Example: Shear Pull-Tests for Hybrid bolts in 3DEC
Problem Statement
Note
The project file for this example may be viewed/run in 3DEC.[1] The data files used are shown at the end of this example.
Simple Shear Test
A simple shear test is simulated using two blocks (Figure 1). The bottom of the left block is prevented from moving in the vertical direction and the top of the right block is moved downwards at a constant velocity. A hybrid bolt spans the joint from left to right. A normal stress of 1 MPa is applied. The friction angle of the joint is set to 40º and the cohesion is 0.
For the hybrid bolt, the dowel segment is assigned a yield strength of 0.063 MN and a strain limit of 0.41. Figure 2 shows the bolt contribution versus shear displacement. The bolt contribution is essentially the shear stress minus the frictional strength (\(\sigma_n \tan \phi\)). At about 7 mm of shear displacement, the dowel segment yields. At about 3.5 cm, the cable itself yields in tension. Finally after about 4.1 cm of shear, the dowel ruptures and the bolt fails.
Figure 1: Blocks and bolt configuration in the shear test. Model is shown after bolt rupture.
Figure 2: Bolt contribution in the shear test.
blocks.dat
;
;Build model for hybrid bolt calibration
;
model new
fish automatic-create off
model random 10000
model large-strain on
;
fish define params
; block dimensions
global block_lenH = 0.95
global block_lenV = 2.0
global edge_length_=0.125 ; zone size
; block properties
global ymod_=40e9
global pratio_=0.25
global dens_=2500
; joint properties
global jkn_=3e11
global jks_=3e11
global jfric_=40.0
;hybrid bolt parameters
global area_=201e-6
global e_=1.4e11
global grout_stiff_=3e8
global grout_strength_=2e5
global cable_yield_=100e3
global cable_strain_limit_=0.2 ; tensile
global dowel_stiffness_=1.0e7
global dowel_yield_=62.8e3
global dowel_strain_limit_=0.41 ; shear
global dowel_length_=0.1
global segment_length_=0.1
; calculated parameters
global bolt_len=block_lenH*2.
end
[params]
=====================================================
;
;make 2 blocks
block create brick 0 [block_lenH] 0 [block_lenH] 0 [block_lenV]
block create brick [block_lenH] [2*block_lenH] 0 [block_lenH] 0 [block_lenV]
block zone generate edgelength [edge_length_]
; zone and contact properties
block zone cmodel elastic
block zone property young [ymod_] poisson [pratio_] density [dens_]
block contact jmodel assign mohr
block contact property stiffness-normal [jkn_] ...
stiffness-shear [jks_] ...
friction [jfric_]
block contact material-table default property stiffness-normal [jkn_] ...
stiffness-shear [jks_] ...
friction [jfric_]
;
; apply common boundary conditions
block hide range position-x 0 [block_lenH] not
block gridpoint apply velocity-z 0 range position-z 0
block hide off
;
block gridpoint apply velocity-y 0 range position-z -1000 1000
; use combined damping to stop vibrations.
block mechanical damping combined
model save 'blocks'
shear_test.dat
;;-----------------------------------------------------------------------------
;; Shear test
;;-----------------------------------------------------------------------------
model restore 'blocks'
; define parameters for shear loading
fish define params_shear
; boundary conditions
global normal_stress = 1.0e6
global zvel_=-0.1
; calculated values
local normal_force = normal_stress * block_lenH*block_lenV
global friction_force = normal_force*math.tan(jfric_*math.degrad)
end
[params_shear]
; boundary conditions
block face apply stress-xx [-1.0*normal_stress] range position-x 0
block face apply stress-xx [-1.*normal_stress] range position-x [block_lenH*2.]
;
block hide range position-x 0 [block_lenH]
block gridpoint group 'top' range position-z [block_lenV]
block hide off
model solve
;
block gridpoint initialize displacement 0 0 0
block contact reset displacement
;
; apply shear load
block gridpoint apply velocity-z [zvel_] range group 'top'
;
; Function to calculate bolt contribution to resisting shear load
[global max_force = 0.0]
[global bolt_contribution = 0.0]
;
fish define reaction_force
local temp_ = 0.0
loop foreach local gi block.gp.list
if block.gp.group(gi) = 'top'
temp_ = temp_ - block.gp.force.reaction.z(gi)
end_if
end_loop
reaction_force = temp_
bolt_contribution = temp_ - friction_force
end
;
fish history reaction_force
fish history bolt_contribution
block history displacement-z ...
position [1.5*block_lenH] [0.5*block_lenH] [0.5*block_lenV]
model history mechanical unbalanced-maximum
history interval 1000
;
;to run the test - stop when rupture
fish define run_it
local test_ = true
local max_force = -1e12
loop while test_ = true
command
model cycle 10000
end_command
if max_force < bolt_contribution
max_force = bolt_contribution
else
if bolt_contribution < max_force/10.
test_ = false
end_if
end_if
end_loop
end
model save 'ini_shear.sav'
=================================================================
; Test perpendicular bolt 90 degrees
; Change dincl_ to test other bolt angles
;
model restore 'ini_shear'
[global dincl_=90.]
