Application of p-y approach in analyzing pile foundations in frozen ground overlying liquefiable soils

http://www.scar.ac.cn Sciences in Cold and Arid Regions 2013, 5(4): 0368 0376 DOI: 10.3724/SP.J.1226.2013.00368 Application of p-y approach in analyzing pile foundations in frozen ground overlying liquefiable soils ZhaoHui Yang 1*, XiaoYu Zhang 2, XiaoXuan Ge 3, Elmer E. Marx 4 1. Dept. of Civil Engineering, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA 2. PND Engineers, Inc., 1506 West 36th Ave., Anchorage, AK 99503, USA 3. Northern Geotechnical Engineering, Inc., 11301 Olive Lane, Anchorage, AK 99515, USA 4. State of Alaska DOT&PF, Bridge Section, 3132 Channel Drive, Juneau, AK 99801, USA *Correspondence to: Ph.D., ZhaoHui Yang, Professor of Dept. of Civil Engineering, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA. Tel: (907) 786-6431; Fax: (907) 786-1079; E-mail: zyang2@uaa.alaska.edu Received: May 18, 2013 Accepted: July 19, 2013 ABSTRACT Two major earthquakes in Alaska, namely the 1964 Great Alaska Earthquake and the 2002 Denali Earthquake, occurred in winter seasons when the ground crust was frozen. None of the then-existing foundation types was able to withstand the force from the lateral spreading of frozen crust. This paper presents results from the analysis of pile foundations in frozen ground overlying liquefiable soil utilizing the Beam-on-Nonlinear-Winkler-Foundation (BNWF) (or p-y approach). P-multipliers were applied on traditional sandy soil p-y curves to simulate soil strength degradation during liquefaction. Frozen soil p-y curves were constructed based on a model proposed in a recent study and the frozen soil mechanical properties obtained from testing of naturally frozen soils. Pile response results from the p-y approach were presented along with those from fluid-solid coupled Finite Element (FE) modeling for comparison purpose. Finally, the sensitivity of pile response to frozen soil parameters was investigated and a brief discussion is presented. Keywords: frozen ground crust; lateral spreading; liquefaction; p-y approach; pile foundation 1 Introduction Liquefaction and associated ground failures have been commonly observed in past major earthquakes across the world. A substantial portion of these ground failures and structural damages was a direct result of or related to liquefaction and lateral spreading of the ground crust. Lateral spreading is particularly damaging if a non-liquefiable crust rides on top of a liquefied soil (e.g., Hamada et al., 1986; Japanese Geotechnical Society (JGS), 1996, 1998). One of the lessons learned from two major earthquakes in Alaska was that the freezing of ground crust can generate greater lateral forces that are crucial when considering northern-area foundation design (Ross et al., 1973; Shannon and Wilson Inc., 2002). Li et al. (2011) studied the effect of ground crust freezing on pile performance embedded in lateral spreading condition using solid-fluid coupled Finite Element modeling. Two cases of the same soil-foundation system were modeled: one named "frozen case" (with a frozen ground crust) representing typical winter conditions in Alaska, and the other named "unfrozen case" (with an unfrozen ground crust) representing summer conditions. Both models have liquefiable soils underlying the ground crust which has a small slope angle that is common in a bridge site. It was found that pile bending moment near the crust-liquefiable soil interface increase significantly from unfrozen case to frozen case, suggesting a larger demand in bending capacity. Zhang et al. (2012) proposed a simplified method which utilizes the frozen soil p-y model developed by Li (2011). This p-y approach was proven effective in predicting pile performance under lateral spreading. This p-y approach was further validated by results from a shake table test as reported in Yang et al. (2012b).

