Roles of pile-group and cap-rotation effects on seismic failure mechanisms of partially-embedded bridge foundations: Quasi-static tests

Soil Dynamics and Earthquake Engineering 132 (2020) 106074

Contents lists available at ScienceDirect

Soil Dynamics and Earthquake Engineering journal homepage: http://www.elsevier.com/locate/soildyn

Roles of pile-group and cap-rotation effects on seismic failure mechanisms of partially-embedded bridge foundations: Quasi-static tests Tengfei Liu a, Xiaowei Wang b, a, Aijun Ye a, * a b

State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, No. 1239 Siping Road, Shanghai, 200092, China College of Civil and Transportation Engineering, Hohai University, No. 1 Xikang Road, Nanjing, 210024, China

A R T I C L E I N F O

A B S T R A C T

Keywords: RC pile-group foundations Partially-embedded Scour Seismic failure mechanism Quasi-static test Cap rotation Axial load variations Pile group effects

Pile foundations, especially partially embedded in soils, are vulnerable parts of bridges under seismic loadings. In this study, to investigate seismic failure mechanisms of partially-embedded reinforced concrete (RC) pile-group foundations, a series of quasi-static cyclic loading tests were conducted on 1 � 1, 2 � 2 and 2 � 3 pile-foundation specimens in sand. Observed hysteretic behavior and pile damage were recorded, along with pile curvature distributions. Then, numerical models based on the Beam-on-Nonlinear-Winkler-Foundation (BNWF) approach were developed and validated by test data. The failure process of each specimen was reached, characterized by the sequence and locations of plastic hinges on piles. Combining the test and numerical results, seismic failure mechanisms of all partially-embedded pile specimens with different layouts are revealed: side piles yield before center piles, each pile forms two plastic hinges, and pile heads yield before underground portions. Special at­ tentions are paid to the roles of cap rotation and pile-group effect (PGE) on the failure mechanisms. The results reveal that the existence of PGE leads to lower lateral loads and greater displacements at different limit states such as the first yielding and ultimate states etc., while the impact of cap rotation only increases corresponding lateral displacements at these limit states.

1. Introduction Reinforced concrete (RC) pile foundations are extensively utilized in bridges because of economical and easy-to-build advantages. Typically, pile foundations can be categorized into two types:(1) fully embedded and (2) partially embedded pile foundations. A fully embedded pile foundation can sometimes become partially embedded due to natural hazards, such as riverbed scour [1–4]. According to previous studies [5, 6], about 60% bridge failures in the U.S. during the past 30 years were related to the scour of bridge foundations. Compared with fully embedded pile foundations, partially embedded ones have unsupported portions, which may reduce the stability and lateral resistance of pile foundations. In this regard, assessing seismic behavior of partially-embedded pile foundations draws increasing attention. Currently, bridge design guidelines [7–9] adopt the capacity design strategy, in which inelastic behavior on pile foundations were not allowed. To reach this, a large plenty of reinforcements are needed for the piles, inevitably reducing the cost-effectiveness. Nevertheless, recent post-earthquake reconnaissance [10–12] still reported plastic damage to pile foundations. In this regard, utilizing pile foundations as

energy-dissipating components tends to be a reasonable choice. To this end, it is necessary to investigate seismic failure mechanisms of pile foundations. Quasi-static testing is an effective method to investigate the seismic behavior of pile foundations. In pioneering work [13–16], single-pile specimens were adopted and subjected to predefined loading patterns, which may not accurately represent the complicated soil-pile-interaction problem. To avoid this limitation, Chai and Hutchinson [17] conducted field tests on full-scale extended pile-shafts (i.e., single pile-column) in homogenous cohesionless soil to investigate flexural strengths and ductile capacities of the test piles. Compared with single piles, pile-group foundations have two instinct characteristics. One is the pile-group effect (PGE) induced by limited pile-to-pile dis­ tances as well as the complex soil-pile-interaction [18,19], the other is cap-rotation effect induced by the rotation of the cap in a pile group under lateral cyclic loads, which inevitably lead to variations of axial loads on piles. These variations of axial loads probably influence yielding and ultimate curvature capacities as well as curvature demands of pile sections [20]. Regarding this, the seismic failure mechanisms of pile-group foundations under lateral loadings are expected to be

* Corresponding author. E-mail addresses: [email protected] (T. Liu), [email protected] (X. Wang), [email protected] (A. Ye). https://doi.org/10.1016/j.soildyn.2020.106074 Received 19 September 2019; Received in revised form 30 January 2020; Accepted 3 February 2020 Available online 12 February 2020 0267-7261/© 2020 Elsevier Ltd. All rights reserved.

T. Liu et al.

Soil Dynamics and Earthquake Engineering 132 (2020) 106074

different from single piles. Very few studies have been reported in this field. Ye et al. [21] studied the seismic performance of 2 � 2 elevated pile-cap foundations (EPFs, can be regarded as partially-embedded pile-group foundations) in sands by quasi-static tests. Wang et al. [20] extended this work and revealed seismic failure mechanisms of 2 � 3 EPFs with varying aboveground heights. However, the combined/se­ parate impact(s) of cap rotation and PGE were not documented in these studies. On the other hand, various numerical and analytical methods have been developed to predict lateral responses of soil-pile systems [22–30]. Generally, the BNWF method [31–33] is more advocated in practice due to its merits of low computational costs and easy applications, as compared to the three-dimensional finite element (FE) method with soil continua [34–38]. With this in view, the scope of this paper is to investigate seismic failure mechanisms of partially-embedded pile-group foundations for bridges, emphasizing the roles of cap rotation and PGE. First, quasistatic loading tests were carried out on three specimens with different pile layouts (1 � 1, 2 � 2 and 2 � 3). Global hysteretic behavior, pile physical damage, and curvature distributions along piles were inter­ preted. Then based on the BNWF approach, numerical models are built in OpenSees [39] and verified using the experimental results. After that, seismic failure mechanisms of partially-embedded RC pile-group foun­ dations with different pile layouts are revealed through comprehensive analyses on the experimental and numerical results, among which the combined/separate impact(s) of cap rotation and PGE are highlighted.

that differences in cap dimensions between the studied cases should have little effect on the lateral behavior of pile foundations [41]. Fig. 1 illustrates the test setup and pile layouts for all specimens. Each spec­ imen was embedded in the same soil box of 3.2 � 1.6 � 4.2 m (Length � Width � Height). The boundary condition effect of this soil box has been examined and verified by Wang et al. [20] and will be re-verified in this study. The pile center-to-center spacing is 3D, the aboveground height of piles is 5.33D ¼ 0.8 m and the embedded depth is long enough (24.67D ¼ 3.7 m) to develop full underground pile damage [42,43]. In this study, constant vertical loads were applied on caps to simulate initial vertical loads provided by superstructures, corresponding to a nominal axial compressive ratio α ¼ P/fcAg ¼ 0.05, for each pile, where P ¼ vertical load on each pile ¼ 47.44 kN, fc ¼ uniaxial compressive strength of concrete cover, Ag ¼ gross area of piles. It is worth noting that this axial compressive ratio, α, (i.e., 0.05) falls into the common range for practice based on engineering judgements of the authors. For the single pile case S1 shown in Fig. 1(a), both the joints A and B of the horizontal actuator were locked against rotation while the joint C of the vertical actuator was free to rotate. In this regard, the small pilecap of the single pile S1 is not free to rotate and its rotation is partially restrained by the horizontal actuator. In other words, the head of the single pile S1 is not free, thereby it can be approximately regarded as an individual pile among a pile-group, but with neither pile-group effect nor cap-rotation effect (note that in this paper, cap-rotation effect refers to the variation of pile axial loads induced by cap rotation of pile-group, here in the case S1 for single pile, constant axial load was imposed). It should be noted that the restraint condition of single pile case may be not completely the same to the pile-group cases, but the setup of the actuators is what we can do the best at hand to achieve a similar restraint condition, as close as possible, among them. Note that the close restraint condition among the studied cases will be further justified later in Sec­ tion 3.4 using curvature distribution responses. The soil profile consists of two layers: (1) bottom layer: compacted gravel (0.5 m thick) and (2) upper layer: homogenous dense sand (3.5 m thick). Note that the gravel layer in S1 could resistant vertical load satisfactorily as expected. However, in pile-group cases (S4 and S6), to ensure the lateral loadings run successfully during the tests, steel blocks were placed at the bottom of the soil box (Fig. 1(b and c)) to avoid specimen settlements induced by the excessive axial loads for the gravel layer. The seismic behavior of pile foundations under lateral loading is affected by the vertical loads on piles. As mentioned above, the axial loads on piles are designed based on the compressive capacity of pile section, rather than the vertical resistance offered by soils and pile tips. Though S1, S4, and S6 are not strictly the same in pile-tip support, the designed vertical loads on each pile are equal (axial compressive ratio ¼ 0.05) and remain stable during tests. Considering this, though there were tiny settlement of S1 and negligible vertical displacements of S4/ S6 during tests, the seismic behavior is hardly affected by the difference of pile-tip boundary conditions between S1 and S4/S6. So the pile tips of all specimens can be modeled as vertically fixed in numerical models.

