. It should be noted that the input value of soil unit weight does not have any effect to the limit load of this problem since the analysis condition is undrained.

The embedded wall is modeled as elastic material of the non-porous type. Its properties correspond to reinforced concrete wall, where the unit weight = 24 kN/m3, Poisson's ratio = 0.21 and Young's modulus = 2.545 107 kPa. Because of elastic material modeling of embedded wall, there is no failure of the wall in the analysis. This assumption is realistic in actual design practice. The embedded wall must be designed to have enough thickness and reinforcement in resisting shear and bending modes such that the failure of the system is governed by the failure of the soil before the failure of the wall happens. The embedded wall has the length of L, and thickness of D.

The boundary condition of this problem corresponds to a typical pattern used in finite element analysis of geotechnical engineering. The bottom boundary plane is defined as zero movements for both horizontal and vertical directions. The left and right boundary planes are defined as zero horizontal movement, while it only vertical movement is allowed, as shown in Figure 2.

The interaction between the clay and the wall is modeled using soil-structure interface. These interface elements are modeled around both sides of the embedded wall and at its base, as shown in Figure 2. The interface roughness between the clay and the wall is controlled by Rinter, which is the soil-wall adhesion factor. In this analysis, Rinter has the value of 0.67, which is the typical value for most soil-structure interface. Thus, according to the Mohr-Coulomb material, the undrained shear strength for the interface element, ci = 0.67su. In addition, for embedded wall subjected to horizontal force and moment, there is a possibility that separation can happen behind the interface between the clay and the wall. Thus, the condition of no-tension of effective stress is also applied at those interface elements.

The embedded wall is loaded at the top with the horizontal force, H and the moment, M. The results of analyses are presented in terms of relationship between dimensionless parameters of failure horizontal load, H/suD and embedded length ratio, L/D. The analyses consider several ratios of L/D, ranging from 5-80. The larger value of L/D, the more slender of the embedded wall. For each case of analysis, the thickness of the wall, D is changed while the length of the wall remains constant, giving rise to different values of L/D.


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(a) (b) Figure 2. Numerical models of finite element analysis, (a) Schematic model

(b) Geometry model

Mesh Model Figure 3 shows a typical mesh used in the finite element analysis of embedded wall subjected to horizontal load and moment at its top. Triangular types of solid elements are used for modeling both clay and wall. There are 15 nodes for each triangular element, corresponding to the cubic strain element type. In addition, very fine mesh distributions are employed in order to obtain accurate result of limit state.

Figure 3. Typical mesh used in the finite element analysis with 15 nodes and 12 stress

points

Results According to the modeling section of embedded wall as described earlier, results of present study are compared with previous research works for different aspects of analyses as follows.


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Comparisons with Bromss method (1964, 1965) [1], [2] Figure 4 shows a model of free head standing embedded wall proposed by Bromss method (1964, 1965) [1], [2]. The wall is extended above the ground surface by the eccentricity distance of e. Thus, when the parameter, e is divided by the length of the wall, L, additional dimensionless parameter, e/D becomes apparent, which is also one of normalized parameters used in Bromss method. The study compares ultimate lateral resistance of the present analyses with those of Broms, for the case of e/D = 0, 1, 8, and 16, as shown in Figure 5. It should be noted that the problem of free standing embedded wall loaded by purely horizontal force with the eccentricity distance, e, is statically equivalent to that of embedded wall subjected by horizontal force and moment applied at its top, where e=M/H.

In comparing with Bromss method, the ultimate lateral resistance of plane strain finite element analyses based on one unit length out-of-plane must be multiplied with the wall thickness in order to obtain the full load of the pile, assuming that the pile geometry is square or circular. It can be seen from Figure 5 that for all cases of L/D, the ultimate lateral resistance from Bromss method is significantly higher than about 1.5-1.7 times that from finite element analyses, particularly for very large values of L/D. However, the difference between those analyses seems to be much smaller for the case of smaller ratio of L/D.