369 This paper briefly introduces the p-y approach in predicting pile performance under lateral spreading conditions in cold regions. Frozen soil p-y curve is used to simulate frozen soil-pile interaction. Also, the latest results of naturally frozen soil testing are used to construct p-y curves. The pile performance predicted by the p-y approach is discussed and compared with solid-fluid coupled Finite Element modeling results. In addition, the sensitivity of the pile performance to the frozen soil property is analyzed. 2 Frozen soil p-y curve 2.1 Frozen soil p-y model To simulate the interaction of frozen soil and pile, an appropriate p-y model is essential. Crowther (1990) carried out a study to analyze laterally loaded piles embedded in layered frozen soil and had constructed a frozen soil p-y curve based on frozen soil shear strength and strain criteria and considered creep effect, which made it inappropriate for analysis of pile performance during earthquake loading. Li (2011) proposed a p-y curve based on back-calculated p-y values and existing p-y curves for weak rock (Reese, 1997) and clay (Matlock, 1970). This frozen soil p-y curve was used in this study. Figure 1 shows the p-y model, which consists of a cubic section and a constant section, as described by Equations (1) and (2). the pile diameter and x fs is the frozen soil depth. y m is the pile deflection corresponding to half of the ultimate soil resistance, p u. y m = k m b (5) where k m is a constant and equals to the strain at which 50% of the ultimate strength is developed. The value of y u can be determined by solving for the intersection of Equations (1) and (2), and is expressed in Equation (6). 2.2 Frozen soil properties y u = 8y m (6) In order to construct the p-y curve for a specific type of frozen soil, two mechanical properties of frozen soil are needed: q u and k m. However, frozen soil properties including stiffness, shear strength and permeability can change by orders of magnitude (Akili, 1971; Stevens, 1973; Haynes and Karalius, 1977; Vinson et al., 1983; Zhu and Carbee, 1983; Zhang, 2009). A testing program using naturally frozen soils including seasonally frozen soil and permafrost was carried out to study these mechanical properties (Yang et al., 2012a). Forty-five seasonally frozen soil and 23 permafrost specimens of high quality and different orientation, including vertical and horizontal, were tested. Testing results show that, for the seasonally frozen soil specimens tested, k m varies from 0.04% to 0.12% and does not show any obvious relation to temperature. q u varies from 1.9 to 7.1 MPa and can be approximated by a linear function of temperature, T, as defined in Equation (7). Figures 2 and 3 show the test results of the compressive strength (q u = σ m ) and strain corresponding to 50% of the compressive strength (k m = ε 50 ). Detailed testing results can be found in Yang et al. (2012b). q u = σ m = 0.35 T + 1.80 ( 12 C < T < 2 C) (7) Figure 1 Sketch of the p-y curve for frozen soil (Li, 2011) p = (p u /2)*(y/y m ) 1/3 for y y u (1) p= p u for y>y u (2) where p u is the ultimate resistance of frozen soil and can be derived through Equations (3) and (4); p represents soil lateral resistance per pile unit length (kn/m); and y is the lateral deflection corresponding to each lateral load p. p u = q u b[1.5+0.25(x fs /b)] for 0 X fs 12b (3) p u = 4.5q u b for X fs >12b (4) where q u is the compressive strength of the frozen soil, b is 3 Analysis of pile performance with p-y approach 3.1 Soil-pile system Concrete-filled steel-pipe (CSP) piles are widely used for constructing highway bridge foundations in Alaska. For this analysis, pile dimensions and parameters were selected based on the North Fork Campbell Creek Bridge constructed in 2007 in Anchorage, Alaska. The total length of the piles is 24 m with 3 m above the ground surface. An idealized soil profile was created based on soil conditions at this site. The soil profile has a 2-m-thick ground crust layer consisting of clayey silts that freezes in winter and thaws in summer (also referred to as the active layer). The 2-m-thick active layer overlies a 6-m-thick loose sand layer resting on a 6-m-thick medium dense sand layer and a 7-m-thick dense sand layer. A 3 sloping ground surface as

370 measured at the site was used. All the soil layers except for the active layer are assumed to be saturated. Figure 4 illustrates the typical soil profile at the bridge site. Table 1 pre- sents the properties of the unfrozen soil layers. A temperature profile decreasing linearly from 12 to 0 C was assumed for the frozen active layer. Figure 2 Ultimate compressive strength vs. temperature for seasonally frozen soil. CH refers to horizontally oriented soil specimens, and CV refers to vertically oriented specimens Figure 3 ε 50 (k m as used in this paper) vs. temperature Figure 4 The soil-pile system of a typical bridge foundation used in Alaska The CSP pile has an outer diameter of 0.9 m and a wall thickness of 0.019 m (D/t = 48). Ten steel reinforcing bars (#11) are evenly placed at 0.4 m away from the pile center, which represents a longitudinal reinforcing ratio of 1.52%. Note that the CSP pile connects with the cap beam with a 5-cm gap by which only the reinforced-concrete portion of the pile is extended to the cap beam. Figure 5 shows both the CSP and "gap" sections of the foundation. This "gap" section of the pile has a much smaller plastic hinging moment than the CSP section. This gap design intends to prevent hinging in the pile cap beam by acting as a seismic "fuse". A moment-curvature analysis was conducted based on steel and concrete parameters, and the results are shown in Figures 6 and 7. The first yield bending moment (M y ) and ultimate moment capacity (M c ) of the pile sections were determined by the yield and rupture strains of the outmost steel fibers, respectively. The CSP section has a M y of 6,200 kn m and M c of 11,000 kn m, and the "gap" section has a M y of 1,096