2. Experimental program 2.1. Test setup The prototype structure in this study is a 2 � 3-pile-group-supported river-crossing simply supported multi-span girder bridge with individual spans of 30 m and deck-width of 16.25 m. The 2 � 3 pile-group proto­ type, with 0.9-m diameter and 27.0-m length, is cast-in-place bored and partially embedded into sandy deposits. The embedded depth of piles is approximately 22.2 m, corresponding to an aboveground height of 4.8 m. Scaled pile specimens were prepared for quasi-static tests. Before introducing the similarity coefficients, it is worth noting that for labo­ ratory tests of soil-structure specimens with limited dimension of soil box (3.2 � 1.6 � 4.2 m (Length � Width � Height)) under 1g gravita­ tional field, it is very difficult to perfectly follow similarity laws (e.g., Iai [40]) in terms of both the soil and pile, especially for RC piles in soils [19]. Therefore, only the piles are scaled down, while soils are prepared to have reasonable relative densities that can provide appropriate boundary conditions to the models. The similarity coefficients in length and force of the studied speci­ mens are 1/6 and 1/36, respectively. In addition, different specimens were prepared based on the scaled 2 � 3 pile groups by varying the pile layouts to 1 � 1 and 2 � 2. In total, three 1/6-scale RC pile specimens, characterized by different layouts (1 � 1, 2 � 2 and 2 � 3), were tested to investigate seismic failure mechanisms. The units for test setup de­ scriptions and associated results hereinafter are all on the scaled models. For construction expedience, square section is used. The width of pile section is D ¼ 0.15 m. The specimens are labeled as S1, S4, and S6, respectively. Table 1 summarizes the configuration of test models. Note

2.2. Pile properties Fig. 2 shows the reinforcing configuration of individual piles. The longitudinal steel ratio was 0.02, provided by four Ф12 rebars, with 2 cm concrete cover. The pile was confined by Ф8 transverse hooped bars at vertical intervals of 5 cm in the region beneath the cap up to 200 cm

Table 1 Details of test specimens. Case S1 S4 S6

Pile layout 1�1 2�2 2�3

Pile

RC cap

Section width (m)

Full length (m)

Aboveground height (m)

Embedded depth (m)

Length (m)

Width (m)

Height (m)

0.15 0.15 0.15

4.50 4.50 4.50

0.80 0.80 0.80

3.70 3.70 3.70

0.55 1.00 1.45

0.55 1.00 1.00

0.40 0.40 0.60

2

T. Liu et al.

Soil Dynamics and Earthquake Engineering 132 (2020) 106074

Fig. 1. Schematic illustrations of (a) S1, (b) S4 and (c) S6 along with (d) photograph of the test (S4).

Fig. 2. Reinforcement details of test pile (unit: cm).

(Part A in Fig. 2(a)). In the remaining portion (Part B in Fig. 2(a)), the same transverse bars were utilized but at larger vertical intervals of 10 cm. The volumetric transverse reinforcement ratios in Part A and B were 0.036 and 0.018, respectively. Additionally, to ensure rigid pile-cap connections, the rebars were extended into the RC cap with sufficient lengths (30 cm, 30 cm, and 50 cm for S1, S4, and S6, respectively) [20]. The uniaxial compressive strength of concrete was fc ¼ 42.14 MPa. According to tension tests of the longitudinal rebars, a well-defined yield stress of fy ¼ 542.44 MPa was obtained, together with an elastic modulus of 206 GPa. The ultimate stress was fu ¼ 695.10 MPa, corresponding to the ultimate strain of εu,s ¼ 0.099. By contrast, the transverse bar did not have a well-defined yield stress. The nominal yield stress corresponding to 0.2% strain was f’y ¼ 320.13 MPa. The software XTRACT [44] was utilized to ascertain the moment-curvature relationship of the pile section (Fig. 3). Note that the first-yielding curvature (ϕy) corresponds to the first yielding of the longitudinal bar, whereas the ultimate curvature (ϕu) is determined by the crushing of the concrete core or snapping of the longitudinal bar, whichever occurs first. The ultimate strain of concrete core (εu ¼ 0.0216) is given by Eq. (1) [45].

εu ¼ 0:004 þ

0:9ρs f ’y 300

Fig. 3. Pile moment-curvature behavior under axial load P ¼ 0.05 fcAg.

In this study, the equivalent-yielding state of the specimen is defined as that the equivalent-yielding curvature of the pile-section (ϕe) is firstly reached. Here ϕe is determined by the ideally bilinear moment-curvature relationship considering energy equivalence. As indicatively depicted in Fig. 3, for specimen S1 with the pre-loaded vertical load of 47.44 kN, ϕe ¼ 0.0354 rad/m and ϕu ¼ 1.999 rad/m. 2.3. Soil details This test employed yellow silicon sand to prepare the soil deposit, which is classified as poorly graded sand (SP) based on the Unified Soil Classification System [46]. The grading curve of test sand is shown in Fig. 4. The maximum and minimum dry bulk densities were 16.68 kN/m3 and 14.03 kN/m3, respectively. In each case, the measured unit weight was approximately 15.62 kN/m3, corresponding to a relative density of Dr ¼ 65%. The internal friction angle was 31� . Main physical properties of test sand are summarized in Table 2. As mentioned above, the gravel layer only serves in increasing ver­ tical resistances of piles in the tests. Please note, due to the limitation of lab facilities, the gravel layer underlying the homogenous sand could not

(1)

where ρs ¼ transverse volumetric ratio of pile, f’y ¼ yield stress of transverse bar (MPa). 3

T. Liu et al.

Soil Dynamics and Earthquake Engineering 132 (2020) 106074

cm) and one SPC (depth ¼ 60 cm) were glued on the East and North sides of soil box (Fig. 1), respectively, to verify the boundary condition. Fig. 5 (f) illustrates the strain gauges (SGs) attached to the longitudinal rebars labeled “a” and “b” (see Fig. 5(a)). It is worth noting that the maximum embedded depth of SGs, i.e. 13.3D (200 cm), is sufficient to capture the underground pile damage, according to previous study by Wang et al. [20]. 2.5. Loading scheme In these tests, the lateral loading was displacement-controlled, with the protocol shown in Fig. 6. By connecting a 150 kN/�250 mm-ca­ pacity hydraulic actuator with the cap, the lateral loading started at 5 mm and gradually increased until the end of loading (defined below). In each case, the lateral loading rate was as follows: before the displace­ ment level of 10 mm, the loading rate was 0.5 mm/s, then increased to 1.0 mm/s until 80 mm, after which level the loading rate became 2.0 mm/s until end of loading. Each loading level was cycled three times.

Fig. 4. Grain size distribution of test sand.

3. Test results

Table 2 Material properties of silicon sand.

3.1. Verification of boundary condition

Property (Unit)

Value

Property (Unit)

Value

Dry density, γ (kN/m3)

15.62

16.68

Minimum dry density, γmin (kN/m3) Average grain size, D50 (mm) Coefficient of uniformity, Cu Maximum void ratio, emax Void ratio, e

14.03

Maximum dry density, γmax (kN/m3) Relative density, Dr (%) Friction angle, θ (degree) Coefficient of curvature, Cc Minimum void ratio, emin

31 0.93 0.589

0.172 2.22 0.889 0.696

To verify the boundary condition of soil box, Table 3 compares the soil pressure values on the outer face of pile #4 of S4 (nearest to the soil box wall, see Fig. 5(a)) and East wall of soil box (perpetual to the loading direction, see Fig. 1(c)) at the same depth of 6.0D ¼ 90 cm. It can be found that, the soil pressure on East wall of soil box was less than 10% of that on outer face of pile #4 before the displacement level of 130 mm. Additionally, in S6, the SPCs at depths ranging 45–90 cm glued on the outer surface of pile #6 did not work properly during tests. However, it is found that, with the loading displacement increases from 40 mm to 170 mm, the soil pressure at depth of 90 cm on the East wall of soil box only ranges from 4.07 kPa~6.78 kPa, which is rather small. All the re­ sults indicate that the boundary condition is generally negligible though not fully eliminated.

65

be fully compacted, leading to its mechanical properties immeasurable. However, since most laterally loaded piles in practice exhibit “flexible” behavior and the deformation and internal forces below a specific embedded depth (“active length” in Ref. [47], usually less than 10D~15D according to Refs. [48–50]) are negligible [47], the gravel layer (embedded depth ¼ 23.33D~24.67D) has little to no effect on the lateral behavior of test specimens. Therefore, the absence of mechanical properties of the gravel layer, which can also be ignored in numerical models, is generally acceptable. Test specimens were installed as follows: The gravel was firstly placed at the bottom of the soil box and compacted to a height of 0.30 m. It is noted that, in case S4 and S6, the steel block was placed on the center of the soil-box bottom before the gravel. After that, the specimen was moved into the soil box by a travelling crane and stood on the compacted gravel layer (S1) or the steel block (S4 and S6) vertically. Then the upper layer of gravel around the specimen was placed and compacted to 0.20 m. After that, the 3.5-m-depth homogenous sand was prepared layer-by-layer, each in approximate 0.27 m. The total embedded depth of piles was 3.7 m (24.67D). Finally, the vertical and lateral actuators were connected to the specimen (see Fig. 1).

