EVALUATION OF IN-GROUND PLASTIC- HINGE LENGTH AND DEPTH RECOMMENDATIONS FOR PILES IN MARINE OIL AND LNG TERMINALS

Transcription

1 California Polytechnic State University, San Luis Obispo From the SelectedWorks of Rakesh K. Goel July, 1 EVALUATION OF IN-GROUND PLASTIC- HINGE LENGTH AND DEPTH RECOMMENDATIONS FOR PILES IN MARINE OIL AND LNG TERMINALS Rakesh K. Goel, California Polytechnic State University - San Luis Obispo Available at:

2 REPORT No. CP/SEAM-1/1 STRUCTURAL ENGINEERING AND APPLIED MECHANICS EVALUATION OF IN-GROUND PLASTIC-HINGE LENGTH AND DEPTH RECOMMENDATIONS FOR PILES IN MARINE OIL AND LNG TERMINALS BY RAKESH K. GOEL FINAL REPORT PREPARED FOR CALIFORNIA STATE LANDS COMMISSION CONTRACT NO. C- July, 1 Department of Civil and Environmental Engineering California Polytechnic State University San Luis Obispo, CA 7

3 ABSTRACT This investigation evaluated the current recommendations for plastic-hinge length and depth for pre-stressed concrete and hollow-steel piles for different soil conditions typical of those in Marine Oil and LNG Terminals. Nonlinear behavior for both pile and soil were considered and MOTEMS specified strain levels were used to compute the pile capacity. All analyses in this study were conducted using OpenSees software developed at the Pacific Earthquake Engineering Research Center. The approach used in this investigation for estimating the plastic-hinge length and depth is similar to that used in development of current MOTEMS recommendations. This investigation led to several important findings that have significant implications for estimating seismic capacity of piles in Marine Oil and LNG Terminals. The plastic-hinge length was found to be different for two MOTEMS seismic design levels: longer for level 1 compared to level seismic design of pre-stressed concrete piles, and longer for level compared to level 1 seismic design for hollow-steel piles. These trends were related to the slope of the curvature distribution in the plastic-hinge region: a milder slope led to longer plastic-hinge length and vice versa. It was found that the slope of the curvature distribution became steeper for level compared to level 1 after the crushing of concrete in pre-stressed concrete piles due to brittle material behavior, whereas it became milder for level compared to level 1 for hollow-steel piles due to ductile material behavior. For pre-stressed concrete piles, the MOTEM recommended plastic-hinge length is adequate for the level design whereas the POLB recommendation is adequate for level design for certain pile and soil configurations only. When inadequate, the POLB recommendation may lead to an un-conservatively larger seismic displacement capacity estimation. The MOTEMS as well as the POLB recommended plastic-hinge lengths for level 1 are much smaller than the values found in this investigation and thus will lead to overly conservative lower pile displacement capacity for seismic design level 1. Furthermore, the current recommendations lead to a depth of plastichinge that is much shallower than that found in this investigation: approximately one-diameter in the current recommendations versus two- to seven-diameters found in the current study depending on soil type. For hollow-steel piles, MOTEMS do not specify the plastic-hinge length but POLB specifies a value of two-diameter. It is found that the POLB recommendation in most cases leads to a much shorter plastic-hinge length which may lead to an overly-conservative smaller seismic displacement capacity. While there are no recommendations for depth of plastic-hinge in hollowsteel piles, this investigation found it to vary between three- and twelve-diameters depending on the soil type. The results were found to be independent of the pile diameter. It was found that the depth of the plastic-hinge below ground is independent of the MOTEMS seismic design level for both pre-stressed concrete and hollow-steel piles and the plastic-hinge migrates deeper for softer soils. The plastic-hinge length is essentially unaffected by the lower- and upper-bound soil properties for the three types of sands considered in this investigation. For clays, however, the plastic-hinge length tends to be longer for lower-bound and shorter for upper-bound soil properties compared to the nominal soil value. Furthermore, the plastic-hinge depth, in general, is shallower for upper-bound and deeper for lower-bound soil properties because the plastic-hinge tends to migrate deeper for softer soils. i

4 The general engineering practice uses a single value of plastic-hinge length in estimating displacement capacity of piles for both seismic design levels. Since results presented in this investigation show that plastic-hinge lengths for the two design levels may differ significantly, it is recommended that that two separate analyses be conducted using different plastic-hinge lengths for the two seismic design levels to more realistically estimate the displacement capacity at both design levels. ii

5 ACKNOWLEDGMENTS This research investigation is supported by the California State Lands Commission (CSLC) under Contract No. C- for Development of LNGTEMS/MOTEMS Performance-Based Seismic Criteria. This support is gratefully acknowledged. The author would especially like to thank Dr. Avinash Nafday and Martin Eskijian, who were the CSLC Project Managers for this contract. Also acknowledged are contributions of Hosny Hakim, John Freckman, Kendra Oliver, and Alex Augustin, all from the CLC for their valuable feedback during this project. In addition, the author wishes to acknowledge contribution of Drs. Arul Arumoli and Raj Vartharaj in developing soil properties used in the reported investigation. The results used to prepare a few figures in this report were generated by Neda Saeedy, graduate student in the Department of Civil and Environmental Engineering at California Polytechnic State University, San Luis Obispo, as part of her master s thesis. The author also wishes to acknowledge her contributions to this report. iii

6 TABLE OF CONTENTS ABSTRACT... I ACKNOWLEDGMENTS... III TABLE OF CONTENTS... IV INTRODUCTION... 1 ANALYTICAL APPROACH... SOIL TYPES CONSIDERED... 7 VERIFICATION OF ANALYTICAL APPROACH PRE-STRESSED CONCRETE PILES... 1 HOLLOW-STEEL PILES... 1 CONCLUSIONS AND RECOMMENDATIONS... REFERENCES... 7 APPENDIX A: SELECTION OF DISTRIBUTED-PLASTICITY ELEMENT... iv