371 kn m and M c of 1,894 kn m. Figure 5 Configuration of the "gap" and the CSP sections moment-curvature relations. The unfrozen sands are modeled with the p-y curve proposed by the American Petroleum Institute (API) (1987). Under seismic loading, liquefaction occurs below the frozen crust and ground lateral deformations occur. Lateral spreading was assumed constant in the frozen ground crust and linearly decreasing in the liquefied loose and medium sand layers. Figure 8 shows a sketch of the lateral spreading demands. The far-field ground displacement obtained from the FE model (Zhang, 2012), 1.43 m, was applied at the ground crust. In practice, the free-field displacement can be estimated using empirical or analytical methods. The pile top was not allowed to rotate due to constraint of the bridge superstructure and pile cap beam. A constant constraint force (estimated as 1,500 kn) was applied on the pile top in an opposing direction to simulate bridge deck constraint. Figure 6 Moment-curvature curve for the "gap" section Figure 8 Imposed displacement loading 3.3 The p-y curves Figure 7 Moment-curvature curve for the CSP section 3.2 Modeling with p-y approach LPILE (http://www.ensoftinc.com) was used to perform the lateral analysis. LPILE is a commercial program to analyze laterally loaded piles using the p-y method. The capability of defining user-input p-y curves enables the simulation of frozen soil-pile interaction. The total length of the pile is 25.05 m and it was discretized into 500 elements with soil p-y springs connected with each pile node below the ground surface. Two nonlinear sections the CSP section and the "gap" section were defined based on the specified The p-y curve proposed by Li (2011) was used to model frozen soil. Table 2 summarizes the soil parameters used in this analysis. The user-input p-y curves were specified in LPILE for the top (0 m) and bottom layer ( 2 m) of the frozen crust and these curves are shown in Figure 9. For unspecified frozen soil layers, LPILE uses linear interpolation to generate the p-y curve. As can be seen from Figure 9, the p-y curve at the ground surface is much stiffer than that at the bottom of the frozen crust, due to temperature increase with depth. Soil lateral resistance reduction in loose and medium dense sand layers due to full or partial liquefaction needs to be considered. P-multipliers were used to approximate soil resistance reduction in this analysis. Referring to the solid-fluid coupled Finite Element modeling (Zhang, 2012), excess pore pressure ratios (r u ) induced for loose and medium dense sand layers was used to determine these ratios. The loose and medium dense sand layers were assumed

372 fully liquefied (i.e., r u =100%), and a p-multiplier of 0.1 was used; the dense sand layer only underwent partial liquefaction and a p-multiplier of 0.5 was used. A sketch of the p-multiplier variation with pile depth is shown in Figure 10. 4 Results 4.1 P-y curves at selected depths Figures 11 and 12 show the p-y curves for frozen crust and sand layers, respectively. Comparing these figures, one can see that the frozen soil p-y curves are generally much stronger than the unfrozen layers. Even though at a depth of 20 m, dense sand exhibits high ultimate soil resistance ranging from 4,500 to 5,500 kn/m, the corresponding deflection value for the ultimate resistance is much larger than that of frozen soil. Note that frozen soil resistance decreases with depth due to increasing temperature while unfrozen sand resistance increases with depth due to increased effective confinement. Depth (m) Soil type Status Table 1 Summary of the soil properties for unfrozen layers Permeability, k (m/s) Mass density, γ (kg/m 3 ) Shear modulus, G (kpa) Bulk modulus, K (kpa) Friction angle, φ ( ) 2 to 8 Loose sand Unfrozen 6.6 10 5 1.9 10 3 5.5 10 4 1.5 10 5 30 0.1 8 to 14 Medium dense sand Unfrozen 6.6 10 5 1.9 10 3 7.5 10 4 2.0 10 5 33 0.1 14 to 21 Dense sand Unfrozen 6.6 10 5 2.1 10 3 1.3 10 5 3.9 10 5 40 0.1 Peak shear strain, γ max Soil type Depth (m) Status Table 2 Soil parameters for defining p-y curves Effective unit weight, γ (kn/m 3 ) Friction angle, φ ( ) Soil modulus, k (kpa/m) Axial strain corresponding to 50% of ultimate compressive strength, ε 50 Unconfined ultimate compressive strength, q u (MPa) Frozen soil 0 12 C 18 0.001 5.8 Frozen soil 2 1 C 18 0.001 2.0 Loose sand 2 to 8 Unfrozen 7 29 5,430 Medium dense sand 8 to 14 Unfrozen 10 35 16,000 Dense sand 14 to 21 Unfrozen 11 40 33,900 Figure 9 User-defined p-y curves for frozen silts Figure 10 P-multipliers distribution along pile depth. r u refers to excess pore pressure ratio