Figure 4. Problem geometry of pile in Bromss (1964, 1965) [1], [2] model

(a) (b)


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(c) (d)

Figure 5. Comparison of ultimate lateral resistance between the finite element analysis and Broms (1965) [2], (a) e/D = 0, (b) e/D = 1, (c) e/D = 8, (d) e/D = 16

Purely Lateral load or Purely Applied Moment Figures 6-13 show examples of predicted failure mechanisms from finite element analyses. Figure 6-9 correspond to the case of purely lateral load of embedded wall, while Figure 10-13 correspond to the case of purely applied moment of embedded wall. For each case, the failure results include deformed mesh, total increment vector, and incremental shear strain contour. Comparisons are made for three cases of wall thickness ratio, L/D = 5, 40, and 80. The case of L/D = 5 corresponds to a relatively thick wall, while the case of L/D = 80 corresponds to a relatively slender wall. For purely horizontal load (Figure 6-9), the failure mechanism of the embedded wall happens such that the wall rotates about some point near its tip without translation movement of the wall. Near the ground surface, the front side fails in the passive state condition, while the back side fails in the active mode. On the other hand, for purely applied moment (Figure 10-13), the embedded wall fails by wall rotation at about the mid point of the wall without translation movement of the wall. The failure zone of passive and active modes of purely applied moment is much smaller than that of purely horizontal load.

Figure 6. Deformed mesh for purely lateral load, where L/D = 5, 40, 80


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Figure 7. Total increment vectors for purely lateral load, where L/D = 5, 40, 80

Figure 8. Incremental shear contours for purely lateral load, where L/D = 5, 40, 80

Figure 9. Plastic points of for purely lateral load, where L/D = 5, 40, 80

Figure 10. Deformed mesh for purely applied moment, where L/D = 5, 40, 80

Figure 11. Total increment vectors for purely applied moment, where L/D = 5, 40, 80


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Figure 12. Incremental shear strain contours for purely applied moment, where L/D = 5, 40, 80

Figure 13. Plastic points for purely applied moment, where L/D = 5, 40, 80 Figure 14 shows the results of purely horizontal ultimate load, H/suD or purely

ultimate moment, M/suLD for the case of plane strain condition without considering scaling effect to the actual pile geometry. It can be seen that the selected dimensionless terms, H/suD and M/suLD give the best result, yielding the linear relationship between those values and L/D. Thus, mathematical equation for predicting those values has much simpler form because of linear relationship.

(a) (b)

Figure 14. Normalized limit state solutions, (a) purely lateral load, (b) purely applied moment


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Combined Lateral load and Moment In order to include the complete loading state of embedded wall, this section presents the case of embedded wall subjected to combined horizontal load and moment. Figure 15-18 show the results of failure mechanism for the case of L/D = 5, 40, and 80. For all cases, the ratios of applied moment to horizontal load are constant, namely M/HL = 1/30. The failure mechanism of this case is similar that that of pure horizontal load. This is because the applied moment ratio, M/HL is small.

Figure 15. Deformed mesh of combined lateral load and moment, where L/D = 5, 40, 80, and M/HL = 1/30

Figure 16. Total increment vectors of combined lateral load and moment, where L/D = 5, 40, 80, and M/HL = 1/30

Figure 17. Incremental shear strain contour of combined lateral load and moment, where L/D = 5, 40, 80, and M/HL = 1/30

Figure 18. Plastic points of combined lateral load and moment, where L/D = 5, 40, 80, and M/HL = 1/30

The failure envelope of embedded wall subjected to combined lateral load and moment is obtained by analyzing two different cases, as shown in Figure 1b. The first case corresponds to the case where lateral load and moment produce overturning to the same


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direction, labeled as I in the first quadrant. The second case corresponds to the case where lateral load and moment produce overturning to the opposite direction, labeled as II in the second quadrant. The remaining of the graph in the third and fourth quadrants is obtained from the symmetry of the problem. In particular, the result of first quadrant is equal to that of the third quadrant, while that of the fourth quadrant is equal to that of the second one. The failure envelope is plotted as a function of ultimate lateral resistance, H/suD and ultimate moment resistance, M/suLD, as shown in Figure 19. Figure 19a, 19b, and 19c show the case of embedded wall ratios, L/D = 5, 40, and 80, while Figure 19d compares all failure envelopes for different values of L/D. It can be seen that each failure envelope has the form of elliptical shape, which is also rotated about 3/4 from the positive horizontal axis. However, the rotated ellipse is not symmetrical at its rotated major and minor axes. The non-symmetry of the ellipse happens at both ends of the major axis, resulting in distorted form of rotated ellipse. However, it can be seen that the distorted and rotated ellipse does hold convexity condition, where the classical concept of failure envelope is still valid. The size of rotated ellipse is controlled by the ratio of L/D. The higher the ratio of L/D, the larger the size of the rotated ellipse.

