Loading and Sequential Modeling

By applying different model loading conditions at different stages of an analysis, it is possible to simulate changes in physical loading, such as sequences of excavation and construction. Changes in loading may be specified in a number of ways — e.g., by applying new stress or displacement boundaries, by changing the material model in blocks to either a null material or to a different material model, or by changing material properties.

It is important to recognize that sequential modeling follows the stages of an engineering work.

In most analyses, each work stage corresponds to a different static solution following a loading change — i.e., physical time is not a parameter. 3DEC can perform calculations for heat transfer and dynamic mechanical analysis as well (seeSections 1 and2in Optional Features). In these cases, a static solution for an equilibrium stress state may be followed, for example, by a dynamic calculation for an applied explosive excitation or a transient calculation for flow through joints.

Time-dependent behavior, on the other hand, cannot be simulated directly. Some engineering judgment must be used to estimate the effects of time. For example, a model parameter may be changed after a pre-determined amount of displacement or strain has occurred. This displacement may be estimated to have occurred over a given period of time.

A loading change must cause unbalanced forces to develop in order to effect a change in model response. Therefore, changing the elastic properties will have no effect, whereas changing strength properties will if the change causes the current stress state to exceed the failure limit.

The recommended approach to sequential modeling is demonstrated by the following example.

This problem involves the stability analysis of an underground opening in jointed rock and includes the evaluation of different types of support measures. The stages to be analyzed are:

(1) equilibration at the in-situ stress state;

(2) excavation of the tunnel; and (3) application of the tunnel support.

The objective is to investigate the stability of the excavation under in-situ conditions and assess the effect of the support measures. Three types of support are evaluated: local reinforcement rock bolts, cable bolts and a continuous concrete liner. Note that this model is greatly simplified for rapid execution, but it still illustrates the recommended steps for loading and sequential modeling.

The tunnel is located in rock containing three major faults: one dipping at 65^◦with a dip direction of 40^◦; the second dipping at 70^◦with a dip direction of 270^◦; and the third dipping at 60^◦with a dip direction of 130^◦. The tunnel is horseshoe-shaped and is centered along thez-axis of the model.

The tunnel is created with the TUNNEL command. A second TUNNEL command is also used to define the location of the concrete liner. Note that this must be done before any cycling is performed. The model is created by the following series of commands beginning withExample 3.17:

Example 3.17 Stability analysis of an underground excavation — initial model

new

poly brick -10 10 -10 10 -10 10

; --- tunz: FISH function to define tunnel geometry parameters

---; ... tunnel along z axis, from ZZA to ZZB

; ... semi-circular roof, centered at (TXC,TYC)

;

tx1i = txc + tri * cos(180*degrad)

ty1i = tyc + tri * sin(180*degrad) tx2i = txc + tri * cos(135*degrad) ty2i = tyc + tri * sin(135*degrad) tx3i = txc + tri * cos(90*degrad) ty3i = tyc + tri * sin(90*degrad) tx4i = txc + tri * cos(45*degrad) ty4i = tyc + tri * sin(45*degrad) tx5i = txc + tri * cos(0*degrad)

tunnel a txb1 tyb1 zza tx1 ty1 zza tx2 ty2 zza tx3 ty3 zza &

tx4 ty4 zza tx5 ty5 zza txb2 tyb2 zza &

b txb1 tyb1 zzb tx1 ty1 zzb tx2 ty2 zzb tx3 ty3 zzb &

tx4 ty4 zzb tx5 ty5 zzb txb2 tyb2 zzb &

reg 5

;

; create inner surface

tunnel a txb1i tyb1i zza tx1i ty1i zza tx2i ty2i zza tx3i ty3i zza &

tx4i ty4i zza tx5i ty5i zza txb2i tyb2i zza &

b txb1i tyb1i zzb tx1i ty1i zzb tx2i ty2i zzb tx3i ty3i zzb &

tx4i ty4i zzb tx5i ty5i zzb txb2i tyb2i zzb &

reg 7

;

; --- NOTE: region inside inner surface is REG 7

; region between surface (to be liner) is REG 5

;

gen ed 5

;

; liner find reg 5 gen ed 2

;

find reg 7 gen ed 5

;

save tun_z.sav

pl hold dip 70 dd 210 color mat ret

Figure 3.26shows the resulting model configuration. The tunnel geometry parameters are defined in the FISH functiontunz. The inner region of the tunnel is assigned region number 7, and the region corresponding to the liner is assigned region number 5. Note that the tunnel is created first and then the physical joint set is generated. Blocks are joined automatically with the TUNNEL commands. Zone generation is performed separately for the rock blocks, the liner blocks and the interior region of the tunnel.