7 INTRODUCTION The current standard used for the engineering analysis of Marine Oil Terminals, the Marine Oil Terminal Engineering and Maintenance Standards (MOTEMS) (MOTEMS, 1), was developed by the California State Lands Commission and has been adopted as part of the California Building Code, Title, Part, Chapter 1F. It was developed as part of the Lempert- Keene-Seastrand Oil Prevention and Response Act of 1, which was passed by California legislature, and became an enforceable part of the California Building Code on February, (Eskijian, 7). MOTEMS describes the seismic analysis procedure for two performance levels and specifies earthquake motions to be used in the analysis. Level 1 has a 7-year return period, based on the risk level, and should cause no or minor damage with little to no interruption in service. Level, on the other hand, has a 7-year return period with controlled inelastic behavior with repairable damage and may results in temporary closure of service which should be restorable within months (Goel and Saeedy, ). In addition to the California Building Code, MOTEMS seismic provisions have been referenced in the National Earthquake Hazard Reduction Program and has become the approved methodology of the US military wharf and pier facilities in high seismic areas for seismic assessment (Eskijian, 7). Furthermore, MOTEMS provisions have been used in projects in Washington state (Wray et al., 7; Klusmeyer and Harn, ) which were not originally under the MOTEMS jurisdiction. Seismic analysis in MOTEMS requires that nonlinear static procedures be used to determine the seismic displacement capacity of piles in Marine Oil Terminal structures. Displacement capacity of a pile can be defined as the maximum displacement that can occur without exceeding material strain values (Goel and Saeedy, ). Estimation of displacement capacity of the pile according to the MOTEMS procedure requires monitoring of material strains during the nonlinear static pushover analysis. The pile is typically modeled as a Winkler beam (linearelastic beam-column elements connected at ends by nonlinear moment-rotation springs and laterally supported below the mud line by soil springs) (Figure 1). The rigid-perfectly-plastic moment-rotation relationship of the springs is computed from the moment-curvature relationship (Figure ) and the estimated length of the plastic-hinge. The limiting value of the plastic rotation in the hinge at a selected design level is defined as: P P L y 1 L (1) where P = plastic rotation, L = maximum pile-section curvature without exceeding MOTEMS specified material strain limits, y = yield curvature, and L p = plastic-hinge length. The relationship presented in Equation (1) was developed based on the simplifying assumption that the inelastic deformation in a cantilever member (Figure a) may be estimated by idealizing the actual height-wise distribution of curvature (dashed line in Figure c) with a distribution that includes superposition of a linear distribution with the maximum value equal to the yield curvature, y, at the cantilever base and a constant plastic curvature, P = L, over the plastichinge length at the base (solid lines in Figure c) (Priestley, et al., 1). The plastic-hinge length was calibrated so that the simplified curvature distribution gives the same plastic rotation and hence the same deflection as that in the actual structure. This indicates that the plastic-hinge length will be shorter if the slope of the curvature distribution in the plastic zone is steeper. On the other hand, the plastic-hinge length will be longer if the slope of the curvature distribution in the plastic-hinge zone is milder.

8 P P F F Linear Element Element Hinge Mud Line Mud Line Soil Spring Bedrock (a) Pile (b) Model with Hinges Figure 1: Computer modeling of piles in Marine Oil and LNG Terminals. M y M y Moment, M Moment, M φ y φ L θ P Curvature, φ Rotation, θ (a) M φ for Pile Section (b) M θ for Pile Hinge Figure : Pile moment-curvature and moment-rotation relationships.

9 Δ L L p φ p φ y (a) Member (b) BM (c) Curvature Figure. Inelastic deformation of a cantilever pile: (a) Member deformation, (b) Bending moment, and (c) Actual curvature (dashed line) and idealized curvature (solid line). Clearly, the typical analytical procedures that are used in seismic evaluation of piles in Marine Oil and LNG Terminals require a prior knowledge of plastic-hinge length, and plastic-hinge depth in some cases. The MOTEMS specified plastic-hinge length recommendations were adopted from those in Priestley et al. (1) which were based on the work by Budek et al. (1) (). These recommendations provide in-ground plastic-hinge length as a fraction of pile diameter for normalized stiffness and height parameters (Figure a). Although not specified in MOTEMS, Priestley et al. (1), and Budek et al. (1) () also make recommendations for in-ground plastic-hinge depth (Figure b). The in-ground plastic-hinge depth recommendations are needed to ensure sufficient confinement in the plastic-hinge region to avoid premature failure. Plastic-hinge depth is also specified as a fraction of pile diameter for normalized stiffness and height parameters (Figure b). Plastic Hinge Length / Pile Diameter H/D=1 H/D= H/D= H/D= H/D=. 1 (a) 1 KD /D * EI e Plastic Hinge Depth / Pile Diameter (b) H/D= H/D= H/D= H/D= H/D=1 1 1 KD /D * EI e Figure : Current recommendations for (a) Plastic-hinge length from MOTEMS Figure 1F- 7- and (b) Plastic-hinge depth from Priestley et al. (1). These recommendations were developed for a -ft (1. m) diameter Cast-In-Drilled-Hole (CIDH) reinforced concrete pile that is commonly used in bridges in California (Budek et al., 1). Also, the recommendations were developed based on the assumptions that (1) limiting material strain is equal to ultimate failure strain in confined concrete, () soil is linear elastic, and () subgrade modulus increases linearly with depth below ground. However, piles used in Marine Oil and LNG Terminals are much smaller in cross sectional area than the -ft (1. m) CIDH reinforced concrete piles used by Budek et al. (1). For example, new wharf type

