Explicit dynamics: P and S wave speeds in a soil column from virtual geophones
Explicit dynamics (waves in a continuum)PASS · 0.68%A Ricker pulse (15 Hz) pressure (P) or shear traction (S) is applied at the free end of a laterally confined soil column; an absorbing boundary closes the far end. Virtual geophones record particle velocity; the wave speed is the cross-correlation lag between two geophones 800 m apart, compared with sqrt((K + 4/3 G)/rho) and sqrt(G/rho). The amplitude of the plane wave must equal p/(rho c_p) and tau/(rho c_s). The script shows the P run; the S run (shear traction, u_x = u_z = 0 rollers on the lateral faces, h = 1.25 m) is executed by the verification runner the same way.A Ricker pulse (15 Hz) pressure (P) or shear traction (S) is applied at the free end of a laterally confined soil column; an absorbing boundary closes the far end. Virtual geophones record particle velocity; the wave speed is the cross-correlation lag between… show full text
- Tolerance:
- 5%
Problem statement
- Geometry
- Column 1500 × 5 × 5 m (P: 300 HEX8 elements, h = 5 m; S: 1200 elements, h = 1.25 m); lateral faces confined (symmetry for P; u_x = u_z = 0 rollers for S).
- Material
- Soil: E = 5 GPa, nu = 0.25, rho = 2000 kg/m³ (c_p = 1732.05 m/s, c_s = 1000 m/s).
- Boundary conditions
- Face x = 0: Ricker pressure 1 MPa, 15 Hz (P) or y-traction 1 MPa (S); face x = 1500 m: Lysmer–Kuhlemeyer absorbing boundary; time-step factor 0.8.
- Measured quantity
- Geophones at x = 300, 700, 1100 m; cross-correlation lag of the velocity records a→c; peak velocity at a.
WebCAE Terminal
Paste these commands into the Terminal panel inside WebCAE. They use the same text DSL as the application; run one command per line:
units mm
material E=5000000000 nu=0.25 density=2000
box dx=1500000 dy=5000 dz=5000
mesh hex nx=300 ny=1 nz=1
explicit endTime=1.425833 dtScale=0.8 saveStride=1000000 bulkQ1=0 bulkQ2=0
bc explicit_pressure surface number 1 value=1000000 ricker=15
bc explicit_absorbing surface number 2
bc explicit_symmetry surface number 3
bc explicit_symmetry surface number 4
bc explicit_symmetry surface number 5
bc explicit_symmetry surface number 6
explicit geophone at=300000,0,0 name=a
explicit geophone at=700000,0,0 name=b
explicit geophone at=1100000,0,0 name=c
solve explicit
probe explicit_wave_speed geophone=a geophone2=c component=vx method=xcorr from=0.157735 to=0.821688 id="cp"
probe explicit_geo_peak geophone=a component=vx id="va"
probe explicit_geo_peak geophone=c component=vx id="vc"
probe explicit_steps id="steps"Results comparison
| Reference value | c_p = 1732.05 m/s, c_s = 1000 m/s |
| Our result | c_p = 1726.21 m/s, c_s = 999.115 m/s |
| Deviation | 0.68% |
| Tolerance | 5% |
| Status | PASS · 0.68% |
| Element family | Solid element |
| Mesh details | P: 300×1×1 HEX8 (h = 5 m, 798 steps); S: 1200×1×1 HEX8 (h = 1.25 m, 5032 steps);: webcae_solve (native) |
Updated: 2026-10-22 · version not recorded