3DEC (Version 3.00)

Itasca Consulting Group, Inc.

x Y z

dip= 70.00 above dd = 210.00 center 0.000E+00 0.000E+00 0.000E+00 cut-pl. 0.000E+00 mag = 1.00 cycle 0

27-Aug-02 13:59

Figure 3.26 3DEC model of tunnel region

Material properties are assigned to the rock blocks (mat 1), the concrete liner blocks (mat 5), the rock joints (jmat 1), the concrete-concrete joints (jmat 5) and the concrete-rock interface (jmat 6).

The in-situ stress state and boundary conditions are applied assuming the tunnel is at a depth of 200 m and the ratio of horizontal to vertical stress is 0.5. Note that for a practical simulation, the boundaries are too close to the tunnel excavation and should be moved to a greater distance to minimize their influence on the model results — seeSection 3.4.4.2.

The commands to assign material properties and achieve the initial stress state are listed in Exam-ple 3.18.

Example 3.18 Stability analysis of an underground excavation — initial equilibrium stress state

---; density = 2700 kg/m3 = 0.0027e6 kg/m3

; E=50 GPa, Poisson’s ratio=0.2

prop mat 1 dens 0.0027 k 27778 g 20833

;

; MAT=5 : concrete liner

---; density = 2400 kg/m3 = 0.0024e6 kg/m3

; E=30 GPa, Poisson’s ratio=0.2

prop mat 5 dens 0.0025 k 16667 g 12500

;

; JMAT=1 : rock joints ---prop mat 1 kn 10000 ks 2000 fric 25

;

; JMAT=5 : concrete-concrete joints (elastic) ---prop mat 5 kn 30000 ks 12000 coh 1e6 tens 1e6

;

; JMAT=6 : concrete-rock interface ---prop mat 6 kn 10000 ks 2000 fric 0.001

;

; assign material numbers

---; initially all materials are rock change mat 1

change jmat 1

;

; insitu stress state

---; assume tunnel at 200 m depth

; vertical stress: syy=(0.0027*g)*(y-200)

; at y=0: syy=-5.4

; y-gradient of syy: 0.027

; (positive: less compression going up)

; horizontal sxx=szz=0.5*syy

;

insitu stress -2.7 -5.4 -2.7 0 0 0 &

ygrad 0.0135 0.027 0.0135 0 0 0

;

; gravity grav 0 -10 0

;

; boundary conditions for insitu stress state

---; top of model (y=10): syy=-0.027*190=-5.13 bound yr 9.9 10.1 stress 0 -5.13 0 0 0 0

; bottom

bound yr -10.1 -9.9 yvel 0

; sides

bound xr -10.1 -9.9 xvel 0 bound xr 9.9 10.1 xvel 0 bound zr -10.1 -9.9 zvel 0 bound zr 9.9 10.1 zvel 0

;

; histories to monitor convergence ---hist nc=1 unbal

; top of model

hist xdis 0 10 0 ydis 0 10 0 zdis 0 10 0

;

save tun_c0.sav cycle 500

save tun_c.sav pl hold hist 2 3 4 ret

The maximum unbalanced force in the model and displacements at the top boundary are monitored to help make sure that an initial equilibrium stress state is reached within 1000 cycles. Figure 3.27 shows thex-, y- and z-displacement histories for the gridpoint (x = 0, y = 10, z = 0) at the top of the model.

3DEC (Version 3.00)

Figure 3.27 Displacement histories at top of model

If the tunnel is excavated without support, a rock wedge detaches and falls from the roof. This is shown by running Example 3.19; the tunnel is excavated with the DELETE command, and the y-displacement at a location in the roof is monitored while the model is cycled. Figure 3.29 plots they-displacement history and indicates that the position is moving downward. Figure 3.28 shows a close-up view of the detached wedge, with surrounding blocks hidden for better viewing.