Figure 11 P-y curves for the frozen crust 4.2 Pile response Figures 13a to 13d show the displacement, rotation, bending moment and shear force results obtained from the Figure 13 373 Figure 12 P-y curves for sand layers LPILE analysis, respectively. For comparative purposes, the maximum values of corresponding variables from the solid-fluid coupled FE modeling (Zhang, 2012) are also shown. Comparison of results from the LPILE analysis and the solid-fluid coupled FE modeling The predicted pile deflection shape from the LPILE analysis agrees well with that from the FE modeling (Figure 13a). However, the confinement effect of the frozen ground crust as modeled by LPILE seems to be less pronounced because the undeformed portion of the pile is effectively shorter for the LPILE analysis than was found in the FE analysis.

374 This is further shown by comparing the rotation of the pile shown in Figure 13b. In the FE model, a sharp rotation change of the pile occurs at the bottom of the frozen crust; a similar change in rotation occurs within the frozen crust layer in the LPILE model. This implies the p-y curves for frozen soil may be too soft as defined in the LPILE analysis. Figure 13c shows the bending moment distribution along the pile depth. It is evident that prediction by the p-y approach compares favorably with that from the FE modeling. The p-y approach is able to predict the formation of the two plastic hinges (location where the moment demand exceeds the yield moment) at locations similar to those predicted by the FE modeling. However, the peak bending moments at both plastic hinges were under-predicted by the p-y approach. The p-y approach predicts that the maximum bending moment for the upper plastic hinge is 10,390 kn m (11,060 kn m by the FE model), and that for the lower plastic hinge is 8,963 kn m (11,620 kn m by the FE model). The p-y approach under-predicts the maximum bending moment of the upper and lower plastic hinges by 6% and 23%, respectively. It is likely that the prediction of the maximum bending, particularly for the lower plastic hinge, can be improved by using a different approach in selecting the p-multipliers used to account for degradation of the liquefied soil resistance. Figure 13d shows the shear force distribution versus depth. For the p-y approach, the shear force changes sharply in the frozen crust in a similar manner as observed for the FE model. It changes slowly in loose and medium dense sand layers because of low soil resistance due to partial or full liquefaction. The p-y approach predicts that the maximum shear force in the frozen crust is 5,987 kn m (9,330 kn m by the FE model). This suggests that the p-y curves used in this analysis are on the soft side. 5 Sensitivity of pile response to the frozen soil properties and p-multipliers As shown previously in Figures 2 and 3, q u and ε 50 of frozen soil fall into relatively large ranges. In order to study the sensitivity of pile performance to these soil parameters, two extreme cases, namely a stiff case and a soft case, are modeled. In the stiff case, the upper-bound q u and lower-bound ε 50 were used to construct frozen soil p-y curves, while in the soft case, the lower-bound q u and upper-bound ε 50 were applied. The pile dimensions and soil parameters except for frozen soil are identical as introduced in Section 3. Table 3 summarizes the soil parameters for the sensitivity study. Figures 14a, b compare the frozen soil p-y curves at 0.0 m, 0.5 m, 1.0 m, 1.5 m and 2.0 m for the stiff case and soft case, respectively. Depth (m) Temperature ( C) Table 3 Soil parameters defining p-y curves Soft case ε 50-max [d] q u-max [e] (MPa) Stiff case ε 50-min [f] (%) q [g] u-min (MPa) (%) 0 12 4.4 0.07 7.1 0.04 0.5 9 3.2 0.12 6.4 0.05 1.0 6 2.5 0.12 5.4 0.04 1.5 3 2.2 0.12 3.0 0.06 2.0 1 1.6 0.12 3.0 0.06 Figure 14 P-y curves for frozen silts for sensitivity study: (a) stiff case; (b) soft case