;To create bolt
[global x1 = block_lenH-0.5*bolt_len*math.sin(dincl_*math.degrad)+0.001]
[global y1 = 0.5*block_lenH]
[global z1 = 0.5*block_lenV+0.5*bolt_len*math.cos(dincl_*math.degrad)]
[global x2 = block_lenH+0.5*bolt_len*math.sin(dincl_*math.degrad)-0.001]
[global y2 = y1]
[global z2 = 0.5*block_lenV-0.5*bolt_len*math.cos(dincl_*math.degrad)]
[global bolt_beg=vector(x1,y1,z1)]
[global bolt_end=vector(x2,y2,z2)]
structure hybrid create by-line [bolt_beg] [bolt_end] maximum-length [segment_length_]
; cable properties
structure hybrid property cross-sectional-area [area_] young [e_] ...
grout-stiffness [grout_stiff_] grout-cohesion [grout_strength_] ...
yield-tension [cable_yield_] tensile-failure-strain [cable_strain_limit_]
; dowel properties
structure hybrid property dowel-active-length [dowel_length_] dowel-stiffness [dowel_stiffness_] ...
dowel-yield [dowel_yield_] dowel-failure-strain [dowel_strain_limit_]
;to plate both ends:
structure link attach x rigid range position-x [bolt_beg->x]
structure link attach y rigid range position-x [bolt_beg->x]
structure link attach z rigid range position-x [bolt_beg->x]
structure link attach x rigid range position-x [bolt_end->x]
structure link attach y rigid range position-x [bolt_end->x]
structure link attach z rigid range position-x [bolt_end->x]
structure mechanical damping combined-local
structure hybrid history dowel-strain position 0 0 0
;run the test - stop when rupture
[run_it]
model save 'shear-90'
program return
=================================================================
; Test bolt at 70 degrees
;
model restore 'ini_shear'
[global dincl_=70.]
;To create Inclined bolt
[global x1 = block_lenH-0.5*bolt_len*math.sin(dincl_*math.degrad)+0.001]
[global y1 = 0.5*block_lenH]
[global z1 = 0.5*block_lenV+0.5*bolt_len*math.cos(dincl_*math.degrad)]
[global x2 = block_lenH+0.5*bolt_len*math.sin(dincl_*math.degrad)-0.001]
[global y2 = y1]
[global z2 = 0.5*block_lenV-0.5*bolt_len*math.cos(dincl_*math.degrad)]
[global bolt_beg=vector(x1,y1,z1)]
[global bolt_end=vector(x2,y2,z2)]
structure hybrid create by-line [bolt_beg] [bolt_end] max-length [segment_length_]
; cable properties
structure hybrid property cross-sectional-area [area_] young [e_] ...
grout-stiffness [grout_stiff_] grout-cohesion [grout_strength_] ...
yield-tension [cable_yield_] tensile-failure-strain [cable_strain_limit_]
; dowel properties
structure hybrid property dowel-active-length [dowel_length_] dowel-stiffness [dowel_stiffness_] ...
dowel-yield [dowel_yield_] dowel-failure-strain [dowel_strain_limit_]
;to plate both ends:
structure link attach x rigid range position-x [bolt_beg->x]
structure link attach y rigid range position-x [bolt_beg->x]
structure link attach z rigid range position-x [bolt_beg->x]
structure link attach x rigid range position-x [bolt_end->x]
structure link attach y rigid range position-x [bolt_end->x]
structure link attach z rigid range position-x [bolt_end->x]
structure mechanical damping combined-local
;run the test - stop when rupture
[run_it]
model save 'shear-70'
Simple Pullout Test
The same block and bolt configuration from the simple shear test is used in the pullout test. In this case no normal stress is applied and the right boundary of the right block is moved to the right at a constant velocity.
Figure 3 shows the block and cable configuration at the end of the test. Figure 4 shows the bolt contribution in this test. Since there is no tensile strength on the joint, the bolt contribution is simply equal to the tensile force applied at the right boundary. This plot shows the initial elastic axial deformation, and then the start of grout failure at around 2 mm of displacement. Finally, the cable yields in tension after 3 mm of pull, at which time the bolt behaves plastically and the contribution no longer increases.