Example 3.19 Stability analysis of an underground excavation — unsupported tunnel

rest tun_c.sav

; delete interior blocks remove reg 5 7

;

; history point at tunnel roof reset disp time hist

3DEC (Version 3.00)

Itasca Consulting Group, Inc.

HISTORY PLOT 27-Aug-02 14:10 cycle 5500

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

(E-001) -2.8

-2.4 -2.0 -1.6 -1.2 -0.8 -0.4 0.0

(E-002)

Hist. no. 1 -2.227E-02 to -6.176E-05 VS

Time

Figure 3.28 y-displacement history at tunnel roof

3DEC (Version 3.00)

Itasca Consulting Group, Inc.

dip= 90.00 above dd = 180.00 center 0.000E+00 0.000E+00 0.000E+00 cut-pl. 0.000E+00 mag = 2.00 cycle 5500

27-Aug-02 14:10

Figure 3.29 Close-up view of wedge in roof (surrounding blocks hidden)

The effect of rock bolt support is evaluated first for local reinforcement elements (STRUCT axial) and then for fully-bonded cable elements (STRUCT cable). SeeSection 4in Theory and Background for a detailed description of these two types of structural support.

Example 3.20lists the commands to excavate the tunnel and install the local reinforcement elements, andExample 3.21lists those for cable element support. Note that we use the REMOVE command to excavate the tunnel this time. This has the same effect as the DELETE command, but now we can view the excavated region with the PLOT exc command. The reinforcement elements and cable elements are positioned in the same locations in the side walls and roof of the tunnel. Figure 3.30 shows the location of the cable elements around the tunnel excavation.

3DEC (Version 3.00)

Itasca Consulting Group, Inc.

dip= 80.00 above dd = 190.00 center 0.000E+00 0.000E+00 0.000E+00 cut-pl. 0.000E+00 mag = 2.00 cycle 500

27-Aug-02 14:07

Figure 3.30 Cable bolts positioned around tunnel excavation

Example 3.20 Stability analysis of an underground excavation — local reinforcement support

rest tun_c.sav

;

; delete interior blocks remove region 7

; delete liner blocks remove reg 5

; install axial elements

---struct axial -8 -2 -5 -3.9 -2 -5 prop 7 struct axial -8 -2 0 -3.9 -2 0 prop 7 struct axial -8 -2 5 -3.9 -2 5 prop 7

struct axial -6.8 6.8 -5 -2.8 2.8 -5 prop 7

struct prop 7 rkax 250 rlen 0.10 rult 0.55

;

reset disp time hist

; history point at tunnel roof hist ydis 0 4 0

Example 3.21 Stability analysis of an underground excavation — fully grouted cable support

rest tun_c.sav

; install cable elements

---struct cable -8 -2 -5 -4.05 -2 -5 prop 8 seg 4

struct cable 8 -2 5 4.05 -2 5 prop 8 seg 4

struct cable 6.8 6.8 -5 2.85 2.85 -5 prop 8 seg 4 struct cable 6.8 6.8 0 2.85 2.85 0 prop 8 seg 4 struct cable 6.8 6.8 5 2.85 2.85 5 prop 8 seg 4

;

struct cable 0 4.1 -5 0 8 -5 prop 8 seg 4 struct cable 0 4.1 0 0 8 0 prop 8 seg 4 struct cable 0 4.1 5 0 8 5 prop 8 seg 4

;

; start with high SBOND

struct prop 8 area 5e-4 e 100000 yield 0.55 kbond 15e4 sbond 1e6

;

reset disp time hist

; history point at tunnel roof hist ydis 0 4 0

;

cycle 500

;

; set real SBOND

struct prop 8 sbond 0.8

;

cy 1500

;

save tun_cab.sav

pl hold wire exc cable blue dip 80 dd 190 mag 2 pl hold hist 1

ret

The roof is stabilized for both types of reinforcement. They-displacement history now indicates that the wedge movement stops at roughly 25 mm displacement for both the reinforcement elements and the cable elements (seeFigures 3.31and3.32).

3DEC (Version 3.00)

Figure 3.31 y-displacement history at tunnel roof — reinforcement element support

Figure 3.32 y-displacement history at tunnel roof — cable support

The axial forces that develop in the support are greatest in the roof elements. This is shown for both the reinforcement elements and the cable elements by the axial force plots inFigures 3.33and 3.34.