375 Figure 15 shows the bending moment and curvature of the pile versus depth for the stiff and soft cases. It is seen from Figure 15a that only the upper plastic hinge zone is sensitive to the variation of frozen soil resistance. For the upper plastic hinge zone, the maximum bending moment for the soft case is 9,200 kn m, and that for the stiff case is 9,900 kn m, or 8% increase. Because these are plastic moments, this difference is not expected to be large. Also, the location of the upper plastic hinge is not sensitive to frozen soil resistance. From Figure 15b, however, the maximum curvature for the upper plastic hinge zone increases from 0.050 rad/m to 0.085 rad/m from the soft case to the stiff case, or 70% increase. This result indicates that the effective plastic hinge length is reduced in the stiff case and demonstrates that a greater strain in the pipe is anticipated for the same deformation demand. Stated another way, the analytical plastic hinge length is reduced as the frozen soil stiffness increases. Figure 15 Bending moment and curvature versus depth The p-multiplier approach has been successfully applied to the p-y resistance of sand for approximating the effects of liquefaction on soil resistance reduction for design purposes (Boulanger et al., 1997; Wilson, 1998; JRA, 2002). However, there are different methods to select p-multipliers and the suggested p-multiplier values vary widely. For example, Ashford and Rollins (2002) suggest that the p-multiplier can vary from 0.0 to 0.3 for loose and medium dense sand, and from 0.2 to 0.5 for dense sand. To investigate the sensitivity of pile responses to p-multipliers in frozen soil conditions, two cases were considered in this analysis. As listed in Table 4, one case was defined with the lower value of the p-multiplier used for each layer (referred to as p-multiplier min ), and the other was defined with the higher value for each layer (referred to as p-multiplier max ). The stiffest frozen crust resistance was used for both cases. Figure 16a compared the bending moment results from these two cases, and Figure 16b compared the curvature of these two cases. Figures 16a,b indicated that the variation of p-multipliers only affect the response of the lower plastic hinge. For the lower plastic hinge, the maximum bending moment for the p-multiplier min case is 9,300 kn m, and that for the p-multiplier max case is 9,800 kn m, or 5% increase. Figure 16b shows, however, when the p-multiplier changes from lower to higher values, the maximum curvature for the lower plastic hinge increases from 0.055 rad/m to 0.080 rad/m, or 45% increase. Also, the location of the plastic hinge only changes slightly. In summary, the curvature of the lower plastic hinge is sensitive to the p-multiplier. The location of the lower plastic, curvature, and location of the upper plastic hinge are not sensitive to the p-multiplier. As with the stiffer frozen soil condition, the analytical plastic hinge length is found to decrease with increasing liquefied soil stiffness (larger p-multipliers). Table 4 Range of the p-multiplier values Case Frozen crust Loose sand and medium dense sand layers Dense sand layer p-multiplier max 1 0.3 0.5 p-multiplier min 1 0.0 0.2 6 Conclusion The p-y approach was used to predict pile foundation response in laterally spreading ground with a frozen crust. The sensitivity of the pile foundation to frozen soil mechanical properties and the p-multipliers was investigated. A good agreement in terms of pile deformation, shear force, and bending moment was found between the results obtained from the p-y approach and those from fluid-solid coupled FE modeling. It is therefore concluded that the p-y

376 approach is quite effective in modeling the performance of pile foundations subject to lateral spreading with the presence of a frozen crust. This study also found that pile foundation response, particularly the curvature at the upper or lower plastic hinge, is sensitive to frozen soil resistance or the liquefied soil p-multiplier. In general, the analytical plastic hinge length of the pile decreases with increasing soil stiffness and, consequently, the steel pipe strains are greater in stiffer soils for a given deformation. It is therefore recommended that efforts should be devoted to obtaining accurate evaluation of the mechanical properties of frozen crust and selecting p-multipliers in design practices. 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