3.2. Lateral load versus displacement Fig. 7 presents the lateral load-deflection relationships. Generally, the plump hysteretic loops indicate ductile properties for the specimens. To be specific, for S1, peak values of lateral strengths were Vmax ¼ 19.37 kN and Vmin ¼ 16.01 kN in the push and pull direction, corresponding to displacement levels of 99.8 mm and 98.6 mm, respectively. For S4, maximum positive and negative lateral loads are Vmax ¼ 62.25 kN and Vmin ¼ 55.05 kN at 110.1 mm and 133.6 mm, respectively, which are much greater than S1 owing to increasing lateral stiffness. In S6, larger peak lateral forces (Vmax ¼ 85.37 kN and Vmin ¼ 86.92 kN) are reached at displacement levels of 123.0 mm (push) and 113.0 mm (pull). Lateral strengths decrease gradually after reaching peak values in all cases. Specifically, the lateral forces at loading-ends show gradual degradation of 5.3% (18.3%), 22.5% (10.6%), and 16.7% (17.7%) in the push (pull) direction than corresponding peak strengths for S1, S4, and S6, respectively. Note that in the tests, the lateral loadings ended when the lateral strength fell by 15% or irreparable pile damage emerged. However, the ultimate limit states of specimens discussed below are defined as either over 15% degradation of lateral strength or ultimate pile curvature (ϕu) is reached, whichever occurs first.

2.4. Instrumentation Fig. 5 depicts the detailed instrumentation in each case. Four displacement transducers (DTs) and one inclinometer were attached to the cap to monitor its displacement and rotation (Fig. 5(b and c)). Half of the piles were instrumented with three pairs of DTs to obtain average pile curvatures at pile heads (Fig. 5(d)). The other half of piles were glued with 6 pairs of soil pressure cells (SPCs) on inner and outer sur­ faces at an interval of 1.0D ¼ 15 cm (maximum embedded depth 6.0D ¼ 90 cm) to record the soil pressure along different rows of piles, as shown in Fig. 5(e). In addition, two SPCs (embedded depths ¼ 45 cm and 90

3.3. Observed pile damage To investigate seismic failure mechanisms of the pile models, it is important to detect their damage during and after the tests. 4

T. Liu et al.

Soil Dynamics and Earthquake Engineering 132 (2020) 106074

Fig. 5. Details of instrumentation.

3.3.1. Aboveground part During and after the tests, physical damage to aboveground piles was detected, as presented in Fig. 8. The first concrete cracks were detected at side-pile heads at displacement levels of 30 mm, 20 mm, and 30 mm for S1, S4, and S6, respectively, as shown in Fig. 8(a)–(c). The concrete cover of the center-pile head in S6 also cracked at 40 mm. Then more visible cracks continued to occur and spread horizontally and diago­ nally. The inner-face concrete cover began to spall at 90 mm and 80 mm at side-pile heads in S4 and S6, respectively, as illustrated in Fig. 8(d and e). Definitions of face locations and No. of piles are shown in Fig. 5, the same below. Additionally, concrete cover spalling of center piles in S6 appeared at 120 mm (Fig. 8(f)), but less severe than side piles. At 160 mm, concrete core crushing was inspected at side-pile heads in S4 and S6, as shown in Fig. 8(h and i). However, concrete core crushing at side pile head of S1 was not found until end of loading (Fig. 8(g)). This may be caused by the difference of axial-load variations at side-pile heads during lateral loading, which will be simulated by numerical modeling in Section 4.3. In summary, almost all aboveground damage was located in pile head regions, up to 1.0D length from the cap-pile interface, indicating the formation of aboveground plastic hinges.

Fig. 6. Protocols of lateral loading. Table 3 Comparison of soil pressure on side pile and soil box wall in the loading direction. Location of SPCs on pile #4 (kPa) (1) on East wall of soil box (kPa) (2) (2)/(1) (%)

Displacement level (mm) 40

80

90

100

110

130

33.65 2.71

51.28 2.71

54.49 4.07

56.09 4.07

64.10 5.42

78.53 6.78

8.1%

5.3%

7.5%

7.2%

8.5%

8.6%

3.3.2. Underground part After tests, all specimens were excavated to detect pile damage below the soil surface. Fig. 9 depicts the final underground pile damage, in which embedded depths are marked for easy inspections. It is obvious that the failure mode was flexural for all specimens (i.e., with apparent horizontal cracks). Locations of underground plastic hinges in each specimen are summarized in Table 4. It can be found that (1) less severe 5

T. Liu et al.

Soil Dynamics and Earthquake Engineering 132 (2020) 106074

Fig. 7. Experimental lateral displacement-force relationships:(a) S1; (b) S4 and (c) S6.

Fig. 8. Physical damage of aboveground piles during and after tests from (a) S1 pile #1 (30 mm); (b) S4 pile #2 (20 mm); (c) S6 pile #4 (30 mm); (d) S4 pile #3 (90 mm); (e) S6 pile #4 (80 mm); (f) S6 pile #5 (120 mm); (g) S1 pile #1 (120 mm); (h) S4 pile #3 (160 mm); (i) S6 pile #4 (160 mm).

damage was observed in the center piles than that in the side piles; (2) the embedded depth of underground plastic hinge of side piles was increased by the increasing pile rows; (3) shallower plastic hinges were formed on the side piles than the center piles. The first finding can be explained by the fact that during the test, side piles interchange between leading and trailing rows. The leading rows of piles suffer greater internal forces than the middle and trailing rows under lateral loading [20]. This explanation also applies to the third finding, which leads to a smaller bending moment gradient and thereby

a greater depth-to-maximum-moment for the center piles, as compared to the side piles. The second finding is induced by the effect of pile-group reduction. More rows of piles results in lower soil reaction applied on the leading piles, consequently leading to a smaller gradient of bending moment along piles, which thereby increases the depth-to-maximum-moment. In Fig. 10, post-test elevation views of S4 and S6 are illustrated. The pinching of side piles was obvious for both specimens. The minimum net side-to-side spacing of adjacent rows of piles dropped to 21.6 cm and 6

T. Liu et al.

Soil Dynamics and Earthquake Engineering 132 (2020) 106074

Fig. 9. Underground pile damage from (a) S1; (b) S4; (c) S6 (pile #1); (d) S6 (pile #2). Table 4 Observed damage regions of underground piles. Case

S1

S4

Pile

Side pile

Side pile

Embedded depth of severe damage region a

a

S6 Side pile a

3.0D~4.0D ~6.0D

4.3D~5.3D ~7.3D

Center pile a

5.0D~6.0D ~7.0D

5.3D~6.7Da~8.7D

Depth of most severe underground pile damage.

center and trailing piles in the tests. Nevertheless, leading and trailing piles of S4 and S6 interchange during the cyclic loading. For better ex­ planations, the leading piles mentioned below refer to those in the pull direction (i.e., pile #1 as shown in Fig. 5). Recall that the first-yielding state of the pile section is defined as when the first-yielding curvature (ϕy) is reached, which is ϕy ¼ 0.0326 rad/m. Note that the minor impact of axial load variations on ϕy is detailed later in Section 4 “BNWF Model”. Fig. 11 presents curvature distributions along piles in all cases, with which the yielding sequence of the specimens can be determined. Note that some SGs at pile heads malfunctioned during the tests and their values are estimated based on linear trends, as depicted by dashed lines in Fig. 11. Additionally, in S4, the SGs on piles below the embedded depth of 8D did not work properly and no strain data was recorded during the test, so pile curvature in this region (embedded depth ¼ 8D13.3D) is not plotted in Fig. 11(b). Also, some abnormal curvature data (e.g., at depth of 90 cm or 105 cm for cases S1 and S6) are excluded from the drawing in Fig. 11. It can be found that pile heads yield before un­ derground pile portions in all cases. More specifically, in S1 (Fig. 11(a)), the pile head yields before a displacement level of 50 mm. Combined with the testing phenomenon described above, 30 mm tends to be the first-yielding displacement of S1. Then, the first yielding of the under­ ground part occurs at about 60 mm (embedded depth ¼ 4D). In S4 (Fig. 11(b)), the pile head and the underground pile yield at displace­ ment levels of 40 mm and 90 mm, respectively. A lager depth-tomaximum-curvature of 5D is observed for this case. In S6 (Fig. 11(c and d)), the first-yielding of leading and center pile heads emerge at 40 mm and 50 mm, respectively. Then subgrade leading and center piles yield at 100 mm and 120 mm, respectively, with depths of maximum curvatures at 6D and 7D, respectively. It should be noted that the observed regions of severe pile damage match well with the recorded maximum pile curvatures, as shown in Fig. 11. In addition, to quantitatively verify the similar restraint condition for cap/pile-head across different cases, Fig. 12 compares curvature distri­ butions along aboveground piles of S1, S4, and S6 at a given small displacement level of 20 mm (before the yielding of pile head). It can be seen that the pile-head curvatures are non-zero, and more importantly they are quite close among the studied cases, indicating that the pile-

Fig. 10. Elevation views of (a) S4 and (b) S6 after loading.