Figure 3.33 Axial forces in reinforcement elements

3DEC (Version 3.00)

Figure 3.34 Axial forces in cable elements

The model of a tunnel excavation and support sequence should simulate the change in stresses around the tunnel as the excavation advances, before the tunnel support is installed. This can be done in a 3DEC model by alternately excavating the tunnel in sections and installing support after each excavation section. This is the recommended approach to simulate support loading changes due to tunnel advancement.

Alternatively, in this simplified model we simulate the effect of tunnel advancement by reducing the tractions at the tunnel periphery in increments and installing the liner before the tractions are completely removed. This demonstrates an approach for simulating a gradual excavation of a tunnel section. Example 3.22 shows the data file for this approach.

Example 3.22 Stability analysis of an underground excavation — reduce tunnel tractions by 50% and install liner

rest tun_c.sav

; delete interior blocks delete region 7

;

; excavate liner blocks (not deleted) excavate reg 5

;

; history point at tunnel roof

hist xdis 0 4 0 ydis 0 4 0 zdis 0 4 0

;

; simulate the removal of approximately 50% of insitu stress

; applying at liner-rock interface a stress state

; syy=-2.7 sxx=szz=-1.35

;

bound -4.1 -3.9 -4.1 0.1 -11 11 str -1.35 -2.7 -1.35 0 0 0 bound 3.9 4.1 -4.1 0.1 -11 11 str -1.35 -2.7 -1.35 0 0 0 bound -4.1 4.1 -4.1 -3.9 -11 11 str -1.35 -2.7 -1.35 0 0 0

; note: need to include all faces on tunnel surface

; (inner radius must be a bit smaller than 4.0) bound yr -0.1 4.1 cyl 0 0 -11 0 0 11 3.5 4.1 &

str -1.35 -2.7 -1.35 0 0 0

;

; must again fix end-surfaces that were freed by BOU STRESS bou zr -10.1 -9.9 zvel 0

bou zr 9.9 10.1 zvel 0

;

; check that sum of applied forces on tunnel surface is zero pr -5 5 -5 5 -11 11 bou for

pause

;

cycle 2000

;

save tun_l1.sav pause

;

; insert liner

---; remove loads from tunnel surface

;

bound -4.1 -3.9 -4.1 0.1 -11 11 xfree yfree zfree bound 3.9 4.1 -4.1 0.1 -11 11 xfree yfree zfree bound -4.1 4.1 -4.1 -3.9 -11 11 xfree yfree zfree

bound yr -0.1 4.1 cyl 0 0 -11 0 0 11 3.5 4.1 xfree yfree zfree

The BOUND command is used to apply 50% of the in-situ stress state to the liner-rock interface, and the BOUND range covers all faces on the tunnel surface. The applied stresses at the tunnel surface should produce traction forces on the surface that sum to zero; this can be checked with the PRINT bound force command. The model is cycled to an equilibrium state with tunnel tractions reduced by 50%. Then, the tractions are removed completely, and the liner is installed (with the FILL region command). Figure 3.35 shows the liner blocks created for this model. The model is cycled to a new equilibrium state. The load that develops in the liner is due to the reduction of the tractions from 50% to zero.

Note that the selection of a 50% reduction in tunnel tractions in this example is arbitrary and only for demonstration purposes. If it is necessary to simulate a gradual excavation, it may be necessary to reduce the tractions in smaller increments to minimize the effects of transient stress waves on the response of the model.

3DEC (Version 3.00)

Figure 3.35 Thick concrete liner support — liner blocks

The displacement of the roof is monitored inFigure 3.36. Roughly 1 mm of vertical displacement occurs when the tractions are reduced by 50% and an additional 1 mm displacement after the tunnel tractions are completely removed and the liner is installed.

3DEC (Version 3.00)

Figure 3.36 y-displacement history at tunnel roof — tunnel liner added after

If a more representative model of the liner behavior, including an elastic-plastic response, is required, then mixed-discretization zoning (see Section 3.3.2) should be used to define the liner with a minimum of five m-d zones across the liner thickness. The POLY prism command can be used to create liner blocks for the m-d zones. Example 3.23 presents a data file to create the liner with m-d zoning.

