Numerical Simulation of Underground RC Structures During Earthquakes
〇 Ming-wu WANG・Susumu IAI・Tetsuo TOBITA
１．Introduction 3. Results and comparisons
Conclusions
erical simulation are consistent wit
Many underground structures during the Hyogoken-Nanbu earthquake were destroyed. In order to insure the safety of underground structures and develop a rational seismic design guideline, seismic performance of underground RC structures of nuclear power plant subjected to strong motions requires further attention. Analytical method based on the effective stress analysis, FLIP is widely used to study seismic response of structures and to verify results from centrifuge modeling.
LUpp er -100 0 100 200 300 400 500 0 10 20 30 No rm al S tres s (k Pa)
—Effect ive stress
—Total stress
Computed Saturation model
LMiddle -100 0 100 200 300 400 500 0 10 20 30 No rm al Stres s (k Pa)
—Effect ive stress
—Total stress
Computed Saturation model
LBottom -100 0 100 200 300 400 500 0 10 20 30 Time (s) No rm al Str ess (k Pa)
—Effect ive stress
—Total st ress
Computed Saturation model
LUp p er -100 0 100 200 300 400 500 0 10 20 30 No rm al S tress (k Pa)
Computed Dry model
LMiddle -100 0 100 200 300 400 500 0 10 20 30 No rm al Stres s (k Pa)
Computed Dry model
LBot tom -100 0 100 200 300 400 500 0 10 20 30 Time (s) No rm al S tres s (kPa)
Computed Dry model
RCTop M iddle 0 100 200 300 0 10 20 30 Norm al Stre ss (k Pa) — Computed
— M easured Saturation model
RC Top Right 0 100 200 300 0 10 20 30 No rm al S tres s (k Pa) — Computed
— M easured Saturation model
2．Centrifuge test and numerical modeling
4.
Results of num
h the one obtained from centrifuge tests. Displacements and plastic yielding area of RC structures and earth pressures of saturation model are larger than those of dry model. Compared with results of dry model, values of normal stress acting on the upper side of the RC structure in saturation model is smaller. This may be due to the arching effects induced by shaking.
Fig. 1 Centrifuge test model y
x 0 10 m
Bottom boundary fixed
MPC Uxof sand nodes at both lateral boundarues
MPC Uxof RC vertical side nodes and sand nodes
Nonlinear beam element
MPC Ux, Uy 0.00m -6.87m 15.87m 30.00m Mutli-spring element + Porewater element
Linear beam element
--30.00m y
x 0 10 m
Bottom boundary fixed
MPC Uxof sand nodes at both lateral boundarues
MPC Uxof RC vertical side nodes and sand nodes
Nonlinear beam element
MPC Ux, Uy 0.00m -6.87m 15.87m 30.00m Mutli-spring element + Porewater element
Linear beam element
--30.00m y
x 0 10 m
Bottom boundary fixed
MPC Uxof sand nodes at both lateral boundarues
MPC Uxof RC vertical side nodes and sand nodes
Nonlinear beam element
MPC Ux, Uy 0.00m -6.87m 15.87m 30.00m Mutli-spring element + Porewater element
Linear beam element
--30.00m y
x 0 10 m
Bottom boundary fixed
MPC Uxof sand nodes at both lateral boundarues
MPC Uxof RC vertical side nodes and sand nodes
Nonlinear beam element
MPC Ux, Uy 0.00m -6.87m 15.87m 30.00m Mutli-spring element + Porewater element
Linear beam element
--30.00m
Fig. 2 Mesh，boundary, element type for numerical modeling
0 10 20 30 40 50 60 70 80 90 100
1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01
Shear strain γ Sh e ar m od ul us G (M pa) σm'=120kPa,Dr=84% σm'=120kPa,Dr=84% σm'=100kPa,Dr=84% FLIP : σm'=98kPa
0.00 0.05 0.10 0.15 0.20 0.25 0.30
