Dynamic response of composite caissonpiles foundations Maosong Huang Department of Geotechnical Engineering Tongji University, Shanghai, China
Outline of talk 1 Introduction 2 Lateral response 3 Seismic response 4 Centrifuge tests 5 Concluding remarks -2-
1 Introduction Railway and highway channel across Qiongzhou straits in south China sea Site of the project: Qiongzhou Straits Hainan Island -3-
1 Introduction Site of the project: Qiongzhou Straits Hainan Island average width: 29.5 km narrowest point: 18 km Railway Ferry Service across Qiongzhou Straits (currently) Debate over the choice of a bridge or a tunnel for a long time West line: bridge (maximum water depth 55m) Middle line: easy connection tunnel (short) bridge (maximum water depth 75m) West line middle line Hainan Island -4-
Cable stayed bridge Suspension bridge Sutong (1088m, China, 2008) Akashi Kaikyo (1991m, Japan, 1998) Qiongzhou Straits Bridge (3000m) 2 1500m cable stayed bridge 3000m suspension bridge -5-
1 Introduction Caisson foundations have been widely used to support bridges. Examples: Tagus bridge (Portugal), supported on perhaps the tallest (88 m high) caisson in the world; San-Francisco-Oakland bay bridge whose major pier is founded on a 75 m high caisson. Massive caissons played a major role in the survival of several bridges during the Kobe 1995 earthquake. Despite their large dimensions, caisson foundations have been shown not to be immune to seismic loading as it was believed for many years. This was confirmed in the Kobe (1995) earthquake, which caused many structures founded on caissons to suffer severe damage. (Gerolymos and Gazetas, 2006)
Possible choice of deepwater foundations for Qiongzhou Strait bridge (pre-construction design) Caisson foundation (118m high) Composite caissonpiles foundation (88m high caisson, 90m long pile) -7-
1 Introduction The composite caisson-piles foundation (CCPF) was proposed in the pre-construction investigation report for the highway channel across Qiongzhou straits between the mainland and Hainan Island of China, with the expectation that adding piles beneath the caisson can improve its behavior under lateral and seismic loads. The important issue is how the piles added beneath the caisson can influence the whole system. -8-
2 Lateral response 2.1 Impedance matrix of the caisson in layered soils Four-spring Winkler model for caissons Equilibrium of external loads, soil resistance and inertial forces with respect to the base center ~ K 2 b Mb Kb Pb HH K b ~ K ~ K ~ K h HH MH n i1 u ~ K HM ~ K ~ k xi MM u b the horizontal displacement of the base center θ- the rotation d i n n ~ ~ ~ ~ ~ ~ K HM K MH k xi d i z KMM Kr k i i1 i1 Gerolymos and Gazetas (2006) xi di z 1 d 12 2 2 ~ i i k i -9- di
2 Lateral response Complex stiffness of the distributed translational springs k x, static ~ k x kk K H x, static I tw is the horizontal embedment factor ~ k x I d tw 1 ic k ~ ~ 1 2 ~ k k 1 d k x 1 k 1k 1, static i 3 c 1 x x I tw emb 1 I 1 Complex stiffness of the distributed rotational springs k tw 1, static Г w is the rocking embedment factor K M Γ d w 1 Gerolymos and Gazetas (2006) -10-
2 Lateral response Modification and verification of the four-spring Winkler model (1) Modification of the embedment factors difference between the depth-width ratios of rigid caissons (0.5 d/b 4) and those of shallow footings (d/b 1) Horizontal embedment factor I tw I tw 0.5 0.8 1.3 d d d 10.21 1.43 0.30 B B B Rocking embedment factor Г w d Γ w 0.6 2.5 d d 12.09 5.18 B B Gerolymos and Gazetas (2006) Gazetas (1991) for shallow footings -11-
2 Lateral response Horizontal embedment factor Rocking embedment factor No modification is needed for the horizontal embedment factor I tw A new expression of the rocking embedment factor Г w Γ w 0.6 2.5 d d 12.25 7.01 B B -12-
2 Lateral response (2)Verification by frequency domain finite element simulations with the sponge boundary The reflection of outgoing waves back into the region of interest can be avoided by enclosing the region in a sponge layer having high damping coefficients. The damping is introduced by means of Rayleigh damping and is gradually increased with distance to avoid any spurious reflections due to sudden change in impedance. Sponge Boundary Varun, Assimaki, Gazetas (2009) Truncated numerical domain -13-
2 Lateral response Dynamic response of a cylindrical caisson in homogeneous soil Horizontal displacements Rotation angles Homogeneous soil -14-