24.5 cm from original 30 cm in S4 and S6, respectively, corresponding to embedded depths of 6.0D and 5.7D. The pinching of underground side piles is attributable to the facts that the leading piles suffer greater soil reaction than the trailing piles and that side piles interchange between leading and trailing rows under lateral cyclic loading [20], as mentioned before. 3.4. Curvature distribution along piles and yielding limit state determination As mentioned above, leading piles bear larger lateral forces than 7

T. Liu et al.

Soil Dynamics and Earthquake Engineering 132 (2020) 106074

Fig. 11. Curvature distribution along leading piles of (a) S1; (b) S4; (c) S6 and center piles of (d) S6.

effects will be thoroughly studied later in this paper. 4. BNWF model 4.1. Model description Based on the BNWF method, FE models of soil-pile-interaction sys­ tems are developed in OpenSees (Fig. 13). The cap is modeled with elastic beam-column elements, and the piles are simulated using displacement-based beam-column elements with 5 integration points. The element lengths vary from 0.10 m to 0.20 m [51]. Note that hori­ zontal and vertical translational degree-of-freedoms (DOFs) at pile tips (along y and z axes shown in Fig. 13(a)), perpendicular to the loading, are fixed for computational efficiency while those along to the loading direction and rotational DOFs are free to represent the boundary con­ ditions in the tests. Additionally, to ensure the fixed pile-head/cap connection, the cap center in S1 is restrained against all rotational DOFs. Also noteworthy is that the P-Δ effect is considered in the FE models. The pile section is discretized into 225 concrete fibers and 4 steel fibers. This fiber-discretization can produce stable curvature responses, as compared to a more refined discretization, for the adopted displacement-based beam-column element [52,53]. Concrete fibers adopt the Kent-Scott-Park [54] constitutive model, with confinement effect accounted [55]. Fig. 13(d) illustrates the cyclic behavior of steel. The longitudinal bar is modeled by the Parallel material consisting of the Steel 02 [56] and the Hysteretic material model for better convergence, as described in Wang et al. [20]. The soil reaction is modeled using discrete nonlinear zero-length elements, i.e., p-y springs [23], as shown in Fig. 13(a and e). The

Fig. 12. Comparison of curvature distributions along different rows of above­ ground piles of S1, S4, and S6 at the same displacement level of 20 mm (before the yielding of pile head).

head restraint conditions are quite close across these cases (S1, S4, and S6) at the beginning of loading. In other words, the single pile case S1 can be approximately regarded as a single pile in pile-group cases of S4 and S6, but with neither pile-group effect nor cap-rotation effect. These 8

T. Liu et al.

Soil Dynamics and Earthquake Engineering 132 (2020) 106074

Fig. 13. Schematic illustrations of BNWF model: (a) 3D model; and constitutive models of (b) unconfined concrete; (c) confined concrete; (d) longitudinal steel; (e) py spring.

American Petroleum Institute (API) method [57] is adopted to define p-y springs, as given in Eq. (2). � � nh h p ¼ Apu tanh y (2) Apu

where pud and pus are the ultimate resistance of soil in the deep and shallow portion, respectively; C1, C2, and C3 are coefficients determined by Fig. 14(b); γ ¼ unit weight of soil (kN/m3); D ¼ width of pile (m); h ¼ depth (m). It should be noted that although some concerns have been raised about the validity of the API method [30,59], it still gains recognition due to its convenient applications in the platform of Open­ Sees, which motivates the employment of this method in the present study. In S4 and S6, PGE should be carefully considered. Since the leading and trailing rows of pile groups interchange during the reversed cyclic loading, the PGE is taken into account by multiplying the soil resistance of single pile p-y curves by an overall group reduction factor for all piles in the group [60–63]. In light of these studies, the group reduction factors in the present study are rigorously calibrated until well agree­ ments between the numerical and experimental results are reached. To be specific, the group reduction factors are fg ¼ 0.61 and 0.40 for S4 and S6, respectively. For better readability, main parameters to define the numerical model are summarized in Table 5, all of which are calculated based on the physical properties of soils (Table 2) and pile dimensions (pile diameter D ¼ 0.15 m, etc.). Specifically, A is suggested to be 0.9 for

where p ¼ soil reaction at unit pile length (kN/m); A ¼ loading factor (0.9 for cyclic loading); h ¼ depth (m); pu ¼ ultimate bearing capacity at depth of h (kN/m); nh ¼ initial modulus of subgrade reaction (kN/m3); y ¼ lateral deflection (m). Note that the nh value obtained by Chai and Hutchinson [17] for piles under large lateral deflections (similar to the situation in this study) is about 1/5–1/4 of the value recommended by ATC-32 [58] (Fig. 14(a)), not to mention the greater nh in API [57]. Hence, the nh is chosen to be 1/5 of the recommended value from ATC-32 [58]. The ultimate lateral resistance of soil, pu, can be calculated by Eqs. (3)–(5). pus ¼ ðC1 h þ C2 DÞγh

(3)

pud ¼ C3 Dγh

(4)

pu ¼ minfpus ; pud g

(5)

Fig. 14. Key parameters defining p-y springs:(a) Suggested nh value from ATC-32 [58]; (b) Coefficients as function of θ [57]. 9

T. Liu et al.

Soil Dynamics and Earthquake Engineering 132 (2020) 106074

axial load variations are detected in the single pile case (S1). More specifically, after reaching the equivalent-yielding limit states, axial loads in leading piles of S4 and S6 gradually increase to maximum values of 141.25 kN and 126.05 kN, respectively, and then drop to 125.83 kN and 109.99 kN, respectively. According to the above-described test phenomena, pile-head plastic hinges in the pile-group models should occur after 50 mm. Therefore, the cross-section axial loads when plastic responses occur should range from 125.83 kN to 141.25 kN and from 109.99 kN to 126.05 kN for S4 and S6, respectively. These two ranges correspond to relatively stable ultimate curvatures of 0.835 rad/m and 0.860 rad/m for S4 and S6, respectively. Furthermore, as shown in Fig. 17(b), a parametric analysis is con­ ducted in XTRACT [44] to reveal the sensitivity of axial load (P) on ϕe and ϕu values, which are critical to define the limit states of specimens. The axial load ratio, α, varies from 0.05 (tension) to 0.15 (compres­ sion). This large range is sufficient to cover the axial load variations in piles during the full cyclic tests. Obtained ϕe and ϕu values are sum­ marized in Table 7. It is found that ϕe is generally not sensitive to axial loads, even under such a large range of α, (coefficient of variance (COV) is as low as 3.85%). Therefore, a constant ϕe of 0.0354 rad/m is adopted in this paper for convenience. However, ϕu is strongly sensitive to axial loads (COV ¼ 35.41%), especially under compression. This is the reason why FE models are developed to determine ϕu. Nevertheless, it should be noted that the studied range of axial loads in Fig. 17(b) is much larger than the abovementioned ranges of axial loads for S4 and S6 when plastic pile responses take place.

Table 5 Parameters for numerical modeling. Property (Unit)

Value

Property (Unit)

Value

Cyclic loading factor, A Coefficient, C2 Width of pile, D (m)

0.9 2.804 0.15

Coefficient, C1 Coefficient, C3 Group reduction factor, fg

Embedded depth, h (m)

0-3.5

Soil reaction at unit pile length, p (kN/m) Ultimate resistance of soil in the deep portion, pud (kN/m) Lateral deflection, y (m)

–

Initial modulus of subgrade reaction, nh (kN/m3) Ultimate bearing capacity, pu (kN/m) Ultimate resistance of soil in the shallow portion, pus (kN/m)

2.089 32.515 0.61 (S4), 0.40 (S6) 2277.64

–

– –

–

cyclic loading [57]; C1, C2, and C3 are determined based on the friction angle θ ¼ 31� according to Fig. 14(b); since Dr ¼ 0.65%, the suggested nh value of ATC-32 [58] (Fig. 14(a)) is 11388.20 kN/m3, and its 1/5 of this value, 2277.64 kN/m3, is adopted according to Ref. [17], as discussed above; the embedded depth, h, ranges from 0 to 3.5 m. 4.2. Model validation Fig. 15 illustrates the lateral displacement-load relationships of test data and numerical simulation for all cases, together with the measured and calculated backbone curves of all specimens. In addition, compari­ sons of responses at different critical states between the BNWF models and tests are listed in Table 6. The errors fall into -10%~23%. Furthermore, Fig. 16 compares the experimental and numerical curva­ ture distributions of all cases at the occurrence of equivalent yielding, with reasonably satisfactory prediction in the curvature values and lo­ cations of plastic hinges. In general, the good matches of hysteretic loops, backbone curves, responses at critical states, along with curvature distributions, between test and numerical results mean that the nu­ merical model is validated and can be used to predict seismic behavior of the soil-pile system.