1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01
Shear strain γ H y st er et ic d a m pi ng f a to r h σm'=120kPa,Dr=84% σm'=120kPa,Dr=84% σm'=100kPa,Dr=84% FLIP : σm'=98kPa Fig. 3 Sand deformation parameters from test and used in FLIP
-80 0 80 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 Shear Strain S hea r S tres s (k P a) S1=0.005 -80 0 80 0 50 100 150
Effective Mean Stress (kPa)
S hea r S tres s (k P a) S1=0.005
Fig. 4 Cyclic curves of undrained simulation using Flipsim
Input Acc -10 0 10 0 10 20 30 Time (s) A cceler ati o n ( m /s 2) Saturation model Input Acc -10 0 10 0 10 20 Time (s) A ccel e rat io n ( m /s 2) Dr 30 y model
Fig. 5 Input-waves of numerical simulation
-σx+EPWP -σy+EPWP τxy Disp -σx+EPWP -σy+EPWP τxy Disp
Fig. 8 Normal stress, shear stress with Max x-displacement of RC structure
Fig. 9 EPWP ratio, deformation of saturation model after shaking Left T op -2000 -1000 0 1000 2000 -0.003 0 0.003 0.006 0.009 0.012 0.015 Curvature (1/m) Bending Moment(kN m) RC
Computed Saturation model
Left 4 -2000 -1000 0 1000 2000 -0.003 0 0.003 0.006 0.009 0.012 0.015 Curvature (1/m) Bending M oment (kN m ) RC
Computed Saturation model
Left 9 -2000 -1000 0 1000 2000 -0.003 0 0.003 0.006 0.009 0.012 0.015 Curvature (1/m) Bending M oment(kN m) RC
Computed Saturation model
Left Bot tom -2000 -1000 0 1000 2000 -0.003 0 0.003 0.006 0.009 0.012 0.015 Bending M oment(kN m) RC
Computed Saturation model
Curvat ure (1/m) Left Top -2000 -1000 0 1000 -0.003 0 0.003 0.006 0.009 0.012 0.015 Curvat ure (1/m) Be nding M oment (kN m) RC Dry model 2000 Computed Left 4 -2000 -1000 0 1000 -0.003 0 0.003 0.006 0.009 0.012 0.015 Curvature (1/m) Bending M oment(kN m) RC Dry model 2000 Computed Left 9 -2000 -1000 0 1000 2000 -0.003 0 0.003 0.006 0.009 0.012 0.015 Bending Moment (kN m) RC
Computed Dry model
Curvat ure (1/m) Left Bottom -2000 -1000 0 1000 2000 -0.003 0 0.003 0.006 0.009 0.012 0.015 Bending Moment (kN m) RC
Computed Dry model
Curvature (1/m) Fig. 7 Bending moment-curvature relationship
Time (s) RC T op Left 0 100 200 300 0 10 20 30 No rm al Stress (k Pa) — Computed
— M easured Saturation model
RC Top M iddle -100 0 100 0 10 20 30 S hearing Stre ss (k Pa) — Computed
— Measured Saturation model
RC Top Right -100 0 100 0 10 20 30 Shea ring S tres s (k Pa) — Computed
— Measured Saturation model
Time (s) RC Top Left -100 0 100 0 10 20 30 Shea ring S tres s (k Pa) — Computed
— Measured Saturation model Structure top A -100 0 100 0 10 20 30 RC Dis placem en t (mm)
Computed Saturation model
Right side sand B -100 0 100 0 10 20 30 Time (s) Dis placem ent (mm) Saturation model Computed PW-S3 0 20 40 60 80 100 0 10 20 30 EP W P (k
Pa) Computed Saturation model
Structure top A -100 0 100 0 10 20 30 RC Dis placem en t (mm) Saturation model Measured
Right side sand B -100 0 100 0 10 20 30 Time (s) D isp lacem en t (mm) Saturation model Measured PW-S3 0 20 40 60 80 100 0 10 20 30 EP W P (
kPa) Measured Saturation model
Structure top A -100 0 100 0 10 20 30 RC Dis placem en t (m m )
Computed Dry model
Right side sand B -100 0 100 0 10 20 30 Time (s) D isplacem en t (m m)
Computed Dry model
RC Structure top A -100 0 100 0 10 20 30 RC Displacem en t (m m ) Dry model Measured
Right side sand B
-100 0 100 0 10 20 30 Time (s) Dis placem en t (m m ) Dry model RC Measured