10 terminals in the Ports of Long Beach and Los Angeles use -inch (.1 m) octagonal prestressed concrete piles. Also, the material strain limits in MOTEMS (Table 1) may differ significantly from those used by Budek at al. (1). In particular, MOTEMS specify different concrete compression and tensile steel strains for the two design levels which differ significantly from the ultimate failure strain in confined concrete used by Budek et al. (1). Finally the current practice uses nonlinear soil properties with lateral force-deformation relationships specified though p-y curves instead of an assumed linearly increasing subgrade modulus with depth. While wharf type Marine Oil and LNG terminals use the typical -inch octagonal concrete pile, steel pipe piles are also used on occasion. However, MOTEMS does not provide recommendations for in-ground plastic-hinge length for steel piles. For steel piles, MOTEMS merely states The plastic-hinge length depends on the section shape and the slope of the moment diagram in the vicinity of the plastic-hinge (MOTEMS, 1). Table 1: MOTEMS Material Strain Limits (Table 17F.) Component Strain Level 1 Level Maximum Concrete Compression Strain c. c. Pile-Deck Hinge Maximum Concrete Compression Strain Inground Hinge c. c. Maximum Reinforcing Steel Tension Strain s.1 s. Pile-Deck Hinge Maximum Reinforcing Steel Tension Strain.1. in-ground Hinge Maximum Prestressing Steel Tension Strain In-ground Hinge s p. (Incremental) s p. (Total) The recommendation for in-ground plastic-hinge length for steel piles is available in the Port of Long Beach (POLB) Wharf Design Criteria (Lai, ). Instead of earthquake level 1 and level, POLB specifies Operating Level Earthquake (OLE) and Contingency Level Earthquake (CLE). An OLE is the equivalent to MOTEMS level 1 with the same 7-year return period and limited damages, and a CLE is equivalent to MOTEMS level with the same 7-year return period and reparable damages. Thus for all future references, OLE and CLE will be referred to as level 1 and level, respectively. It is apparent from the discussion so far that there is a need to evaluate the plastic-hinge length and depth recommendation for typical piles and soil conditions that are used in Marine Oil and LNG Terminals. In order to fill this need, this study re-computed the plastic-hinge length and depth for a -inch (.1 m) octagonal pre-stressed concrete pile, and -, -, and -inch (.1 m,.1 m, and 1. m) steel pipe piles in six different soil conditions. The results of this study are used to evaluate the adequacy of current recommendations and suggest improvements when needed.

11 ANALYTICAL APPROACH To find the plastic-hinge length and depth, the pile (Figure a) was modeled in OpenSees software developed at the Pacific Earthquake Engineering Research Center (McKenna & Fenves, 1).The pile was modeled using force-based distributed-plasticity nonlinear beam-column elements (Figure b); reasons for selecting the force-based elements are presented in Appendix A. Fiber-sections are used to define the section properties of the nonlinear beam-column elements. A nonlinear static pushover analysis is conducted while monitoring material strains and element bending moments. The displacement capacity of the pile, Δ L, is defined as the maximum displacement at the top of the pile without exceeding selected material strain limits. The pushover curve is idealized as a bi-linear curve using an equal-area approach (Figure a) and the yield displacement, y, identified. The bending moments are also monitored during analysis. The location of the plastic-hinge is assumed to occur at the location of the maximum bending moment below ground (Figure c and d). The soil-springs (Figure b) are modeled using bilinear material to capture the nonlinear p-y curves. The spring stiffness is defined as the p-value times the tributary pile length for the node where the spring is attached. The pile above and below ground is modeled with distributed-plasticity elements. P P Δ L Δ y Δ p F F Mud Line Element Node Mud Line Nonlinear Element D p H D p Plastic Hinge Soil Spring Bedrock (a) Pile (b) Model (c) Bending Moment (d) Deflected Shape Figure : Analytical approach for estimating plastic-hinge length and depth. (a) (b) Force, F Δ y Δ L Moment, M Φ y Φ L Displacement, Δ Curvature, Φ Figure : (a) Pushover curve and its bi-linear idealization, and (b) Moment-curvature curve and its bi-linear idealization.

12 A moment-curvature analysis of the pile section is conducted while the material strains and curvature are monitored. The curvature, L, is defined as the maximum curvature without exceeding material strains. The yield curvature, y, is identified using a bi-linear idealization of the moment-curvature relationship (Figure b). The plastic-hinge length, L p, is calculated from L P P where L = maximum curvature, y = yield curvature, and P is the plastic rotation computed from P L y L y H D P in which L = displacement capacity, y = yield displacement, H = height of the pile from ground level (or mud-line) to the aboveground point of contraflexure (Figure d), and D P = Plastic-hinge depth. This approach is similar to that used by Budek et al. (1) in determining the plastic-hinge length and depth recommendations in Priestley et al. (1). The theoretical background presented in this section utilizes a cantilever pile (Figure ). For such piles, the length H is defined as the pile height above the mud-line (Figure d). Typical piles in Marin Oil Terminals, however, may have a fixed or semi-fixed pile-to-deck connection. In such cases, the above formulation still applies, but the length H is defined as height of the pile from ground level (or mud-line) to the aboveground point of contraflexure. () ()

13 SOIL TYPES CONSIDERED Six soil types were considered in this investigation: dense sand, medium sand, loose sand, stiff clay, medium clay, and soft clay (Table ). The soil was modeled as springs below the mud line at the nodes of each beam-column element (Figure b). The nonlinear p-y curves (Figures 7 to ), as well as upper- and lower-bound multipliers, were provided by Arumoli and Vartharaj (1). The lateral force-deformation relationships of soil-springs below ground level are defined by the p-y curves. The upper-bound and lower-bound p-y curves were obtained by multiplying the p-values by 1. and.7 for upper- and lower-bound curves respectively, for all soil conditions. These bounds are intended to encompass all possible soil characteristics, since the values in Table are average values. The subgrade modulus values reported in Table are taken from Table 1F-7- of MOTEMS. Table : Soil Conditions Considered and Subgrade Modulus (Table 1F-7- of MOTEMS). MOTEMS Site Class Shear Wave Velocity (API sand) D. Dense soil - ft/s 1- m/s E. Loose soil < ft/s < 1 m/s (Matlock) D. Dense soil - ft/s 1- m/s E. Loose soil < ft/s < 1 m/s Stand Penetration Resistance Undrained Shear Strength Soil Type Subgrade Modulus, K to Dense 7 pcf kn/m Medium pcf 11 kn/m < Loose pcf 7 kn/m 1- psf - kn/m Stiff pcf 7 kn/m < 1 psf Medium 1 pcf < kn/m 7 kn/m Soft pcf 1 kn/m 7

14 p, kn/m 1 Dense 1 Stiff.... Medium.... Medium p, kn/m Loose Soft p, kn/m.... y, m.... y, m Figure 7: P-Y curves with upper- and lower-bound values for -inch (.1 m) diameter pile.

