Chp 10 (Slope & Tunnel Design)

7/31/2019 Chp 10 (Slope & Tunnel Design)

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Chap 10:Chap 10: Basic design parameters for slope and tunnelBasic design parameters for slope and tunnel

in rockin rock

RockRocktype, orientation and types of weakness planes intype, orientation and types of weakness planes in

rock mass must be verified and assessed during initialrock mass must be verified and assessed during initial

stage of a project through site investigation (SI).stage of a project through site investigation (SI).

During SI, evaluation on geological aspects & detailedDuring SI, evaluation on geological aspects & detailed

assessments on rock mass properties andassessments on rock mass properties and

discontinuities in the field (RQD, RMR & Qdiscontinuities in the field (RQD, RMR & Q--System)System)

should be carried out. Rock cores obtained fromshould be carried out. Rock cores obtained from

drilling can provide ample info on rock properties.drilling can provide ample info on rock properties.

The objectives are to obtain as much reliable andThe objectives are to obtain as much reliable and

objective data as possible.objective data as possible.

oint survey (oint survey (ukurukur kekarkekar) as discussed in Chapter 5 is) as discussed in Chapter 5 is

an essential scope of work during initial fieldan essential scope of work during initial field

assessment. Among the important parameters thatassessment. Among the important parameters that

need to be evaluated include:need to be evaluated include:

-- Types of discontinuities (joint, fault bedding planes)Types of discontinuities (joint, fault bedding planes)

-- Joint aperture (Joint aperture (bukaanbukaan kekarkekar) & matched or filled) & matched or filled

jointjoint

-- Surface texture of joint; roughness & weatheringSurface texture of joint; roughness & weathering

grade.grade.-- Joint orientation (dip angle & dip direction/strike)Joint orientation (dip angle & dip direction/strike)

-- Water conditions in jointWater conditions in joint


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Inclined weakness planes isInclined weakness planes is criticalcritical to any structureto any structure

involving excavation in rock. Thus, parameters such asinvolving excavation in rock. Thus, parameters such as

dip angle and dip direction of the plane must bedip angle and dip direction of the plane must be

determined to verify its effect on the structure.determined to verify its effect on the structure.

Analysis of this data (Analysis of this data (stereonetstereonet projection method)projection method)

indicates the stability of a cut slope in terms ofindicates the stability of a cut slope in terms of

geometrygeometry..

If in terms of geometry the slope is found to be stable,If in terms of geometry the slope is found to be stable,

further verification, in terms of strength & mechanics,further verification, in terms of strength & mechanics,

is necessary (e.g. weathering state, conditions andis necessary (e.g. weathering state, conditions and

shear strength of joint) is necessary.shear strength of joint) is necessary.

Joints (discontinuities) in rockJoints (discontinuities) in rock


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Joints (discontinuities) in rockJoints (discontinuities) in rock

Definition of dip angle, dip direction and strike for an inclined

plane in rock


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Measurement of joint orientation using Bruntons compass.

Fig 10.2 Cross-section of a rock mass with one set of

weakness planes (joints or bedding planes ?) that dips

in 2700 N, dip angle is = 300 .

Proposed cut slope: a-b-c or j-i-h with dip angle = 550.

Chose the most stable slope, in terms of geometry.

This analysis should be undertaken before the slope is

cutThere are 2 conditions for a cut slope to be stable in

terms of geometry:


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Figure 10.2:

Condition 1: If possible, the slope should dip in

opposite direction of the dipping of the weakness

planes. If this is possible then the slope angle

becomes non-critical (depend on other parameters).

Condition 2: If dip direction of the slope is parallel to

the dip direction of the weakness planes, then the

slope angle must be smaller than the dip angle of the

weakness plane ( less than = 550)

Note that slope c-b-e may be more stable than c-b-a

however, aspect on cost on excavation and method forslope stabilisation should be considered accordingly

for the actual excavation. If stabilisation is cheaper

then slope c-b-a is the best choice.


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If in terms of geometry a proposed slope is stable, further

verification on the following factors are essential:

Effect of shear strength of joints on slope stability roughness,

basic friction angle .

Rock strength UCS , Youngs modulus (E), Poissons ratio () &

presence of water in joint.

Long-term effect weathering of joint & rainfall throughout the

service life of the slope.

Effect of these parameters are evaluated during the detaileddesign stage & suitable FOS is applied into the final design of the

slope.

Concept of factor of safety [FOS]:

FOS = [ resisting forces] / [ disturbing forces].

Some of the disturbing forces changes and fluctuates

through time and season: rate of rainfall, weight of

unstable blocks, water in the joint, building of

structure on the slope crest.

Resisting forces: shear strength of weakness plane,

stability imposed by stabilisation methods.


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Inclined joint in rock mass

Critical slope height relative to discontinuity

orientation


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Typical FOS for slopes, based on risk on economy & life.

Consider FIG 22 where an unstable rock block is about to

slide down along a weakness plane (W,, W sin,

W cos& R as defined).

Resisting force = shear stress : = tan + c.