2 Lateral response Dynamic response of a cylindrical caisson in layered soils Horizontal displacements Rotation angles Layered soils -15-
2 Lateral response Good agreements between the finite element simulation and the modified four-spring Winkler model show the significance of the modification on the rocking embedment factor Г w. -16-
2 Lateral response 2.2 Impedance matrix of the pile group in layered soils It is essential to couple the axial vibration into lateral vibration, because the piles will deform vertically once the CCPF rotates, with the vertical reaction forces exerted to the caisson, equivalent to a resultant reaction moment. -17-
2 Lateral response Axial vibration of the pile group d 2 Axial vibration equation of a sole (active) pile d 2 w z i 2 dz hi V i 2 w i z 0 Axial vibration equation of a passive pile z V kpzi icpzi i s w11, i z 2 V i w21, i z i p p w21, i 2 dz h E A (improvement over the interaction factor) Active pile Passive pile Axial displacement at the head of pile k in a pile group w N V V k kj f Vj j1 Dynamic Winkler model for vertical vibration -18-
2 Lateral response Lateral vibration of the pile group Lateral vibration equation of a sole pile d 4 u i dz z 4 hi H i 4 u i z 0 Active pile Passive pile Lateral vibration equation of a passive pile d 4 z H k pxi i cpxi i s, u11, i z 4 H i u21, i z i p p u21, i 4 dz h E I (improvement over the interaction factor) Lateral displacements at the head of pile k in a pile group N uk H j H H α kjf k j1 M j Dynamic Winkler model for lateral vibration -19-
2 Lateral response Axial-lateral coupled vibration of the pile group The resultant forces of the loads undertaken by all the piles must equal the loads applied on the cap u u x ( ) u k k G G 2 G k G G G wk w xk N k1 N k1 N k1 H k H G G M V x M V k k k k V Overall equation for axial-lateral coupled vibration G G O A12 A13 A14 u P A21 A22 A23 O H O A 31 A32 A33 O M O A O O A V O 41 44 Lateral impedance of the pile group 1 G Axial-lateral coupled vibration of the pile group with rigid cap subjected to vertical, horizontal and moment loads R A A A A A A A A A A A A A A A A A A 1 1 1 1 1 HR 12 13 23 22 32 33 23 22 33 23 21 31 13 23 21 14 44 41-20-
2 Lateral response 2.3 Lateral response of CCPFs: verification and example A Winkler model for the lateral response of CCPFs The lateral vibration equation of a CCPF with respect to the base center of its caisson part K u b cp P b The impedance matrix of the CCPF K K K cp c p K c and K p are the impedance matrixes of the caisson and the pile group -21-
Verification frequency-domain FEM with the sponge boundary Sponge boundary Numerical domain Dynamic analysis Homogeneous soil Normalized complex swaying stiffness -22-
Normalized complex cross swaying-rocking stiffness Normalized complex rocking stiffness -23-
2 Lateral response Horizontal displacements and rotation angles of the caisson and the CCPFs These comparisons show that the simplified method agrees well with the numerical simulations, demonstrating the reliability of the simplified method. -24-
Numerical example: a CCPF with different pile lengths Piles make great contribution to the foundation in resisting the lateral loads. The impedances of the foundation increase and the displacements decrease significantly after adding piles beneath the caisson Horizontal displacements and rotation angles of the CCPFs -25-
3 Seismic response 3.1 Method of analysis While considering only linear elasticity, the seismic response of a soil-foundationstructure system can be divided into two parts, i.e. kinematic response and inertial response. -26-
3 Seismic response Kinematic response of a caisson Dynamic equilibrium of the caisson with no mass considered K b u KI KI H eff K b 2 d k xd K h k x 2 2 3 d d k k dk K 2 3 x x r based on the coefficients of the modified four-spring model H H eff eff M eff x ff sin cos 0 h ff 0 eff Vs Vs Vs H k u d K u d 2 M eff k xu ff 0 1 cos d k u ff 0 1 cos d K ru ff 0 sin d Vs Vs Vs Vs Vs
3 Seismic response Kinematic response of a pile group Horizontal displacement of a sole pile subjected to S-wave Horizontal displacement and rotation angle of the head of pile k in a pile group Axial-lateral coupled kinematic response of a pile group 11 cos u p z u ff 0 z Vs k ic px px 4 E I m k ic 2 p p p px px Vs KI kj u ff 0 cos z p N u H V k j s H H αkjf k j1 M j KI kj u ff 0 sin z p Vs V s caused by the vertical load at the head G G O A12 A13 A14 u P A A A O H F KI 21 22 23 H KI A 31 A32 A33 O M FM 1 KI A4 O O A44 V FV kinematic response subjected to S-wave