Figure 3: Blocks and bolt configuration in the pullout test. Model is shown after bolt pullout.
Figure 4: Bolt contribution in the pullout test.
pullout.dat
;;-----------------------------------------------------------------------------
;; Pull-out test
;;-----------------------------------------------------------------------------
model restore 'blocks'
;
; Define parameters for pullout test
[global xvel_ = 1e-2]
;
block gridpoint apply velocity-x 0 range position-x 0
;
block hide range position-x 0 [block_lenH]
block gridpoint apply velocity-z 0 range position-z 0
block gridpoint group 'right' range position-x [block_lenH]
block hide off
;
block gridpoint apply velocity-x [xvel_] range group 'right'
;
[global max_force = 0.0]
[global bolt_contribution = 0.0]
;
fish define reaction_force
local temp_ = 0.0
loop foreach local gi block.gp.list
if block.gp.group(gi) = 'right'
temp_ = temp_ + block.gp.force.reaction.x(gi)
end_if
end_loop
reaction_force = math.abs(temp_)
bolt_contribution = math.abs(temp_); - friction_force
end
;
fish history reaction_force
fish history bolt_contribution
block history displacement-x ...
position [2*block_lenH] [0.5*block_lenH] [0.5*block_lenV]
model history mechanical unbalanced-maximum
history interval 500
;fish function to run the test - stop when rupture
[global gp_monitor = block.gp.near(2*block_lenH,0.5*block_lenH,0.5*block_lenV)]
fish define run_it
local test_ = true
loop while test_ = true
command
model cycle 10000
end_command
if math.mag(block.gp.dis(gp_monitor)) > 8e-3
test_ = false
endif
end_loop
end
;
model save 'ini_pull'
;
=================================================================
;
; Test perpendicular bolt 90 degrees
; Change dincl_ to test other bolt angles
;
model restore 'ini_pull'
[global dincl_=90.]
;To create bolt
[global x1 = block_lenH-0.5*bolt_len*math.sin(dincl_*math.degrad)+0.001]
[global y1 = 0.5*block_lenH]
[global z1 = 0.5*block_lenV+0.5*bolt_len*math.cos(dincl_*math.degrad)]
[global x2 = block_lenH+0.5*bolt_len*math.sin(dincl_*math.degrad)-0.001]
[global y2 = y1]
[global z2 = 0.5*block_lenV-0.5*bolt_len*math.cos(dincl_*math.degrad)]
[global bolt_beg=vector(x1,y1,z1)]
[global bolt_end=vector(x2,y2,z2)]
structure hybrid create by-line [bolt_beg] [bolt_end] maximum-length [segment_length_]
; cable properties
structure hybrid property cross-sectional-area [area_] young [e_] ...
grout-stiffness [grout_stiff_] grout-cohesion [grout_strength_] ...
yield-tension [cable_yield_] tensile-failure-strain [cable_strain_limit_]
; dowel properties
structure hybrid property dowel-active-length [dowel_length_] dowel-stiffness [dowel_stiffness_] ...
dowel-yield [dowel_yield_] dowel-failure-strain [dowel_strain_limit_]
[run_it]
model save 'pull-90'
program return
===============================================================================
;inclined bolt 70 degrees
model restore 'ini_pull'
[global dincl_=70.]
;To create inclined bolt
[global x1 = block_lenH-0.5*bolt_len*math.sin(dincl_*math.degrad)+0.001]
[global y1 = 0.5*block_lenH]
[global z1 = 0.5*block_lenV+0.5*bolt_len*math.cos(dincl_*math.degrad)]
[global x2 = block_lenH+0.5*bolt_len*math.sin(dincl_*math.degrad)-0.001]
[global y2 = y1]
[global z2 = 0.5*block_lenV-0.5*bolt_len*math.cos(dincl_*math.degrad)]
[global bolt_beg=vector(x1,y1,z1)]
[global bolt_end=vector(x2,y2,z2)]
structure hybrid create by-line [bolt_beg] [bolt_end] max-length [segment_length_]
; cable properties
structure hybrid property cross-sectional-area [area_] young [e_] ...
grout-stiffness [grout_stiff_] grout-cohesion [grout_strength_] ...
yield-tension [cable_yield_] tensile-failure-strain [cable_strain_limit_]
; dowel properties
structure hybrid property dowel-active-length [dowel_length_] dowel-stiffness [dowel_stiffness_] ...
dowel-yield [dowel_yield_] dowel-failure-strain [dowel_strain_limit_]
[run_it]
model save 'pull-70'
;------------------------------------------------------------------------------
;end of file
Endnote
⇐ Hybrid Bolt Structural Elements (3D Only) | Example: Simple Tunnel with Hybrid Bolt Support in 3DEC ⇒
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