Normal stress acts across the plane (area A) of the sliding

block :

= (W cos)/A (2)

Shear stress = [(W cos)/A] tan + c . . . . . or,

Resisting force, R = .A = c.A + (W cos) tan (3)


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Block with base area A

R

Wsin

WWcos

(Friction = R)

State of limiting equilibrium : resisting forces = disturbingforces (FOS = 1.0), hence;

R = W sin = c.A + (W cos) tan (4)

If c = 0 condition of limiting equilibrium becomes:

W sin = (W cos) tan.

Shear stress = [(W cos)/A] tan + c or,

Resisting force, R = .A = c.A + (W cos) tan.

Limiting equilibrium (i.e. FOS = 1.0) for dry slope is:

(W sin)/(W cos) = tan, or = (5)


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Limiting equilibrium (i.e. FOS = 1.0) for dry slope is:

(W sin)/(W cos) = tan, or

From the definition of FOS, in this case (friction angle) is

the resisting force & (slope inclination) is the disturbing

force hence,

FOS = /.

In addition to the effect of orientation of weakness

planes in rock (as in slope), the following factors are

equally important:

[a] Size of excavation relative to distribution & scale of

weakness planes in rock mass see Figure.

[b] Shape of tunnel in terms of stability & purpose;

ellipse (most stable), circular, hexagonal &

rectangular (least stable).[c] Rock strength (compression, triaxial and tensile). At

tunnel walls induced stress is compression & at tunnel

roof/floor induced stress is tensile (most critical !).


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[d] Stress distribution following excavation (monitored

by instrumentation).

[e] Geological history of the in situ rock (e.g. remnant

stress due to folding & stress distribution due to

geological structures)

(f) Depth of tunnel from surface, effect of over-burden

stress P = gh & no of joint set (RQD).

The design of the tunnel & subsequent excavation

must be ensured so that the construction stresses do

not exceed the strength of the in situ rock.


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Fig 8.4: Effect of depth of structure on conditions of rock mass; at

depth means less number of discontinuities & rock is under

confined condition (p = gh).

FIG. 6.3 shows the distribution of &r around a circular

tunnel. &r are expressed in terms of v(unit stress) & it

is compression (+ve value).

r is radial distance from tunnel centre to a depth in

surrounding rock & a is tunnel radius.

Curves represent distribution of &r around the tunnel, at

various depth into the tunnel surface:

Point (vertical) at depth (r/a) into the rock.

Point (horizontal) at depth (r/a) into the rock.


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Stress

&r

distribution,

due to the effect of vertical

stressv

only, around

circular tunnel, at

horizontal & vertical axis at

depth (r/a) into the rock

Note:

a is the radius of tunnel, r is

depth into rock mass

surrounding the tunnel

Ais a point on the roof at

vertical axis

B is a point on the tunnel

wall at horizontal axis

B

A

3

2

1

0321 4

r/a

r/a

v v

r

r

3

2

1-1

5

4

+1 0

a

r

At tunnel surface or r/a = 1.0:

at Point A : r = 0 & = v(ve, tensile)

at Point B:r = 0 & = 3v(+ve, compression)

At depth r/a > 1, values ofr & change accordingly asshown in the figure.

At point r/a = 4.0 in the rock mass surrounding the tunnel:

at Point A : r =v(compression) & = 0at Point B : r = 0 & =v


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Note that: At point : when r/a > 4, rv& 0 ( does not exist

anymore &r is approachingv).

At a point : when r/a > 4, r 0 &v(rdoes not existanymore & is approachingv).

The zone beyond which &rvis an area where rockmaterial is not affected by the excavation work. The zone

wherevchanges to &r is termed yield zone i.e. zoneaffected by the excavation. If value of

&

r

are greater

than the strengths of rock mass then, tunnel will fail.

As soon as a tunnel is excavated, surrounding rock mass will be

disturbed formation of yield zone. Design & method of construction

must be carefully considered so that disturbance to surrounding

rock is reduced (thinner yield zone, less affected volume).


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It can be inferred that when a circular opening is excavatedin an ideal rock (elastic, homogeneous), and it is subjectedto a stress in one axis only (z (= gz)), this will induce:

a stress, 3-times higher in value & compressive, actingperpendicular to the first axis.

another stress, of similar value but tensile, acting parallel tothe first axis.

See Case I and Case II in the following figures

Fig 6.4: Case I: whenv 0 &h = 0

v

3v

v


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Fig 6.5: Case II: when v= 0 andh 0

h

h

3h

Law of superposition - case I impose onto case II, & substituting

h = [/(1)]v

v + 3[ /(1 )] v

3 v [ /(1 )] v


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In general, excavation of tunnel in strong & massive

rock at a deeper depth (stress-controlled, P = gh) is

relatively easier than excavation in weak & fractured

rock at shallower depth or near surface (structurally-

controlled).

For civil engineering work, tunnels are generally

located at shallow depth (e.g. highway & LRT tunnel)

Deep tunnels/underground spaces are usually

associated with mining activities & radio activedisposal.

Chp 10 (Slope & Tunnel Design)

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