15 p, kn/m 1 Dense 1 Stiff p, kn/m Medium.... Loose Medium.... Soft p, kn/m y, m.... y, m Figure : P-Y curves with upper- and lower-bound values for -inch (.1 m) diameter pile.

16 p, kn/m 1 Dense 1 Stiff p, kn/m Medium.... Loose Medium.... Soft p, kn/m y, m.... y, m Figure : P-Y curves with upper- and lower-bound values for -inch (1. m) diameter pile. 1

17 VERIFICATION OF ANALYTICAL APPROACH As mentioned previously, the plastic-hinge length and depth recommendations were developed for a -ft (1. m) diameter Cast-In-Drilled-Hole (CIDH) reinforced concrete piles commonly used in bridges in California at the time (Budek et al., 1, ). The original study used simple modeling for capturing nonlinear behavior of pile element: stiffness of each element was softened after initial yielding based on the slope of the moment-curvature at the selected stage (Budek et al., 1). Analyses in the current study were conducted using OpenSees software developed at the Pacific Earthquake Engineering Research Center (McKenna and Fenves, 1). This software is capable of modeling pile elements with distributed-plasticity elements with pile sections modeled as fiber section consisting of un-confined concrete, confined concrete, and steel fibers. Clearly, the analytical approach used by Budek et al. (1) differs from that used in the current study. Therefore, it is useful to verify if the results from the analytical approach in the current study match those from Budek et al. (1). The example pile used in this study is a CIDH pile with depth of ft (. m) below ground and height of ft (1. m) above ground (Figure 1a). The pile section was selected as a -ft (1. m) diameter circular section with -#1 Grade bars (D, MPa), # Grade spiral (D1, MPa) pitched at. in (11 mm), and a in (. mm) cover (Figure 11). The ' concrete strength is selected as f c = ksi (7. MPa). The pile was assumed to carry an axial ' load of.1 f c A g where A g is the total cross-sectional area of the pile. The theoretical momentcurvature relationship of this pile section is shown in Figure 11b. The selected pile section is similar to that used in Budek et al. () and corresponds to pile-height to pile-diameter ratio, H D 1. The limiting value of the section curvature was selected to be that corresponding to confined concrete strain of.1 which equals the ultimate compression strain of the confined concrete in the selected pile section. The pile was discretized with nonlinear beam-column elements (Figure 1b). The soil below ground was modeled with discrete springs attached to element nodes. As in Budek et al. (1, ), the soil was assumed to be linear with its stiffness increasing linearly with depth. The stiffness, k i, of each linear soil spring was computed as: k z LK () i i i in which i z is the depth of the node below ground at which the spring is attached, i L is the node s tributary length, and K is the subgrade reaction modulus of the soil. The subgrade modulus values selected in this verification study include those listed in Table for six different soil types. 11

18 P P F F 1. m ( ft) Element Node Nonlinear Element Mud Line Mud Line. m ( ft) Soil Spring Bedrock (a) CIDH Pile (b) Model Figure 1. Example pile used in the verification study (a) CIDH pile and () Analytical model.. x 1 #@. in. (D1, 11 mm) Cover = in. (. mm) R= in. (. m) #1 Grade Bars (D, MPa) Moment, kn m Curvature, 1/m Figure 11. Example pile used in the verification study: (a) Pile section, and (b) Momentcurvature relationship. Figure compares plastic-hinge length and depth from the analytical approach used in this study with the values estimated from recommendations (Figure ) developed by Priestley et al. (1). The presented results indicate that the analytical approach used in this study leads to a plastic-hinge length that is essentially identical to the value estimated from the recommendation

19 (Figure a) by Priestley et al. (1) for six selected soil types (Figure a). The analytical approach in this study leads to a slightly lower depth of plastic-hinge location compared to the recommendation (Figure b) by Priestley et al. (1) for six selected soil types (Figure b). The difference in the plastic-hinge depth from the two studies is small for medium sand, loose sand, medium clay, and soft clay and may be considered negligible for most practical applications. For dense sand and stiff clay, however, the difference is significant. The large discrepancy for these two soil types is due to errors in extrapolation of the plastic-hinge depth * value. It is useful to point out that 1 KD / D EIe = 11 for dense sand and for stiff * clay, both of which are outside the range of 1 KD / D EIe in Figure b. In this study, the plastic-hinge depths for both dense sand and stiff clay were assumed to be those corresponding * to the highest value of 1 KD / D EIe in Figure b. Such an assumption leads to larger depths because the plastic-hinge depth continues to decrease with increasing values of * 1 KD / D EIe. Plastic Hinge Length / Pile Diameter 1 (a) Priestley et al. (1) Current Study Figure. Comparison of results from Priestley et al. (1) and current study: (a) Plastichinge length, and (b) plastic-hinge depth. The results presented so far indicate that the analytical approach used in this investigation leads to plastic-hinge length values which are similar to and plastic-hinge depth values which are sufficiently close to those from the recommendations of Priestly et al. (1). This is found to be valid for the pile section and soil assumptions used in Priestley et al. (1) as well as Budek et al. (1, ). Therefore, it is concluded that the analytical approach used in this study is compatible with that used in earlier studies (Budek et al., 1, ). Any differences noted in the later part of this study are due to different pile sections, and/or soil assumptions, and/or material strain limits. Plastic Hinge Depth / Pile Diameter (b) 1