Example 3.23 Stability analysis of an underground excavation — liner with m-d zoning

rest tun_c0.sav

; delete interior blocks delete reg 5 7

;

; insert support with POLY prism commands

---;

poly prism a txb1 tyb1 zza tx1 ty1 zza &

tx1i ty1i zza txb1i tyb1i zza &

b txb1 tyb1 zzb tx1 ty1 zzb &

tx1i ty1i zzb txb1i tyb1i zzb &

reg 8

;

poly prism a tx1 ty1 zza tx2 ty2 zza &

tx2i ty2i zza tx1i ty1i zza &

b tx1 ty1 zzb tx2 ty2 zzb &

tx2i ty2i zzb tx1i ty1i zzb &

reg 8

;

poly prism a tx2 ty2 zza tx3 ty3 zza &

tx3i ty3i zza tx2i ty2i zza &

b tx2 ty2 zzb tx3 ty3 zzb &

tx3i ty3i zzb tx2i ty2i zzb &

reg 8

;

poly prism a tx3 ty3 zza tx4 ty4 zza &

tx4i ty4i zza tx3i ty3i zza &

b tx3 ty3 zzb tx4 ty4 zzb &

tx4i ty4i zzb tx3i ty3i zzb &

reg 8

;

poly prism a tx4 ty4 zza tx5 ty5 zza &

tx5i ty5i zza tx4i ty4i zza &

b tx4 ty4 zzb tx5 ty5 zzb &

tx5i ty5i zzb tx4i ty4i zzb &

reg 8

;

poly prism a tx5 ty5 zza txb2 tyb2 zza &

txb2i tyb2i zza tx5i ty5i zza &

b tx5 ty5 zzb txb2 tyb2 zzb &

txb2i tyb2i zzb tx5i ty5i zzb &

reg 8

;

poly prism a txb2 tyb2 zza txb1 tyb1 zza &

txb1i tyb1i zza txb2i tyb2i zza &

b txb2 tyb2 zzb txb1 tyb1 zzb &

txb1i tyb1i zzb txb2i tyb2i zzb &

reg 8

---; density = 2400 kg/m3 = 0.0024e6 kg/m3

; E=30 GPa, Poisson’s ratio=0.2

prop mat 5 dens 0.0025 k 16667 g 12500

;

; JMAT=5 : concrete-concrete joints (elastic) ---prop mat 5 kn 30000 ks 12000 coh 1e6 tens 1e6

;

; JMAT=6 : concrete-rock interface ---prop mat 6 kn 10000 ks 2000 fric 35

;

;

---;

; history point at tunnel roof reset disp time hist

pl hold dip 75 dd 188 color reg pl hold wire zol

pl hold hist 1

pl dip 90 dd 180 x cent -1 2 2 mag 8 sscale 10 princ ccomp ret

Note that the prism-shaped blocks must be created before cycling is initiated. In this example, we

8). The m-d zoning is created with the GEN quad command and only elastic behavior is assigned to the liner material. If we wish to evaluate the elastic-plastic response, the bilinear material model (CHANGE cons 6 with the ubiquitous joint behavior suppressed) can be assigned to the liner material.

The liner supports the entire load in this example. (We could also reduce the tractions as before inExample 3.22.) Figure 3.37 illustrates the liner blocks for this case, andFigure 3.38shows the m-d zoning within the liner.

3DEC (Version 3.00)

Itasca Consulting Group, Inc.

dip= 75.00 above dd = 188.00 center 0.000E+00 0.000E+00 0.000E+00 cut-pl. 0.000E+00 mag = 2.00 cycle 2000

27-Aug-02 14:52

Figure 3.37 Thick concrete liner support — prism-shaped liner blocks

3DEC (Version 3.00)

Itasca Consulting Group, Inc.

x Y z

dip= 75.00 above dd = 188.00 center 0.000E+00 0.000E+00 0.000E+00 cut-pl. 0.000E+00 mag = 2.00 cycle 2000

27-Aug-02 14:52

Figure 3.38 Thick concrete liner support — mixed-discretization zoning in liner blocks

Figure 3.39shows the plot of they-displacement in the roof for this case. Approximately 1.6 mm displacement occurs when the liner supports the tunnel. The stresses in the liner are plotted in Figure 3.40.

Figure 3.39 y-displacement history at tunnel roof — support by prism-shaped liner blocks

Figure 3.40 Principal stress distribution in top section of liner

In document MANUAL 3DEC (Page 143-164)