Note
Go to the end to download the full example code
One Dimensional Terzaghi’s Consolidation Problem with Permeability as Function of Depth#
- Problem description:
The test case is to simulate a one-dimensional Terzaghi’s problem with permeability as a function of the soil depth. A pressure P is applied on the top surface of the soil with depth H and width W. The top surface of the soil is fully permeable and the permeability decreases linearly with depth. The excess pore water pressure for 0.1, 0.2, 0.3, 0.4, and 0.5 day is calculated and compared against the reference results obtained using the PIM method (Figure 5, pg. 5916).
- Reference:
A POINT INTERPOLATION METHOD FOR SIMULATING DISSIPATION PROCESS OF CONSOLIDATION, J.G.WANG, G.R.LIU, Y.G.WU, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 190 (2001),PG: 5907-5922
- Analysis type(s):
Static Analysis
ANTYPE=0
- Element type(s):
2D 4-Node Coupled Pore-Pressure Element (CPT212)
- Material properties:
Youngs modulus, \(E = 4 \cdot 10^7 Pa\)
Poissons ratio, \(\mu = 0.3\)
Permeability value at bottom of the soil, \(fpx = 1.728 \cdot 10^-3 m/day\)
Permeability value at the top of the soil = \(100 * fpx\)
- Geometric properties:
Height, \(H = 16 m\)
Width, \(W = 1 m\)
- Loading:
Pressure, \(P = 1 \cdot 10^4 Pa\)
- Analysis Assumptions and Modeling Notes:
The soil is modeled using 2D CPT212 elements with plane strain element behavior. The UX degree of freedom for all nodes is constrained and the UY degree of freedom at the bottom of the soil is constrained. The pressure degree of freedom at the top edge is constrained to make it fully permeable. Linearly varying permeability of the soil is defined using the TB,PM material model. Static analysis is performed with an end time of 86400 seconds (1 day) and with stepped pressure loading P on the top edge of the soil. The excess water pore pressure at depth H = 6 m is computed for 0.1 (8640 s), 0.2 (17280 s), 0.3 (25920 s), 0.4 (34560 s), and 0.5 days (43200 s) by interpolating the solution obtained at the nearest time points.
# sphinx_gallery_thumbnail_path = '_static/vm295_setup.png'
# Importing the `launch_mapdl` function from the `ansys.mapdl.core` module
from ansys.mapdl.core import launch_mapdl
import numpy as np
# Launch MAPDL with specified options
mapdl = launch_mapdl(loglevel="WARNING", print_com=True, remove_temp_dir_on_exit=True)
# Clear the current database
mapdl.clear()
# Run the FINISH command to exists normally from a processor
mapdl.finish()
# Set the ANSYS version
mapdl.com("ANSYS MEDIA REL. 2022R2 (05/13/2022) REF. VERIF. MANUAL: REL. 2022R2")
# Run the /VERIFY command for VM295
mapdl.run("/VERIFY,VM295")
# Set the title of the analysis
mapdl.title(
"VM295 1D TERZAGHI'S CONSOLIDATION PROBLEM WITH PERMEABILITY AS FUNCTION OF DEPTH"
)
# Entering the PREP7 environment in MAPDL
mapdl.prep7(mute=True)
# Set Parameters
day = 24 * 3600 # SECONDS IN ONE DAY
h = 16 # TOTAL DEPTH OF SOIL IN METERS
w = 1 # WIDTH OF SOIL IN METERS
pres = 1e4 # PRESSURE IN PA
ex = 4e7 # YOUNG'S MODULUS IN PA
tt = 1 * day
Define element type and properties#
Use 2D 4 NOode Coupled Pore Pressure Element (CPT212) and set PLANE STRAIN Formulation Keyopt(3)=2.
mapdl.et(1, "CPT212")
mapdl.keyopt(1, 12, 1)
mapdl.keyopt(1, 3, 2)
ELEMENT TYPE 1 IS CPT212 2-D 4-NODE PLANE STRN COUPLE
KEYOPT( 1- 6)= 0 0 2 0 0 0
KEYOPT( 7-12)= 0 0 0 0 0 1
KEYOPT(13-18)= 0 0 0 0 0 0
CURRENT NODAL DOF SET IS UX UY PRES
TWO-DIMENSIONAL MODEL
Define material#
Set up the material and its type (a single material), Young’s modulus of 4e7 and Poisson’s ratio of 0.3 is specified.
mapdl.mp("EX", 1, ex)
mapdl.mp("NUXY", 1, 0.3)
# Set parameters
fpx = 1.728e-3 / day / 1e4 # PERMEABILITY FROM REFERENCE
one = 1.0
# Define TB material properties
mapdl.tb("PM", 1, "", "", "PERM") # DEFINING PERMEABILITY FOR THE SOIL
mapdl.tbfield("YCOR", 0) # LOCATION Y = 0
mapdl.tbdata(1, fpx, fpx, fpx) # PERMEABILITY VALUES AT LOCATION Y=0
mapdl.tbfield("YCOR", h) # LOCATION Y=16
# PERMEABILITY VALUES AT LOCATION Y=16, LINEAR VARIABLE PERMEABILITY
mapdl.tbdata(1, fpx * 100, fpx * 100, fpx * 100)
mapdl.tb("PM", 1, "", "", "BIOT") # DEFINING BIOT COEFFICINET FOR SOIL
mapdl.tbdata(1, one) # BIOT COEFFICIENT
DATA FOR PM TABLE FOR MATERIAL 1 AT TEMPERATURE= 16.0000
LOC= 1 1.00000e+00
Define geometry#
Set up the nodes and elements. This creates a mesh just like in the problem setup.