20 PRE-STRESSED CONCRETE PILES The plastic-hinge length and depth recommendation in this study are developed for a typical - inch (.1 m) octagonal pre-stressed concrete pile (Figure 1a) used in typical wharf type Marine Oil and LNG Terminals. The material properties of the pile are selected as: unconfined concrete ' compressive strength f c =. ksi (. MPa) and pre-stressing steel tendon yield strength, f y = 7 ksi (1 MPa). The pile section consists of 1 pre-stressing tendons each with area of.17 in (1 mm ), #11 wire spiral pitched at. in (. mm), and in (7. mm) cover. The steel tendons are pre-stressed to 7% of their yield stress. The pile supports an axial load equal to % of its axial load capacity. The pile is considered to be free to deflect horizontally and free to rotate at its top. The pile depth below ground level (or mud line) is fixed at ft (. m). The pile height above ground level is varied between ft (.1 m) and ft (1. m) which correspond to pile height to pile diameter ratio, H D, between 1 and. The pile section moment-curvature relationship is shown in Figure 1b. As mentioned previously, the pile and the soil springs are modeled in OpenSees (McKenna and Fenves, 1). The soil springs are modeled using bi-linear material to capture p-y curves shown in Figure 7. The spring stiffness is defined as the p-value times the tributory pile length for the node where the spring is attached. The pile above- and below-ground is modeled with forcebased distributed-plasticity elements. 1 #11 in. (. mm) R= in. (. m) 1 Strands Area =.17 in., (1 mm ) (a) Moment, kn m Cover= in. (7. mm)..1. Curvature, 1/m Figure 1. Pre-stressed reinforced-concrete pile considered: (a) Pile section, and (b) Moment-curvature relationship. Figure 1 presents length and depth of the in-ground plastic-hinge for the selected pile, six soil types, and two MOTEMS seismic design levels. Also included in Figure 1a are the in-ground plastic-hinge lengths estimated from current MOTEMS recommendations (Figure a) as well as from POLB, and in Figure 1b the plastic-hinge depth from Priestley et al. (1) (Figure b). These results lead to the following important observations. First, the plastic-hinge length differs for two MOTEMS seismic design levels (Figure 1a). In particular, the plastic-hinge length for Level 1 is longer than that for Level. This trend is applicable for all soil types and pile H D values. However, the difference between plastic-hinge (b) 1

21 length for level 1 and tend to be larger for softer soils such as loose sand and soft clay compared to stiffer soils such as dense sand and stiff clay. (a) H/D = 1 1 (b) H/D = 1 POLB H/D = 1 H/D = POLB Plastic Hinge Length / Pile Diameter POLB H/D = H/D = Plastic Hinge Depth / Pile Diameter 1 1 H/D = H/D = POLB POLB Level 1 MOTEMS Figure 1F 7 Level H/D = 1 Level 1 Priestley et al., 1 Level H/D = Figure 1. In-ground plastic-hinge (a) length and (b) depth for pre-stressed concrete piles in Marine Oil and LNG Terminals (Adapted from Saeedy, 1).

22 In order to understand reasons for different plastic-hinge length for the two seismic design level, compared in Figure are the height-wise distribution of normalized curvature in pre-stressed concrete piles for six soil types and H D 1. It is also useful to recall that the plastic-hinge length will be shorter if the slope of the curvature distribution in the plastic zone is steeper and longer if the slope of the curvature distribution is milder (see Figure ). The results presented in Figure clearly show that the slope of the curvature distribution in the plastic-hinge zone is much milder for level 1 compared to level for all soil type, which explains the observation in Figure 1 of a longer plastic-hinge length for level 1 compared to level. Furthermore, results in Figure show that the difference in the slope of the curvature distribution in the plastic-hinge zone is much larger for softer soils such as loose sand and soft clay compared to stiffer soils such as dense sand and stiff clay, which explains a much larger difference in the plastic-hinge length between the two seismic design level for softer soil types compared to stiffer soil types observed in Figure 1. Dense Medium Loose Pile Height/Pile Diameter 1 Stiff Medium Soft Pile Height/Pile Diameter 1 Level Level Φ/Φ max Φ/Φ max Φ/Φ max Figure. Height-wise distribution of normalized curvature in pre-stressed concrete piles with H D 1 for six soil types and seismic design levels 1 and. 1

23 Second, the MOTEM recommended plastic-hinge length appears to be adequate for the level design for most soil types, except for soft clay, as apparent from very similar values from the results obtained in this study and from the MOTEMS recommendation (Figure 1). The slightly shorter values of the plastic-hinge length from the MOTEMS recommendation for soft clays is due to extrapolation assumptions used in estimating the plastic-hinge length from Figure a for * MOTEMS. In particular, the value of 1 KD / D EIe for the selected pile is lower than the * first data point available at 1 KD / D EIe = for curves in Figure a. In this investigation, * * the plastic-hinge length was capped at the value at 1 KD / D EIe = if the 1 KD / D EIe value for the selected pile was lower. However, the trend in Figure a indicates a longer plastichinge length for lower values of 1 KD / D EIe which in turn indicates that the values of the * plastic-hinge length from the MOTEMS may end up being similar to that from the current study if additional data were available. The Port of Long Beach (POLB) recommends plastic-hinge length equal to two times the pile diameter regardless of the soil type or H D value. The results presented in Figure 1a indicate that the POLB recommendation is reasonably close to the values from the MOTEMS as well as from the current investigation for level seismic design for all soil types for H D = 1 and, and for medium and soft clays for remaining values of H D. For other cases, the POLB recommendation leads to slightly longer plastic-hinge length. Since longer plastic-hinge length leads to larger pile displacement, the POLB recommendation may lead to un-conservatively larger seismic displacement capacity for level seismic design for a few soil types and H D values. The MOTEMS as well as the POLB recommended plastic-hinge lengths for level 1 are much smaller than the values found in this investigation. Since shorter plastic-hinge length lead to smaller displacement capacity, it appears that current the MOTEMS and POLB in-ground plastic-hinge length recommendation will lead to overly conservative lower pile displacement capacity for seismic design level 1 for all soil types and H D values. It is also useful to point out that the current MOTEMS recommendations for plastic-hinge length, first presented in Priestley et al. (1) and originally reported in Budek et al. (1, ), were computed at failure compression strain in the confined concrete. Clearly, such material strain levels are appropriate for MOTEMS level but not for MOTEMS level 1 for which the material strains are much lower (Table 1). Therefore, it is not surprising that the plastic-hinge length for level 1 found in this investigation differs significantly from the current MOTEMS recommendations. It is useful to emphasize that MOTEMS, POLB, or general engineering practice make no distinction in plastic-hinge length for the two different seismic design levels, i.e., a single value of plastic-hinge length is used in estimating displacement capacity of piles for both seismic design levels. Therefore, results presented in Figure 1 highlight an important short-coming of current analytical procedure: using same plastic-hinge length for both seismic design levels leads to an overly conservative and lower displacement capacity estimate for level 1. Therefore, it is preferable that two separate analyses be conducted using different values of plastic-hinge lengths for the two seismic design levels to more realistically estimate the displacement capacity at both design levels. 17