(a) (b)

(c) (d) Figure 19. Failure envelope for combined lateral load and moment, (a) L/D = 5, (b) L/D =

40, (c) L/D = 80, (d) Comparisons for all ratios of L/D = 5, 20, 40, 60, 80


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Comparison of Failure envelope with Ukritchon (1998) [7] Figure 20 compares the failure envelope from the finite element analysis of the present study and that of Ukritchon (1998) [7]. It should be noted that the results of Ukritchon (1998) are based on the lower (LB) and upper bound (UB) finite element limit analysis and do not consider the effect of wall thickness. In comparing results, the failure envelopes has to be replotted and normalized only by the wall length, L, giving rise to dimensionless parameters as H/suL and M/suL2. It can be seen that the failure envelope of the two results has similar form of rotated nonsymmetrical ellipse, while their size are significantly different. The failure envelope reported by Ukritchon (1998) is much smaller than that of the present study because of different modeling in no-tension condition of soil-structure interface element. For results of Ukritchon (1998), no-tension condition of interface element is modeled such that the total normal stress is always compressive. But, the present study models no-tension condition of interface element such that the effective normal stress is always compressive.

Figure 20. Comparison of failure envelope between the present study and Ukritchon (1998)

Conclusions This research presents the use of two dimensional plane strain finite element model in analyzing ultimate state of embedded wall subjected to combined horizontal load and moment. Unlike previous research works in the past, the present study considers the effect of wall thickness, which corresponds to a more realistic case in the field. The results of analyses are presented in terms of dimensionless variables, namely 1) embedded length thickness ratio, L/D; 2) normalized ultimate lateral resistance, H/suD; and 3) normalized ultimate moment resistance, M/suLD. The ratio of L/D is modeled to have different ranges from 5-80. The studies include analysis of the limit state for purely lateral load, purely applied moment, and combined lateral and moment. The studied results can be used in analyzing and designing embedded wall for plane strain condition or actual pile geometry. However, the latter case requires simple scaling from plane strain solutions to obtain the limit state of actual pile. Comparisons of the latter case show that the ultimate lateral resistance scaled from the plane strain condition is much smaller than that of Broms (1965) [2], which indicates that the results give much conservative calculations. In addition, the failure envelope of H-M has the form of rotated ellipse with distortion at both ends. The


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shape pattern of the present study is similar to that of Ukritchon (1998) [7], but the latter has smaller size due to different modeling of no-tension condition at soil-structure interface.

Acknowledgment The first author would like to thank the department of civil engineering, Chulalongkorn University for financial support of his graduate there, where he received the-100-year university celebration graduate research grant from the department. This allows him to pursue the master study for his interest in course works and research in geotechnical engineering, Chulalongkorn University.

References [1] B.B. Broms, Design of laterally loaded piles, Journal of the soil mechanics and

foundation, division 91 (3), 77-99, 1965. [2] B.B. Broms, Lateral resistance of piles in cohesive soils, Journal of the soil

mechanics and foundation, division 90 (2), 27-63, 1964. [3] H. Blum, Wirtschaftliche dalbenformen und deren berechnung, Bautechnik, Heft 5,

1932.

[4] A. Klar, M. F. Randolph, Upper-bound and load-displacement solution for laterally loaded piles in clays based on energy minimization, Gotechnique 58, N0. 10, 815-820, 2008.

[5] L. Zhang, Nonlinear analysis of laterally loaded rigid piles in cohesive soil, International journal for numerical and analytical method in geomechanics 2013, 37:201-220, 2011.

[6] M. Huang, Q. Huang, Ultimate lateral resistance of sheet pile walls by numerical lower bound analysis, Chinese Journal of Geotechnical Engineering 2007, Vol. 29, Issue (7), 988-994, 2007.

[7] B. Ukritchon, A.J. Whittle, S.W. Sloan, Undrained limit analysis for combined loading of strip footings on clay, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 124(1): 265276, 1998.

[8] A.R. Chaudhry. Static pile-soil-pile Interaction in Offshore pile groups. Thesis (PhD), University of Oxford, England, 1994.

[9] B. Ukritchon. Application of Numerical limit analyses for Undrained stability problems in clay. Thesis (PhD), Massachusetts Institute of technology, USA, 1998.

[10] J.A.T. Ruigrok. Laterally loaded piles models and measurements. Thesis (PhD), Delft University of Technology, Netherlands, 2010.

[11] L.C. Reese, W.F. Van Impe, Single piles and pile groups under lateral loading, Taylor & Francis Group plc, London, UK, 2007.

[12] R.B.J. Brinkgreve, et al., Plaxis 2D Version 8 Manual, A.A. Balkema Publishers, Netherlands, 2002.

Documents

Failure Envelope of Embedded Wall in Clay