mapdl.rectng(0, w, 0, h) # Generate rectangle
# Specifies the divisions and spacing ratio on unmeshed lines
mapdl.lesize(4, "", "", 16)
mapdl.lesize(3, "", "", 1)
# For elements that support multiple shapes, specifies the element shape, set mshape=2D
mapdl.mshape(0, "2D")
mapdl.mshkey(1) # Key(1) = Specifies mapped meshing should be used to mesh
mapdl.amesh(1) # CREATING CPT212 ELEMENTS
GENERATE NODES AND ELEMENTS
IN AREAS 1 TO 1 IN STEPS OF 1
NUMBER OF AREAS MESHED = 1
MAXIMUM NODE NUMBER = 34
MAXIMUM ELEMENT NUMBER = 16
Define boundary conditions#
Fix UX degrees of freedom. Constraining UY DOF AT Location Y=0. Defining the top portion of the soil as permeable. Then exit prep7 processor.
mapdl.d("ALL", "UX", 0) # CONSTRAINING ALL UX DOF
mapdl.nsel("S", "LOC", "Y", 0)
mapdl.d("ALL", "UY", 0) # CONSTRAINING UY DOF AT LOCATION Y=0
mapdl.nsel("ALL")
mapdl.nsel("S", "LOC", "Y", h)
mapdl.d("ALL", "PRES", 0) # DEFINING THE TOP PORTION OF SOIL AS PERMEABLE
# selects all nodes
mapdl.nsel("ALL")
# selects all element
mapdl.esel("ALL")
mapdl.aplot()
# Finish pre-processing processor
mapdl.finish()
***** ROUTINE COMPLETED ***** CP = 0.000
Solve#
Enter solution mode and solve the system.
mapdl.slashsolu()
mapdl.antype("STATIC") # Performing static analysis
mapdl.nropt("UNSYM") # UNSYMMETRIC NEWTON RAPHSON OPTION
mapdl.time(tt) # END TIME
mapdl.nsel("S", "LOC", "Y", h)
# APPLYING Surface PRESSURE LOAD AT TOP OF THE SOIL
mapdl.sf("ALL", "PRES", pres)
# selects all nodes
mapdl.nsel("ALL")
# Specify number of SUBSTEPS
mapdl.nsubst(nsbstp=350, nsbmx=1000, nsbmn=150)
# Controls the solution data written to the database.
mapdl.outres("ALL", "ALL")
mapdl.kbc(1) # STEPPED LOADING
# SOLVE STATIC ANALYSIS
mapdl.solve()
# exists solution processor
mapdl.finish()
FINISH SOLUTION PROCESSING
***** ROUTINE COMPLETED ***** CP = 0.000
Post-processing#
Enter post-processing.
mapdl.post1()
# Set the current results set to the last set to be read from result file
mapdl.set("LAST")
# redirects output to the default system output file
mapdl.run("/OUT")
# reactivates suppressed printout
mapdl.gopr()
PRINTOUT RESUMED BY /GOP
Specify Reference Solution#
mapdl.com("")
mapdl.com("EXCESS PORE PRESSURE IN KILOPASCALS AT LOCATION X=1,Y=6")
mapdl.com("FOR 0.1 DAY (8640 SECONDS),0.2 DAY (17280 SECONDS)")
mapdl.com("0.3 DAY (25920 SECONDS), 0.4 DAY (34560 SECONDS)")
mapdl.com("AND 0.5 DAY (43200 SECONDS) ARE COMPUTED AND COMPARED")
mapdl.com("AGAINST REFERENCE SOLUTION")
mapdl.com("")
Inline functions in PyMAPDL to query node#
q = mapdl.queries
nd1 = q.node(1.0, 6.0, 0.0)
Post-processing: Compute pore pressure#
redirects solver output to a file named “SCRATCH”
mapdl.run("/OUT,SCRATCH")
# Specify load set to read from the result file, load step =1, sub-step=16
mapdl.set(1, 16)
p11 = mapdl.get("P11", "NODE", nd1, "PRES")
t11 = mapdl.get("T11", "ACTIVE", 0, "SET", "TIME")
# Specify load set to read from the result file, load step =1, sub-step=17
mapdl.set(1, 17)
p12 = mapdl.get("P12", "NODE", nd1, "PRES")
t12 = mapdl.get("T12", "ACTIVE", 0, "SET", "TIME")
t1 = day * 0.1
mapdl.com("")
mapdl.com("INTERPOLATE THE RESULTS AT LOCATION (1,6,0) FOR TIME=0.1DAY")
mapdl.com("")
pt1 = (p11 + (t1 - t11) / (t12 - t11) * (p12 - p11)) / 1e3
# Specify load set to read from the result file, load step =1, sub-step=31
mapdl.set(1, 31)
p21 = mapdl.get("P21", "NODE", nd1, "PRES")
t21 = mapdl.get("T21", "ACTIVE", 0, "SET", "TIME")