3 Seismic response Kinematic response analysis of a CCPF Dynamic equilibrium K b u KI KI H Caisson eff KI G u H Kb KI G Heff CCPF M adding the resultant horizontal force H G and moment M G of all the piles Kinematic response of the CCPF subjected to S-wave KI Kb A12 A13 A14 u Heff KI A21 A22 A23 O H FH KI A 31 A32 A33 O M FM KI A14 O O A44 V FV KI u KI G u u KI G The horizontal displacement and rotation angle of the base center of the caisson part equals those of the top of the pile group -29-
3 Seismic response Simplified model for a CCPF-structure system The structure is simplified as lumped mass and an elastic column connected to the foundation, and the foundation is replaced with mass matrix and lateral impedance. u 0 s 2 1 0 s K m ub uk R HV b k Kss Ksb K K K R bs bb HV u s and s as the horizontal displacement and rotation angle of the superstructure, while u b and b of the foundation. -30-
3 Seismic response 3.2 Comparison against time-domain 3D finite element simulation Domain Reduction Method (DRM) (Bielak et al., 2003; Jeremic et al., 2009) DRM is a two-stage finite element method. It was proposed for the aim of reducing computational domain and increasing the efficiency. DRM layer Stage 1: The free field response under earthquake is computed to get the acceleration and displacement histories of the nodes Stage 2: The effective forces of the nodes on the DRM layer are calculated, and the seismic response of computational domain, namely the small region enveloped by the DRM layer is computed. -31-
3 Seismic response Simulation results and comparison with the proposed simplified method Step 1: Simulation of free-field soil Homogeneous soil Young s modulus 41.6 MPa Poisson s ratio 0.30 mass density 1600 kg/m 3 Shear wave velocity 100 m/s damping ratio 5% (Rayleigh damping) Thickness of the soil 100 m. Time history and amplitude spectrum of Corralitos wave -32-
3 Seismic response Step 2: Simulation of foundation-structure system Finite element mesh used in the second stage of DRM -33-
3 Seismic response Displacement time histories at the superstructure Displacement time histories atop the foundation These results show good agreements between the two methods, demonstrating the reliability of the simplified method. -34-
3 Seismic response 3.3 Mechanism and significance of adding piles in seismic problems Model parameters and input motion Predominant frequencies 2Hz 4Hz Geometrical properties of the CCPFstructure system Time history and amplitude spectrum of Shanghai artificial middle wave -35-
3 Seismic response Kinematic and seismic responses in relatively hard soil shear wave velocity 151.9m/s pseudo-resonance frequency 12.6Hz Normalized kinematic horizontal displacements and rotation angles of the foundation pseudo-resonance frequency depends mainly on the shear wave velocity of the soil and the embedment depth of the caisson somewhat alike to the resonance but different from it in mechanism -36-
3 Seismic response Relatively hard soil Since two predominant frequencies of the Shanghai artificial middle wave are about 2 Hz and 4 Hz, which are in the relatively low range in this case, far from the pseudo-resonance frequency, it can be predicted that adding piles in this case will have no significant influence on the seismic response of the CCPF. Acceleration time histories at the superstructure and foundation -37-
3 Seismic response Kinematic and seismic responses in relatively soft soil shear wave velocity 50.6 m/s pseudo-resonance frequency 4.2 Hz Normalized kinematic horizontal displacements and rotation angles of the foundation -38-
3 Seismic response Relatively soft soil Since the pseudo-resonance frequency is close to the second predominant frequency of the Shanghai artificial middle wave, 4 Hz, it can be predicted that adding piles in this case will have great significance in the seismic response. Acceleration time histories at the superstructure and foundation -39-
3 Seismic response Relatively soft soil Horizontal displacement time histories at the superstructure and atop the foundation Rotation angle time histories at the superstructure and atop the foundation -40-