24 Figure 1b presents depth of in-ground plastic-hinges for two MOTEMS seismic design levels along with the current value recommended by Priestley et al. (1). It is apparent that the current recommendation leads to a depth of plastic-hinge that is much shallower than that determined in this investigation. While the current recommendations leads to a depth of plastichinge below ground to be approximately 1D for selected pile type, this study indicates depth varying from D to 7D depending on the soil type. Unlike plastic-hinge length, the depth of plastic-hinge below ground is independent of the MOTEMS seismic design level. As mentioned previously, the practice uses upper- and lower-bound estimates of soil properties, in addition to the nominal values, to bound response estimates for possible variations in the soil characteristics. The preceding discussion clearly indicates that plastic-hinge length and depth depend on soil properties. Since lower- and upper-bound soil characterization affects the initial stiffness of the soil springs (see Figure 7), it is also useful to examine if the plastic-hinge length and depth will also be affected by the lower- and upper-bound properties. For this purpose, the plastic-hinge length and depth are compared in Figure 1 and 17 for lower-bound, nominal, and upper-bound soil properties for level 1 and level, respectively. The results presented in Figures 1a and 17a show that the plastic-hinge length is essentially unaffected by the lower- and upper-bound soil properties for the three types of sands considered in this investigation. For clays, however, the plastic-hinge length tends to be longer for lowerbound and shorter for upper-bound soil properties compared to the nominal soil value. It is expected that softer soil properties will lead to longer plastic-hinge length because of less confinement to the pile which permits more gradual distribution of curvature distribution over height. While lower-bound soil properties lead to lower- and upper-bound soil properties to higher soil spring stiffness for all soils (Figure 7), their effects are more pronounced for clays compared to sands because of significantly lower stiffness for clays compared to sands (Figure 7). The plastic-hinge depth, in general, is lower for upper-bound and deeper for lower-bound soil properties (Figure 1b and 17b). This is expected because softer soil permits deeper migration of plastic-hinge location. 1

25 1 (a) H/D = 1 (b) H/D = 1 1 H/D = H/D = Plastic Hinge Length / Pile Diameter 1 1 H/D = H/D = Plastic Hinge Depth / Pile Diameter H/D = H/D = 1 Nominal H/D = H/D = Figure 1. Level 1 in-ground plastic-hinge (a) length and (b) depth of pre-stressed concrete piles in Marine Oil and LNG Terminals for lower-bound, nominal, and upper-bound soil properties (Adapted from Saeedy, 1). 1

26 (a) H/D = 1 (b) H/D = 1 1 H/D = H/D = 1 Plastic Hinge Length / Pile Diameter 1 H/D = H/D = Plastic Hinge Depth / Pile Diameter H/D = H/D = 1 Nominal H/D = H/D = 1 Figure 17. Level in-ground plastic-hinge (a) length and (b) depth of pre-stressed concrete piles in Marine Oil and LNG Terminals for lower-bound, nominal, and upper-bound soil properties (Adapted from Saeedy, 1).

27 HOLLOW-STEEL PILES Reported in this section are the results for three hollow-steel pile sections: inch (.1 m) diameter with wall thickness of. inch (.7 mm), inch (.1 m) diameter with.7 inch (1 mm) wall thickness, and inch (1. m) diameter with wall thickness of 1 inch (. mm). The yield strength of the steel was ksi ( MPa). As described in the preceding section, the pile is considered to be free to deflect horizontally and free to rotate at its top. The pile depth below ground level (or mud line) is fixed at ft (. m). The pile height above ground level is varied to achieve pile height to pile diameter ratio, H D, between 1 and. Furthermore, the pile and the soil springs are modeled in OpenSees (McKenna and Fenves, 1). The soil springs are modeled using bi-linear material to capture p-y curves shown in Figure 7 to. The spring stiffness is defined as the p-value times the tributory pile length for the node where the spring is attached. The pile above- and below-ground is modeled with force-based distributed-plasticity elements. Figure 1 to present lengths and depths of in-ground plastic-hinges in the -inch (.1 m), -inch (.1 m), and -inch (1. m) diameter hollow-steel piles, respectively, for six soil types, and two MOTEMS seismic design levels. Also included in Figures 1a, 1a, and a are the in-ground plastic-hinge length from current POLB recommendations. These results lead to the following important observations. As noted previously for pre-stressed concrete piles, the plastic-hinge length differs for two MOTEMS seismic design levels (Figure 1a, 1a, and a). This trend is applicable for all soil types and pile H D values. However, the difference between plastic-hinge length for level 1 and tends to be larger for softer soils such as loose sand and soft clay compared to stiffer soils such as dense sand and stiff clay. The plastic-hinge length for level tends to be larger than for level 1 seismic design (Figure 1a, 1a, and a). This trend is opposite to that observed previously for pre-stressed concrete piles where plastic-hinge length was found to be smaller for level compared to level 1 seismic design (Figure 1a). In order to understand reasons for these differences, presented in Figures 1 to are the heightwise distribution of normalized curvatures for three selected hollow-steel piles for six soil types and H D 1. Once again, it is useful to recall that the plastic-hinge length will be shorter if the slope of the curvature distribution in the plastic zone is steeper and longer if the slope of the curvature distribution is milder (see Figure ). The results presented in Figures 1 to clearly show that the slope of the curvature distribution in the plastic-hinge zone is much milder for level compared to level 1 for all soil type, which explains the observation in Figures 1a, 1a, and a of longer plastic-hinge length for level compared to level 1. The opposite trend was visible for pre-stressed concrete piles (Figure ) where the slope of the curvature distribution in the plastic-hinge zone was much milder for level 1 compared to level for all soil types. The milder slope of the curvature distribution in the plastic-hinge zone for hollow-steel piles for the level design level may be attributed to the more ductile nature of steel which permits gradual spread of the curvature over height with increasing pile displacement. For pre-stressed concrete piles, however, the curvature tends to concentrate over a very short length after initiation of concrete crushing that is expected for pile displacements associated with seismic design level. 1