# Specify load set to read from the result file, load step =1, sub-step=32
mapdl.set(1, 32)
p22 = mapdl.get("P22", "NODE", nd1, "PRES")
t22 = mapdl.get("T22", "ACTIVE", 0, "SET", "TIME")
t2 = day * 0.2
mapdl.com("")
mapdl.com("INTERPOLATE THE RESULTS AT LOCATION (1,6,0) FOR TIME=0.2DAY")
mapdl.com("")
pt2 = (p21 + (t2 - t21) / (t22 - t21) * (p22 - p21)) / 1e3
# Specify load set to read from the result file, load step =1, sub-step=46
mapdl.set(1, 46)
p31 = mapdl.get("P31", "NODE", nd1, "PRES")
t31 = mapdl.get("T31", "ACTIVE", 0, "SET", "TIME")
# Specify load set to read from the result file, load step =1, sub-step=47
mapdl.set(1, 47)
p32 = mapdl.get("P32", "NODE", nd1, "PRES")
t32 = mapdl.get("T32", "ACTIVE", 0, "SET", "TIME")
t3 = day * 0.3
mapdl.com("")
mapdl.com("INTERPOLATE THE RESULTS AT LOCATION (1,6,0) FOR TIME=0.3DAY")
mapdl.com("")
pt3 = (p31 + (t3 - t31) / (t32 - t31) * (p32 - p31)) / 1e3
# Specify load set to read from the result file, load step =1, sub-step=61
mapdl.set(1, 61)
p41 = mapdl.get("P41", "NODE", nd1, "PRES")
t41 = mapdl.get("T41", "ACTIVE", 0, "SET", "TIME")
# Specify load set to read from the result file, load step =1, sub-step=62
mapdl.set(1, 62)
p42 = mapdl.get("P42", "NODE", nd1, "PRES")
t42 = mapdl.get("T42", "ACTIVE", 0, "SET", "TIME")
t4 = day * 0.4
mapdl.com("")
mapdl.com("INTERPOLATE THE RESULTS AT LOCATION (1,6,0) FOR TIME=0.4DAY")
mapdl.com("")
pt4 = (p41 + (t4 - t41) / (t42 - t41) * (p42 - p41)) / 1e3
# Specify load set to read from the result file, load step =1, sub-step=76
mapdl.set(1, 76)
p51 = mapdl.get("P51", "NODE", nd1, "PRES")
t51 = mapdl.get("T51", "ACTIVE", 0, "SET", "TIME")
# Specify load set to read from the result file, load step =1, sub-step=77
mapdl.set(1, 77)
p52 = mapdl.get("P52", "NODE", nd1, "PRES")
t52 = mapdl.get("T52", "ACTIVE", 0, "SET", "TIME")
t5 = day * 0.5
mapdl.com("")
mapdl.com("INTERPOLATE THE RESULTS AT LOCATION (1,6,0) FOR TIME=0.5DAY")
mapdl.com("")
pt5 = (p51 + (t5 - t51) / (t52 - t51) * (p52 - p51)) / 1e3
# Store result values in array
P = np.array([pt1, pt2, pt3, pt4, pt5])
# REFERENCE RESULTS, FIGURE 5, PG 5916
# Fill the Target Result Values in array
Target_CP = np.array([5.230, 2.970, 1.769, 1.043, 0.632])
# store ratio
RT = []
for i in range(len(Target_CP)):
a = P[i] / Target_CP[i]
RT.append(a)
# assign labels for days
label = np.array([0.1, 0.2, 0.3, 0.4, 0.5])
Verify the results.#
message = f"""
------------------- VM295 RESULTS COMPARISON ---------------------
Time (day) | TARGET (kPa) | Mechanical APDL | RATIO
-----------------------------------------------------------------
"""
print(message)
for i in range(len(Target_CP)):
message = f"""
{label[i]:.5f} {Target_CP[i]:.5f} {P[i]:.5f} {RT[i]:.5f}
"""
print(message)
message = f"""
-----------------------------------------------------------------
"""
print(message)
------------------- VM295 RESULTS COMPARISON ---------------------
Time (day) | TARGET (kPa) | Mechanical APDL | RATIO
-----------------------------------------------------------------
0.10000 5.23000 5.27900 1.00937
0.20000 2.97000 2.98412 1.00475
0.30000 1.76900 1.74289 0.98524
0.40000 1.04300 1.02083 0.97875
0.50000 0.63200 0.59800 0.94621
-----------------------------------------------------------------
Finish the post-processing processor.#
mapdl.finish()
EXIT THE MAPDL POST1 DATABASE PROCESSOR
***** ROUTINE COMPLETED ***** CP = 0.000
Stop MAPDL.#
mapdl.exit()
Total running time of the script: (0 minutes 1.296 seconds)