4.4. Ultimate limit state determination Based on the above study, the ultimate limit states of all specimens can be determined. Fig. 18 illustrates the identification process of the ultimate limit states for all the specimens. Lateral displacements at the ultimate limit states are 120 cm, 160 cm, and 160 cm for S1, S4, and S6, respectively. Note that the lateral strength of specimen S1 degrades by 15% at the displacement of 120 cm, which is much before the curvature demand reaching its ultimate curvature. This is the reason why the displacement of 120 cm is taken as the ultimate limit state.

4.3. Variation of cross-section axial load for ultimate limit state estimate

5. Discussions on seismic failure mechanisms

As mentioned before, the cross-section ultimate curvature of piles (ϕu) is probably dependent on the varied axial loads induced by the cap rotation. Therefore, the validated numerical model is required to determine the ultimate limit curvature by tracing the varied axial loads at potential locations of plastic hinges, such as pile heads and under­ ground piles at the observed severe damage regions. Fig. 17(a) presents the development of cross-section axial compressive loads at leading pile heads during the tests. It can be seen that significant variations of axial loads are observed for the pile-group cases, as expected. By contrast, no

5.1. Summary of plastic hinge formations and developments To investigate seismic failure mechanisms of pile specimens with different pile layouts (1 � 1, 2 � 2, 2 � 3), the plastic hinge formations and developments are firstly revealed (see Fig. 19). Generally, each pile forms two plastic hinges in all cases: the first one at the pile head (limited to the 1.0D-length region below the cap-pile interfaces) and the second one beneath the ground. Specifically, in S1 (single pile), the

Fig. 15. Comparison of experimental and numerical lateral load-displacement relationships of:(a) S1 (b) S4 and (c) S6. 10

T. Liu et al.

Soil Dynamics and Earthquake Engineering 132 (2020) 106074

Table 6 Comparison of experimental and numerical results. Specimen

Model

S1

Experimental Numerical Error Experimental Numerical Error Experimental Numerical Error

S4 S6

Equivalent-yielding

Peak strength

End of loading

Displacement (mm)

Force (kN)

Displacement (mm)

Force (kN)

Displacement (mm)

Force (kN)

29.1 33.0 13.4% 50.4 47.5 ¡5.8% 50.5 46.5 ¡8.0%

12.08 14.69 21.6% 47.58 52.13 9.6% 70.28 72.08 2.6%

99.8 90.0 ¡9.8% 110.1 120.0 9.0% 123.0 130.0 5.7%

19.37 18.69 ¡3.5% 62.25 64.62 3.8% 85.37 88.18 3.3%

124.7 120.0 ¡3.8% 164.6 160.0 ¡2.8% 170.1 170.0 0.0%

18.34 16.61 ¡9.4% 48.27 58.88 22.0% 71.09 74.25 4.4%

Fig. 16. Comparison of experimental and numerical curvature distributions of: (a) leading pile (S1); (b) leading pile (S4); (c) trailing pile (S4); (d) leading pile (S6); (e) middle pile (S6) and (f) trailing pile (S6) when equivalent yielding occurs.

equivalent-yielding limit states of aboveground and underground pile portions were reached at 30 mm and 60 mm, respectively. The under­ ground plastic hinge was located at an embedded depth of 4D. S1 came into the ultimate limit state at 120 mm. In S4, the equivalent-yielding of pile heads and subgrade parts appeared at 50 mm and 90 mm (embedded depth of underground plastic hinge ¼ 5.3D), respectively. Then the ultimate limit state of S4 was achieved at 160 mm. S6 approximately equivalent-yielded at 50 mm and 90 cm on the top of side and center piles, respectively. Then, the equivalent-yielding of under­ ground side and center piles emerged at 100 mm and 120 mm, respec­ tively. Note that the underground plastic hinge on center piles, i.e., 6.7D, was slightly deeper than that on side piles (6D). S6 reached the ultimate limit state at 160 mm. Compared with the single pile case S1 where cap rotation and PGE are not involved, the pile group cases show significantly different results on the displacement levels and locations of plastic hinges. Therefore, it is

noted that the impact of cap rotation and PGE should be well considered when investigating seismic failure mechanisms of partially-embedded RC pile-group foundations. 5.2. Combined impact of cap rotation and pile-group effects To investigate the combined effects of cap rotation and PGE on seismic failure mechanisms of pile-group specimens, lateral forcedisplacement curves from tests are studied herein. Fig. 20 shows the experimental backbone curves of S4 and S6. Note that, to highlight the combined impacts of cap rotation and PGE, two scenarios of four and six times of the experimental backbone curve of S1 are also presented, which should not exist in engineering practice. Since cap rotation is not involved in case S1, the “4 times_S1 (Test)” scenario in Fig. 20(a) rep­ resents the assumed condition that both the cap rotation and PGE are ignored when loading on S4. The load gap between “S4 (Test)” and “4 11

T. Liu et al.

Soil Dynamics and Earthquake Engineering 132 (2020) 106074

Fig. 17. Varied axial loads on piles: (a) varied axial loads at leading pile heads; (b) pile moment-curvature relationships under varied axial loads. Table 7 Equivalent-yielding and ultimate curvatures of pile section with varied axial loads (P). P/fcAg ϕe (rad/m) ϕu (rad/m)

0.05 0.0336 1.978

0

0.05

0.10

0.15

Mean

Standard deviation

COV

0.0343 1.988

0.0354 1.999

0.0371 0.936

0.0373 0.816

0.0356 1.543

0.00137 0.5463

3.85% 35.41%

Fig. 18. Ultimate limit state definition of specimens of (a) S1; (b) S4; and (c) S6.

Fig. 19. Plastic hinge formation sequences and developments of all specimens: (a) S1; (b) S4; (c) S6.

times_S1 (Test)” highlights the combined impacts of cap rotation and PGE in loading tests. Similar relationship is applied to scenarios of “S6 (Test)” and “6 times_S1 (Test)”. More specifically, it can be found that

the experimental lateral loads of S4 and S6 are always lower than the four- and six-time results of S1, with an average bias of 18.2% and 12.7%, respectively, before reaching the peak-strength limit state of S1 12

T. Liu et al.

Soil Dynamics and Earthquake Engineering 132 (2020) 106074

Fig. 20. Experimental backbone curves of specimens (a) S4 and (b) S6.

(i.e., at the displacement level of 100 mm). The comparison of each limit state in different scenarios are summarized in Table 8. It is found that, at each limit state, the experimental lateral loads of S4 (S6) are -24.9% ~-5.9% (-22.3%~-0.1%) lower than the four-time (six-time) results of S1. In addition, the lateral displacements at individual limit states in S4 and S6 are 10.0% and 66.7% greater than that in S1, which are caused by the combined effects of cap rotation and PGE. Note that, at equivalent yielding limit state, the differences of lateral displacements between scenarios of “S4” (“S6”) and “four-time of S1” (“six-time of S1”) are much significant than the corresponding lateral load differences, reflecting the complex roles of cap rotation and PGE. The pile-group cap rotation induces varied axial loads between different rows of piles, which will not occur in single-pile case S1 (Fig. 17(a)). It is deduced that greater axial loads lead to significantly increased flexural stiffness, but the growth of leading-pile bending moments are minor, consequently, leading-pile-head curvature in S4/S6 are much lower than that in S1. Since ϕe is stable when axial load varies (Fig. 17(b)), the equivalentyielding lateral displacements of S4/S6 are larger than S1. It is also deduced that, among the two impacts, PGE is dominant over cap rota­ tion on the lateral strength of pile-soil systems. Before the pile-head yielding, the pile-soil system remains elastic, leading to limited impact of PGE, hence the corresponding lateral loads between S4 (S6) and their respective counterparts are much lower. Nevertheless, all these