3 Seismic response Relatively soft soil Peak values of seismic results of the foundation-structure system Caisson CCPF All the responses decrease remarkably after adding piles, indicating great significance of the piles. -41-
4 Dynamic centrifuge tests 4.1 Centrifuge model set-up Shaking table Tongji Centrifuge Laminar Box (to eliminate the boundary effect) -42-
4 Dynamic centrifuge tests Tested soil Shanghai sandy silt, relatively dryer (water content 7%), density 1467kg/m 3 Earthquake input motion Acceleration time history for Artificial Middle Shanghai Earthquake (SSE) -43-
4 Dynamic centrifuge tests Test program -44-
-45 Layout of the models and sensors in tests
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4 Dynamic centrifuge tests 4.2 Test results and analysis Test 1: Free field and single pile -structure structure top Ground surface acceleration decays Accelerations -47-
4 Dynamic centrifuge tests Test 2: Caisson-structure and Single pile-structure structure top Single pile-structure Caisson-structure -48-
4 Dynamic centrifuge tests Test 3: CCPF-structure and single pile-structure structure top Accelerations Single pile-structure CCPF-structure -49-
4 Dynamic centrifuge tests Test 4: Grouped piles-structure and single pile-structure structure top Accelerations Single pile-structure Grouped pile-structure -50-
4 Dynamic centrifuge tests Peak accelerations for different type of foundations Relative peak acceleration to the ground surface Test results indicate that, for soil with low stiffness acceleration decays in the process of earthquake wave propagating upwards; adding piles under the caisson could decrease the earthquake responses of both the foundation and structure. -51-
4 Dynamic centrifuge tests 4.3 Comparison of the proposed simplified method with centrifuge tests Simulated results 1 1 0.5 0.5 a (g) 0 a (g) 0-0.5 A2-6 -0.5 A3-6 a (g) 0.5-0.5-1 -1 1 0 0 5 10 15 20 25 30 t (s) A2-5 0 5 10 15 20 25 30 t (s) Test 2: Caisson-structure Acceleration: at the superstructure (upper) and atop the foundation (lower) a (g) -1 1 0.5 0-0.5-1 0 5 10 15 20 25 30 t (s) 0 5 10 15 20 25 30 t (s) Test 3: CCPF-structure A3-5 Acceleration: at the superstructure (upper) and atop the foundation (lower) -52-
4 Dynamic centrifuge tests Comparisons of peak accelerations and strains Reasonable agreement between centrifuge test results and theoretical simulations by the proposed simplified method. Observed peak accelerations atop the foundation are much greater than simulated ones, and this is mainly due to the separation between the foundation and surrounding soil. -53-
5 Concluding remarks (1) A simplified method for lateral vibration and kinematic responses of the CCPF with a dynamic Winkler model is developed, and then a foundation-structure interaction model is created to solve the seismic response of the foundation-structure system subjected to seismic S- wave. Comparing with the 3D finite element and dynamic centrifuge tests, the reliability of this simplified method is verified. (2) Piles make great contribution to the foundation in resisting the lateral loads. The impedances of the foundation increase and the displacements decrease significantly after adding piles beneath the caisson. The increasing rate of the impedances and the decreasing rate of the displacements become smaller while the pile length becomes larger, showing that there is a limitation upon the pile length. -54-
5 Concluding remarks (3) The pseudo-resonance frequencies of the caisson are mainly determined by the soil properties and caisson depth. It may be in danger if its pseudo-resonance frequency is close to the predominant frequency of the earthquake. Discovered in this study is that adding piles under the caisson is an efficient way to increase seismic resistant capability of the soil-foundation-structure system, and the main mechanism of that is the elimination of the pseudo-resonance. (4) Dynamic centrifuge test results reveal that, for soil with low stiffness acceleration decays in the process of earthquake wave propagating upwards; adding piles under the caisson could reinforce the foundationstructure system in resisting earthquakes. In the meanwhile, also indicated is that the traditional grouped pile foundation has a great capability of reducing the earthquake responses, if their construction condition is permitted. -55-
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