28 Results in Figure 1a, 1a, and a also indicated that plastic-hinge length for both design levels tends to be longer for softer soils such as loose sand and soft clay compared to stiffer soils such as dense sand and stiff clay. This is due to the slope of the curvature distribution in the plastichinge zone being much milder for softer soils such as loose sand and soft clay compared to stiffer soils such as dense sand and stiff clay as apparent from results in Figures 1 to. The Port of Long Beach (POLB) recommends plastic-hinge length equal to two times the pile diameter regardless of the soil type or H D value. The results presented in Figures 1a, 1a, and a indicate that the POLB recommendation, in most cases, leads to a much shorter plastic-hinge length. This indicates that the POLB recommendation may lead to overly-conservative smaller seismic displacement capacity for hollow-steel piles. As noted previously for pre-stressed concrete piles, the results for hollow-steel piles also highlight the need for two separate analyses using different values of plastic-hinge lengths for the two seismic design levels. Figures 1b, 1b, and b present depth of in-ground plastic-hinges for two MOTEMS seismic design levels. These results indicate that the depth of the in-ground plastic-hinge varies from D to D depending on the soil type. Unlike plastic-hinge length, the depth of the plastic-hinge below ground is independent of the MOTEMS seismic design level. A comparison of results for three different piles diameters (Figures 1 to ) indicates that results plastic-hinge length as well as depth are very similar for all three diameters. This indicates that the normalized plastic-hinge length and depth values may be considered to be independent of the pile diameter. As mentioned previously, the practice uses upper- and lower-bound estimates of soil properties, in addition to the nominal values, to encompass bound response estimates for possible variations in the soil characteristics. Similar to results presented previously for pre-stressed concrete pile, Figures to present results for hollow-steel piles and lower-bound, nominal, and upperbound soil properties for level 1 and level. As noted previously for pre-stressed concrete piles, the results presented in Figures a to a show that the plastic-hinge length is essentially unaffected by the lower- and upper-bound soil properties for the three types of sands considered in this investigation. For clays, however, the plastic-hinge length tends to be longer for lower-bound and shorter for upper-bound soil properties compared to the nominal soil value. The explanation for this observation is the same as that provided previously for pre-stressed concrete piles. The plastic-hinge depth, in general, is lower for upper-bound and deeper for lower-bound soil properties (Figure 1b to b). This is expected because location of the plastic-hinge migrates deeper for softer soils.

29 1 POLB (a) H/D = 1 (b) H/D = 1 1 POLB H/D = H/D = Plastic Hinge Length / Pile Diameter 1 1 POLB POLB H/D = H/D = Plastic Hinge Depth / Pile Diameter H/D = H/D = 1 POLB Level 1 Level H/D = H/D = Figure 1. In-ground plastic-hinge (a) length and (b) depth for -inch (.1 m) hollowsteel piles in Marine Oil and LNG Terminals (Adapted from Saeedy, 1).

30 1 POLB (a) H/D = 1 (b) H/D = 1 1 POLB H/D = H/D = Plastic Hinge Length / Pile Diameter 1 1 POLB POLB H/D = H/D = Plastic Hinge Depth / Pile Diameter H/D = H/D = 1 POLB Level 1 Level H/D = H/D = Figure 1. In-ground plastic-hinge (a) length and (b) depth for -inch (.1 m) hollowsteel piles in Marine Oil and LNG Terminals (Adapted from Saeedy, 1).

31 1 POLB (a) H/D = 1 (b) H/D = 1 1 POLB H/D = H/D = Plastic Hinge Length / Pile Diameter 1 1 POLB POLB H/D = H/D = Plastic Hinge Depth / Pile Diameter H/D = H/D = 1 POLB Level 1 Level H/D = H/D = Figure. In-ground plastic-hinge (a) length and (b) depth for -inch (1. m) hollowsteel piles in Marine Oil and LNG Terminals (Adapted from Saeedy, 1).

32 Dense Medium Loose Pile Height/Pile Diameter 1 Stiff Medium Soft Pile Height/Pile Diameter 1 Level Level Φ/Φ max Φ/Φ max Φ/Φ max Figure 1. Height-wise distribution of normalized curvature in -inch (.1 m) hollowsteel piles with 1 H D for six soil types and seismic design levels 1 and.

33 Dense Medium Loose Pile Height/Pile Diameter 1 Stiff Medium Soft Pile Height/Pile Diameter 1 Level Level Φ/Φ max Φ/Φ max Φ/Φ max Figure. Height-wise distribution of normalized curvature in -inch (.1 m) hollowsteel piles with 1 H D for six soil types and seismic design levels 1 and. 7

34 Dense Medium Loose Pile Height/Pile Diameter 1 Stiff Medium Soft Pile Height/Pile Diameter 1 Level Level Φ/Φ max Φ/Φ max Φ/Φ max Figure. Height-wise distribution of normalized curvature in -inch (1. m) hollowsteel piles with 1 H D for six soil types and seismic design levels 1 and.