deductions need further demonstration by numerical simulation. 5.3. Separate impact of cap rotation In order to study the separate effect of cap rotation, the validated BNWF model is adopted, in which the cap-orthocenter is modeled as rotational free or fixed (along y axis shown in Fig. 13(a)) for scenarios with or without cap rotation, respectively. Fig. 21 illustrates the com­ parison of numerical backbone curves between S1 and S4 (S6). Note that PGE is not considered by setting a group reduction factor of 1.0 for the pile-group cases. It can be found in both subfigures that, in the scenarios without cap rotation, the lateral loads of S4 and S6 at any given deflection are equal to four and six times of S1, respectively, with the same corresponding displacements at individual limit states. These findings verify the adopted test technique that the fixed-head single pile can be seen as a pile extracted from pile groups, in which both the cap rotation and PGE are not considered. Meanwhile, it can also be found that, the presence of cap rotation of S4 and S6 significantly increases the lateral displacements at individual limit states. For better readability, Table 9 compares the seismic response at each limit state in different scenarios of S4/S6 with or without cap rotation. More specifically, the displacement differences at individual limit states in S4 (between the case with and without cap rotation) are greater than those in S6. For instance, with cap rotation considered, the displacements of S4 corre­ sponding to “Equivalent-yielding”, “Peak strength”, and “Ultimate” limit states increase by 56.1%, 10.0%, and 28.0% than their counterparts, similarly, the corresponding displacements of S6 at those three states rise by 7.6%, 11.1%, and 7.7%, respectively. However, neither the occurrence sequence nor the corresponding lateral strength at each limit state (bias ¼ -4.0%~2.4%) is obviously changed. To investigate the separate impact of cap rotation on seismic per­ formance of pile groups, it is necessary to obtain the distributions of axial and lateral loads between each row piles. Table 10 summarizes the distributions of axial and lateral loads (at pile heads) between every row piles of S4/S6 in scenarios with or without cap rotation at 30 mm. It indicates that, with cap rotation considered, leading-row piles of S4/S6 suffer greater axial and lateral loads than middle-row and trailing-row piles. However, the axial and lateral loads applied on each row piles of S4/S6 are equal in scenarios without cap rotation. Considering this, side piles of pile groups in the scenario with cap rotation are more prone to undergo plastic damage when subjected to cyclic lateral loading. To further reveal the separate effect of cap rotation, seismic behavior of side piles in the pile-group specimens with and without cap rotation are studied. Fig. 22(a and b) present curvature distributions along piles at given deflections of 30 mm (before yielding) and 50 mm (after yielding), respectively. It can be found that smaller curvature responses are obtained in the scenario with cap rotation, which imply greater equivalent-yielding displacements, as above-depicted in Fig. 21. Note

Table 8 Comparison of each limit state of different scenarios. Case

Equivalentyielding limit state

Peak-strength limit state

Ultimate limit state

Δy,e (mm)

Fy,e (kN)

Δy,p (mm)

Fy,p (kN)

Δy,u (mm)

Fy,u (kN)

S1 (Test)

30.0

12.02

100.0

17.51

120.0

16.00

4 times_S1 (Test) (1) S4 (Test) (2) Difference ¼ [(2)–(1)]/ (1) 6 times_S1 (Test) (3) S6 (Test) (4) Difference ¼ [(4)–(3)]/ (3)

30.0

48.08

100.0

70.03

120.0

63.99

50.0 66.7%

45.22 ¡5.9%

120.0 20.0%

57.47 ¡17.9%

160.0 33.3%

48.07 ¡24.9%

30.0

72.12

100.0

105.05

120.0

95.99

50.0 66.7%

72.07 ¡0.1%

110.0 10.0%

85.90 ¡18.2%

160.0 33.3%

74.59 ¡22.3%

Δy,e, Fy,e -lateral displacement and load corresponding to equivalent-yielding limit state, respectively. Δy,p, Fy,p-lateral displacement and load corresponding to peak-strength limit state, respectively. Δy,u, Fy,u -lateral displacement and load corresponding to ultimate limit state, respectively. 13

T. Liu et al.

Soil Dynamics and Earthquake Engineering 132 (2020) 106074

Fig. 21. Comparison of backbone curves of (a) S4 and (b) S6 with and without cap rotation.

greater displacement differences at individual limit states are observed in S4 than S6 (Fig. 21). In summary, the separate effect of axial load variations primarily changes the displacement levels at individual limit states, while slightly affects the lateral strength at individual limit states.

Table 9 Comparison of each limit state of FE models with and without cap rotation. Case

S1_FE without cap rotation (1) S4_FE without cap rotation (2) S4_FE with cap rotation (3) Difference ¼ [(3)–(2)]/(2) S6_FE without cap rotation (4) S6_FE with cap rotation (5) Difference ¼ [(5)–(4)]/(4)

Equivalentyielding limit state

Peak-strength limit state

Ultimate limit state

Δy,e (mm)

Fy,e (kN)

Δy,p (mm)

Fy,p (kN)

Δy,u (mm)

Fy,u (kN)

5.4. Separate impact of pile group effects

33.0

14.69

90.0

18.86

120.0

16.09

33.0

58.70

100.0

75.38

125.0

63.31

51.5

60.13

110.0

72.34

160.0

61.16

56.1%

2.4%

10.0%

¡4.0%

28.0%

¡3.4%

33.0

88.06

90.0

112.95

130.0

90.58

35.5

85.71

100.0

110.93

140.0

89.52

7.6%

¡2.7%

11.1%

¡1.8%

7.7%

¡1.2%

To study the separate impact of PGE on seismic failure mechanisms, the validated numerical model is again employed. Note that the caporthocenter is fixed against rotation to neglect the impact of cap rota­ tion herein. As mentioned before, the group reduction factors are set to be 0.61 and 0.40 for all piles in S4 and S6, respectively, to consider PGE. No group reduction factor is utilized for the reference scenarios without PGE. Fig. 23 presents the backbone curves of S4 and S6 with and without PGE. Lateral displacements and loads corresponding to different limit states of S4 and S6 with and without PGE are listed in Table 11. It can be seen that, without PGE, the lateral strengths at individual limit states of S4 and S6 are enhanced obviously, meanwhile, significant decreases in the corresponding displacements are obtained. As shown in Table 11, in comparison with the scenarios without PGE, the average decreases of lateral strength are 11.3% and 19.7% for S4 and S6, respectively, while the corresponding displacements rise by 15.8% (S4) and 33.4% (S6) averagely when PGE is considered. Another finding is that higher differences of lateral loads and displacements are obtained in S6 than S4. For instance, compared with the scenarios without PGE, peak lateral strengths are dropped by 11.5% and 21.6% for S4 and S6, respectively, meanwhile, the lateral displacements are increased by 11.1% and 22.2% for S4 and S6, respectively. This finding lies in that the soil reaction on piles is reduced when PGE is considered, leading to lower lateral stiffness of the soil-pile systems and smaller gradients of bending moment along piles.

Δy,e, Fy,e -lateral displacement and load corresponding to equivalent-yielding limit state, respectively. Δy,p, Fy,p-lateral displacement and load corresponding to peak-strength limit state, respectively. Δy,u, Fy,u -lateral displacement and load corresponding to ultimate limit state, respectively.

that, in the scenario without cap rotation, the curvature distribution is always the same for S4 and S6. Meanwhile, with cap rotation consid­ ered, lower values of maximum curvature in underground piles are found (Fig. 22), meaning that the underground pile yielding and plastic hinge formation is delayed. In addition, compared with S4, the pile curvature distribution of S6 tends to be less affected by the effect of cap rotation due to its greater rotational stiffness. That is the reason why

6. Conclusions Pile foundations, especially partially-embedded ones, are the seismic

Table 10 Distributions of axial and lateral loads between piles in the scenarios with and without cap rotation (loading displacement ¼ 30 mm). Loads

Scenarios

Axial load (kN)

with cap rotation without cap rotation with cap rotation without cap rotation

Lateral load (kN)

Piles in S4

Piles in S6

Leading-row

Trailing-row

Leading-row

Middle-row

Trailing-row

115.84 47.44 13.20 13.81

20.97 47.44 10.10 13.81

115.41 47.44 14.30 13.81

37.23 47.44 12.70 13.81

10.32 47.44 11.49 13.81

“-“and “þ” mean compressive and tensile axial loads, respectively. 14

T. Liu et al.

Soil Dynamics and Earthquake Engineering 132 (2020) 106074

Fig. 22. Curvature distributions of side piles in scenarios with and without cap rotation (a) at 30 mm and (b) at 50 mm.

Fig. 23. Comparison of backbone curves of (a) S4 and (b) S6 with and without PGE.

vulnerable parts of bridges, which has drawn much attention. In this study, a series of quasi-static tests were conducted on three pile speci­ mens with different pile layouts (1 � 1, 2 � 2, 2 � 3). Then the BNWF method was adopted and validated to reveal seismic failure mechanisms of partially-embedded RC pile-group foundations in sand and to study the combined/separate impact(s) of cap rotation and PGE. Based the work in this paper, main conclusions can be drawn:

(2) For pile groups under cyclic loading, the cap rotation can induce axial load variations on piles. The ultimate curvature of the pile section is strongly dependent on the varied axial loads while the equivalent-yielding curvature is not. The role of cap-rotation ef­ fect can significantly cause lateral displacements at individual limit states of pile groups increase by maximum value of 56.1%. This trend is more obvious in 2 � 2 pile group than 2 � 3 pile group. However, the role of cap rotation hardly affects the cor­ responding lateral loads at these limit states. The above finding implies a future direction to control cap rotation under lateral loads, which can control the ductile behavior of pile group foundations in design. (3) The role of pile group effect can increase lateral displacements at individual limit states by as large as 39.4%, while reduce lateral

(1) Flexural failure modes are detected for partially-embedded pilegroup foundations under lateral loadings. Side pile heads yield firstly in all pile specimens, forming the first plastic hinge below the pile-cap interface up to 1.0D length, followed by the yielding of center pile heads. Subgrade plastic hinges tend to occur after the aboveground ones. 15

T. Liu et al.

Soil Dynamics and Earthquake Engineering 132 (2020) 106074

Uniaxial strength of concrete Yield stress of longitudinal steel and transverse bar Ultimate stress of longitudinal steel εu,s Ultimate strain corresponding to fu εu Ultimate strain of concrete core ϕy, ϕe First and equivalent yield curvatures of pile section ϕu Ultimate curvature of pile section ρs Transverse volumetric ratio of pile Average grain size D50 Dr Relative density of sand θ Friction angle of sand γ max, γmin Maximum and minimum densities of sand γ Dry density of sand Cu, Cc Coefficients of uniformity and curvature emax,emin Maximum and minimum void ratios of sand e Void ratio of sand Vmax,Vmin Maximum and minimum lateral loads on specimen Δ Lateral loading displacement p Soil reaction at unit pile length y Lateral deflection of pile A Loading factor h Depth fg Group reduction factor pu Ultimate bearing capacity at depth of h Initial modulus of subgrade reaction nh pus, pud Ultimate resistance of soil in the shallow and deep portions C1,C2, C3 Coefficients for determining pus and pud Δy,e, Fy,e Lateral displacement and load corresponding to peak-strength limit state Δy,p, Fy,p Lateral displacement and load corresponding to peak-strength limit state Δy,u, Fy,u Lateral displacement and load corresponding to ultimate limit state

fc fy, f’y fu

Table 11 Comparison of each limit state of FE models with and without PGE. Case

Equivalent-yielding limit state

S4 without PGE S4 with PGE Difference S6 without PGE S6 with PGE Difference

Peak-strength limit state

Ultimate limit state

Δy,e (mm)

Fy,e (kN)

Δy,p (mm)

Fy,p (kN)

Δy,u (mm)

Fy,u (kN)

33

59.04

90

75.31

120

65.43

39.5

54.11

100

66.62

140

56.19

19.7% 33

¡8.4% 88.57

11.1% 90

¡11.5% 112.97

16.7% 130

¡14.1% 94.33

46

74.3

110

88.57

180

74.06

39.4%

¡16.1%

22.2%

¡21.6%

38.5%

¡21.5%

Δy,e, Fy,e -lateral displacement and load corresponding to equivalent-yielding limit state, respectively. Δy,p, Fy,p-lateral displacement and load corresponding to peak-strength limit state, respectively. Δy,u, Fy,u -lateral displacement and load corresponding to ultimate limit state, respectively.

loads at these limit states by up to 21.6%. This influence is more significant in 2 � 3 pile group than 2 � 2 pile group. Gathering the above second conclusion, it is reasonable to infer that with the increasing number of row in pile-groups, contribution of the pile group effect tends to increase while that of the pile-cap rotation reduces. Declaration of competing interest Declarations of interest: none. CRediT authorship contribution statement

References

Tengfei Liu: Conceptualization, Methodology, Investigation, Formal analysis, Software, Visualization, Validation, Writing - original draft, Writing - review & editing. Xiaowei Wang: Conceptualization, Funding acquisition, Methodology, Software, Visualization, Writing - original draft, Writing - review & editing. Aijun Ye: Conceptualization, Super­ vision, Funding acquisition, Resources, Writing - original draft, Writing review & editing.

[1] Song ST, Wang CY, Huang WH. Earthquake damage potential and critical scour depth of bridges exposed to flood and seismic hazards under lateral seismic loads. Earthq Eng Eng Vib 2015;14:579–94. https://doi.org/10.1007/s11803-015-00479. [2] Wang C, Yu X, Liang F. A review of bridge scour: mechanism, estimation, monitoring and countermeasures. Nat Hazards 2017;87:1881–906. [3] Han Q, Wen J, Du X, Huang C. Seismic response of single pylon cable-stayed bridge under scour effect. J Bridge Eng 2019;24. https://doi.org/10.1061/(ASCE) BE.1943-5592.0001413. 5019007. [4] Wang X, Ji B, Ye A. Seismic behavior of pile-group-supported bridges in liquefiable soils with crusts subjected to potential scour: insights from shake-table tests. J Geotech Geoenviron Eng 2020. https://doi.org/10.1061/(ASCE)GT.19435606.0002250. [5] Shirole AM, Holt RC. Planning for a comprehensive bridge safety assurance program. Transport Res Rec 1991;1290:39–50. [6] Lagasse PF, Richardson EV. ASCE compendium of stream stability and bridge scour papers. J Hydraul Eng 2001;127:531–3. [7] AASHTO (American Association of State Highway and Transportation Officials). Guide specifications for LRFD seismic bridge design. second ed. 2011. Washington D.C. [8] JSCE (Japanese Society of Civil Engineers). Standard specifications for concrete structures-2002: seismic performance verification. JSCE Guidelines for Concrete 2005;5. [9] MOHURD (Ministry of Housing and Urban-Rural Development of, the People’s Republic of China). Guidelines for seismic design of highway bridges, CJJ 1662011. 2011. Beijing (in Chinese). [10] Bray J, Elderidge T, Frost D, Hashash Y, Kayen R, Ledezma C, et al. Geoengineering reconnaissance of the 2010 Maule, Chile earthquake. GEER Turn Disaster Knowl 2010:1–347. https://doi.org/10.18118/G6NP4W. [11] Ashford SA, Boulanger RW, Donahue JL, Stewart JP. Geotechnical quick report on the Kanto plain region during the March 11, 2011, off Pacific coast of Tohoku earthquake, Japan. Geotech Extrem Events Reconnaiss; 2011. GEER-025a:1–20. [12] Cubrinovski M, Bray JD. Geotechnical reconnaissance of the 2016 Mw 7.8 Kaikoura, New Zealand earthquake. GEER 2017. https://doi.org/10.18118/ G6NK57. [13] Sheppard DA. Seismic design of prestressed concrete piling. PCI J 1983;28:20–49. https://doi.org/10.15554/pcij.03011983.20.49.

Acknowledgment The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (Grant No. 51778469) and the State Key Laboratory of Disaster Reduction in Civil Engineering, Ministry of Science and Technology of China (Grant No. SLDRCE19-B-20). The first author truly appreciates the financial support from the China Scholarship Council. The second author appreciates the support by the China Postdoctoral Science Foundation (Grant Nos: 2018M640448 and 2019T120380). The tests cannot be finished without the assistance of Prof. Jianzhong Li and Mr. Chuan’an Lu. The constructive comments from Prof. Salgado (Purdue University), Dr. Yu Shang, Mr. Lianxu Zhou, and Mr. Deming Zhang to improve the manu­ script are also appreciated. Appendix List of Symbols D Width of pile section α Axial compressive ratio of pile section P Axial load of pile section Ag Gross area of pile section 16