35 1 (a) H/D = 1 (b) H/D = 1 1 H/D = H/D = Plastic Hinge Length / Pile Diameter 1 1 H/D = H/D = Plastic Hinge Depth / Pile Diameter H/D = H/D = 1 Nominal H/D = H/D = Figure. Level 1 in-ground plastic-hinge (a) length and (b) depth of -inch (.1 m) hollow-steel piles in Marine Oil and LNG Terminals for lower-bound, nominal, and upperbound soil properties (Adapted from Saeedy, 1).

36 1 (a) H/D = 1 (b) H/D = 1 1 H/D = H/D = Plastic Hinge Length / Pile Diameter 1 1 H/D = H/D = Plastic Hinge Depth / Pile Diameter H/D = H/D = 1 Nominal H/D = H/D = Figure. Level in-ground plastic-hinge (a) length and (b) depth of -inch (.1 m) hollow-steel piles in Marine Oil and LNG Terminals for lower-bound, nominal, and upperbound soil properties (Adapted from Saeedy, 1).

37 1 (a) H/D = 1 1 (b) H/D = 1 1 H/D = 1 H/D = Plastic Hinge Length / Pile Diameter 1 1 H/D = H/D = Plastic Hinge Depth / Pile Diameter 1 1 H/D = H/D = 1 Nominal H/D = 1 H/D = Figure. Level 1 in-ground plastic-hinge (a) length and (b) depth of -inch (.1 m) hollow-steel piles in Marine Oil and LNG Terminals for lower-bound, nominal, and upperbound soil properties (Adapted from Saeedy, 1). 1

38 1 (a) H/D = 1 1 (b) H/D = 1 1 H/D = 1 H/D = Plastic Hinge Length / Pile Diameter 1 1 H/D = H/D = Plastic Hinge Depth / Pile Diameter 1 1 H/D = H/D = 1 Nominal H/D = 1 H/D = Figure 7. Level in-ground plastic-hinge (a) length and (b) depth of -inch (.1 m) hollow-steel piles in Marine Oil and LNG Terminals for lower-bound, nominal, and upperbound soil properties (Adapted from Saeedy, 1).

39 1 (a) H/D = 1 1 (b) H/D = 1 1 H/D = 1 H/D = Plastic Hinge Length / Pile Diameter 1 1 H/D = H/D = Plastic Hinge Depth / Pile Diameter 1 1 H/D = H/D = 1 Nominal H/D = 1 H/D = Figure. Level 1 in-ground plastic-hinge (a) length and (b) depth of -inch (1. m) hollow-steel piles in Marine Oil and LNG Terminals for lower-bound, nominal, and upperbound soil properties (Adapted from Saeedy, 1).

40 1 (a) H/D = 1 1 (b) H/D = 1 1 H/D = 1 H/D = Plastic Hinge Length / Pile Diameter 1 1 H/D = H/D = Plastic Hinge Depth / Pile Diameter 1 1 H/D = H/D = 1 Nominal H/D = 1 H/D = Figure. Level in-ground plastic-hinge (a) length and (b) depth of -inch (1. m) hollow-steel piles in Marine Oil and LNG Terminals for lower-bound, nominal, and upperbound soil properties (Adapted from Saeedy, 1).

41 CONCLUSIONS AND RECOMMENDATIONS This investigation examined the current recommendations for plastic-hinge length and depth for piles and soil properties typical of those in Marine Oil and LNG Terminals. For this purpose, - inch (.1 m) octagonal pre-stressed concrete and -, -, and -inch (.1m,.1m, and 1,m) hollow-steel piles supported in six different soil types dense sand, medium sand, loose sand, stiff clay, medium clay, and soft clays were analyzed. Nonlinear behavior for both pile and soil were considered and MOTEMS specified strain levels were used and results compared to recommendations in MOTEMS and POLB when appropriate. All analyses in this study were conducted using OpenSees software developed at the Pacific Earthquake Engineering Research Center. This investigation has led to the following conclusions: The plastic-hinge length differs for two MOTEMS seismic design levels. The plastic-hinge length was found to be longer for level 1 compared to level seismic design for pre-stressed concrete piles, whereas the plastic-hinge length was found to be longer for level compared to level 1 seismic design for hollow-steel piles. The trends in plastic-hinge length for the two seismic design levels were found to be related to the slope of the curvature distribution in the plastic-hinge region: a milder slope led to longer plastic-hinge length and vice versa. It was found that the slope of the curvature distribution became steeper for level compared to level 1 after crushing of the concrete in pre-stressed concrete piles due to brittle material behavior, whereas it became milder for level compared to level 1 for hollow-steel piles due to ductile material behavior. For pre-stressed concrete piles o The MOTEM recommended plastic-hinge length is adequate for level design. o The POLB recommended plastic-hinge length is adequate for level design for all soil types for H D = 1 and, and for medium and soft clays for H D =,, and. For remaining cases, the POLB recommendation leads to a slightly longer plastichinge length which may lead to un-conservatively larger seismic displacement capacity. o The MOTEMS and the POLB recommended plastic-hinge lengths for level 1 are much smaller than the values found in this investigation. Therefore, current MOTEMS and POLB in-ground plastic-hinge length recommendations will lead to overly conservative lower pile displacement capacity for seismic design level 1. o The current recommendations lead to a depth of plastic-hinge that is much shallower than that found in this investigation. While the current recommendations lead to a depth of plastic-hinge below ground to be approximately 1D, this study found depths to vary from D to 7D depending on the soil type. o The depth of the plastic-hinge below ground is independent of the MOTEMS seismic design level. For hollow-steel piles: o The POLB recommendation in most cases leads to a much shorter plastic-hinge length implying that the POLB recommendation may lead to an overly-conservative smaller seismic displacement capacity. o The depth of the in-ground plastic-hinge varies from D to D depending on the soil type. o The depth of the plastic-hinge below ground is independent of the MOTEMS seismic design level.