T. Liu et al.

Soil Dynamics and Earthquake Engineering 132 (2020) 106074

[14] Park R, Falconer TJ. Ductility of prestressed concrete piles subjected to simulated seismic loading. PCI J 1983;28:112–44. https://doi.org/10.15554/ pcij.09011983.112.144. [15] Banerjee S, Stanton JF, Hawkins NM. Seismic performance of precast prestressed concrete piles. J Struct Eng 1987;113:381–96. https://doi.org/10.1061/(ASCE) 0733-9445(1987)113:2(381). [16] Budek AM, Benzoni G, Priestley MJN. Experimental investigation of ductility of inground hinges in solid and hollow prestressed piles. Rep No SSRP 1997;97:17. [17] Chai YH, Hutchinson TC. Flexural strength and ductility of extended pile-shafts. II: experimental study. J Struct Eng 2002;128:595–602. https://doi.org/10.1061/ (ASCE)0733-9445(2002)128:5(595). [18] Brown DA, Morrison C, Reese LC. Lateral load behavior of pile group in sand. J Geotech Eng 1988;114:1261–76. https://doi.org/10.1061/(ASCE)0733-9410 (1988)114:11(1261). [19] Wang X, Ye A, Shang Y, Zhou L. Shake-table investigation of scoured RC pilegroup-supported bridges in liquefiable and nonliquefiable soils. Earthq Eng Struct Dynam 2019;48:1217–37. https://doi.org/10.1002/eqe.3186. [20] Wang X, Ye A, He Z, Shang Y. Quasi-static cyclic testing of elevated RC pile-cap foundation for bridge structures. J Bridge Eng 2016;21:04015042. https://doi.org/ 10.1061/(ASCE)BE.1943-5592.0000797. [21] Ye A, Zhang D, Wei H, Han Z. In: Experimental study on seismic performance of elevated pile-cap foundation of bridges. 35th Annu. Symp. London: IABSE; 2011. [22] Basu D, Salgado R. Elastic analysis of laterally loaded pile in multi-layered soil. Geomechanics Geoengin 2007;2:183–96. https://doi.org/10.1080/ 17486020701401007. [23] Boulanger RW, Curras CJ, Kutter BL, Wilson DW, Abghari A. Seismic soil-pilestructure interaction experiments and analyses. J Geotech Geoenviron Eng 1999; 125:750–9. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:9(750). [24] Brown DA, Shie C-F. Three dimensional finite element model of laterally loaded piles. Comput Geotech 1990;10:59–79. https://doi.org/10.1016/0266-352X(90) 90008-J. [25] Gazetas G, Mylonakis G. Seismic soil-structure interaction: new evidence and emerging issues. In: Dakoulas P, Yegian M, Holtz RD, editors. Geotech. Earthq. Eng. Reston, VA: Soil Dyn.; 1998. p. 1119–74. [26] Shang Y, Alipour A, Ye A. Selection of input motion for seismic analysis of scoured pile-supported bridge with simplified models. J Struct Eng 2018;144. https://doi. org/10.1061/(ASCE)ST.1943-541X.0002067. 4018099. [27] Sun K. A numerical method for laterally loaded piles. Comput Geotech 1994;16: 263–89. https://doi.org/10.1016/0266-352X(94)90011-6. [28] Trochanis AM, Bielak J, Christiano P. Three-dimensional nonlinear study of piles. J Geotech Eng 1991;117:429–47. https://doi.org/10.1061/(ASCE)0733-9410 (1991)117:3(429). [29] Wakai A, Gose S, Ugai K. 3-D elasto-plastic finite element analyses of pile foundations subjected to lateral loading. Soils Found 1999;39:97–111. https://doi. org/10.3208/sandf.39.97. [30] Wang X, Ye A, Shafieezadeh A, Li J. Shallow-layer p-y relationships for micropiles embedded in saturated medium dense sand using quasi-static test. Geotech Test J 2017;41. https://doi.org/10.1520/GTJ20160289. 20160289. [31] Allotey N, El Naggar MH. A numerical study into lateral cyclic nonlinear soil–pile response. Can Geotech J 2008;45:1268–81. https://doi.org/10.1139/T08-050. [32] Blanco G, Ye A, Wang X, Goicolea JM. Parametric pushover analysis on elevated RC pile-cap foundations for bridges in cohesionless soils. J Bridge Eng 2019;24: 04018104. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001328. [33] Hutchinson TC, Chai YH, Boulanger RW. Simulation of full-scale cyclic lateral load tests on piles. J Geotech Geoenviron Eng 2005;131:1172–5. https://doi.org/ 10.1061/(ASCE)1090-0241(2005)131:9(1172). [34] Yang Z, Jeremi�c B. Study of soil layering effects on lateral loading behavior of piles. J Geotech Geoenviron Eng 2005;131:762–70. https://doi.org/10.1061/(ASCE) 1090-0241(2005)131:6(762). [35] Elgamal A, Yan L, Yang Z, Conte JP. Three-dimensional seismic response of humboldt bay bridge-foundation-ground system. J Struct Eng 2008;134:1165–76. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:7(1165). [36] Saeedi Azizkandi A, Baziar MH, Rasouli H, Modarresi M, Shahnazari H. Centrifuge modeling of non-connected piled raft system. Int J Civ Eng 2015;13:114–23. [37] Azizkandi AS, Baziar MH, Yeznabad AF. 3D dynamic finite element analyses and 1 g shaking table tests on seismic performance of connected and nonconnected piled raft foundations. KSCE J Civ Eng 2018;22:1750–62. https://doi.org/10.1007/ s12205-017-0379-2. [38] Baziar MH, Rafiee F, Lee CJ, Saeedi Azizkandi A. Effect of superstructure on the dynamic response of nonconnected piled raft foundation using centrifuge

[39] [40] [41] [42] [43]

[44] [45] [46] [47] [48] [49] [50] [51] [52]

[53]

[54] [55] [56] [57] [58] [59] [60] [61] [62] [63]

17

modeling. Int J GeoMech 2018;18:04018126. https://doi.org/10.1061/(ASCE) GM.1943-5622.0001263. Mazzoni S, McKenna F, Scott MH, Fenves GL. OpenSees command language manual. Pacific Earthquake Engineering Research (PEER). Center; 2007. Iai S. Similitude for shaking table tests on soil-structure-fluid model in 1g gravitational field. Soils Found 1989;29:105–18. Mokwa RL. Investigation of the resistance of pile caps to lateral loading. 1999. Virginia Tech. Duncan JM, Evans LT, Ooi PSK. Lateral load analysis of single piles and drilled shafts. J Geotech Eng 1994;120:1018–33. https://doi.org/10.1061/(ASCE)07339410(1994)120:6(1018). Wang X, Shafieezadeh A, Ye A. Optimal EDPs for post-earthquake damage assessment of extended pile-shaft–supported bridges subjected to transverse spreading. Earthq Spectra 2019;35:1367–96. https://doi.org/10.1193/ 090417EQS171M. Chadwell CB, Imbsen RA. XTRACT: a tool for axial force-ultimate curvature interactions. Struct.. Reston, VA: American Society of Civil Engineers; 2004. p. 1–9. https://doi.org/10.1061/40700(2004)178. 2004,. Scott BD, Park R, Priestley MJN. Stress-strain behavior of concrete confined by overlapping hoops at low and high strain rates. J. Proc. 1982;79:13–27. ASTM. Standard practice for classification of soils for engineering purposes (Unified Soil Classification System). ASTM Stand Guid; 2017. D2487-17:1–10. Gazetas G, Dobry R. Horizontal response of piles in layered soils. J Geotech Eng 1984;110:20–40. https://doi.org/10.1061/(ASCE)0733-9410(1984)110:1(20). Kuhlemeyer RL. Static and dynamic laterally loaded floating piles. J Geotech Geoenviron Eng 1979;105:289–304. Randolph MF. The response of flexible piles to lateral loading. Geotechnique 1981; 31:247–59. https://doi.org/10.1680/geot.1981.31.2.247. Velez A, Gazetas G, Krishnan R. Lateral dynamic response of constrained-head piles. J Geotech Eng 1983;109:1063–81. https://doi.org/10.1061/(ASCE)07339410(1983)109:8(1063). He Z, Liu W, Wang X, Ye A. Optimal force-based beam-column element size for reinforced-concrete piles in bridges. J Bridge Eng 2016;21:06016006. https://doi. org/10.1061/(ASCE)BE.1943-5592.0000926. Wang X, Shafieezadeh A, Ye A. Optimal intensity measures for probabilistic seismic demand modeling of extended pile-shaft-supported bridges in liquefied and laterally spreading ground. Bull Earthq Eng 2018;16:229–57. https://doi.org/ 10.1007/s10518-017-0199-2. Wang X, Ye A, Shafieezadeh A, Padgett JE. Fractional order optimal intensity measures for probabilistic seismic demand modeling of extended pile-shaftsupported bridges in liquefiable and laterally spreading ground. Soil Dynam Earthq Eng 2019;120:301–15. https://doi.org/10.1016/j.soildyn.2019.02.012. Kent DC, Park R. Flexural members with confined concrete. J Struct Div 1971;97: 1969–90. Mander JB, Priestley MJN, Park R. Theoretical stress-strain model for confined concrete. J Struct Eng 1988;114:1804–26. https://doi.org/10.1061/(ASCE)07339445(1988)114:8(1804). Filippou FC, Popov EP, Bertero VV. Modeling of R/C joints under cyclic excitations. J Struct Eng 1983;109:2666–84. https://doi.org/10.1061/(ASCE)0733-9445 (1983)109:11(2666). API (American Petroleum Institute). Recommended practice for planning, designing and constructing fixed offshore platforms-working stress design. seventeenth ed. 1987. Washington D.C. ATC (Applied Technology Council). Improved seismic design criteria for California bridges: provisional recommendations. Calif: Redwood City; 1996. Dyson GJ, Randolph MF. Monotonic lateral loading of piles in calcareous sand. J Geotech Geoenviron Eng 2001;127:346–52. https://doi.org/10.1061/(ASCE) 1090-0241(2001)127:4(346). Polam I, Kapuskar M, Chaudhuri D. Modeling of pile footing and drilled shafts for seismic design. 1998. Technical Report MCEER-98-0018. Buffalo, NY. Brown Da, O’Neill MW, Hoit M, McVay M, El Naggar MH, Chakraborty S. Static and dynamic lateral loading of pile groups. Technical Report NCHRP Report No.461. 2001. Washington, D.C. Rollins KM, Olsen KG, Jensen DH, Garrett BH, Olsen RJ, Egbert JJ. Pile spacing effects on lateral pile group behavior: analysis. J Geotech Geoenviron Eng 2006; 132:1272–83. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:10(1272). Fayyazi MS, Taiebat M, Finn WDL. Group reduction factors for analysis of laterally loaded pile groups. Can Geotech J 2014;51:758–69. https://doi.org/10.1139/cgj2013-0202.