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24-088
Underground Mine Ramp Design for Beginners
William G. Pariseau
University of Utah, Salt Lake City, Utah
INTRODUCTION
Safety of mine ramps begins with an analysis of stress that
almost certainly must be done numerically to take into
account ramp geometry, route geology, rock properties, and
pre-ramp stresses. The popular finite element method serves
analysis purposes quite well. As a practical matter several
obstacles to implementation need to be addressed includ-
ing collection of rock and joint properties along the pro-
posed ramp route, selection of ramp type, and specification
of cross-section shape, size, and route grade. Additionally,
stresses along the proposed route must be specified, prefer-
ably from in situ measurements.
One need not be an expert in numerical methods to
proceed to ramp design, although a background in mechan-
ics of materials and rock mechanics is essential, and a first
course in numerical methods is quite helpful. The necessary
software is easily brought to the design task, more accu-
rately, to the task of design evaluation. This software also
addresses other important mine design problems including
design of safe (1) main entries in stratified ground, (2) bar-
rier pillars, (3) bleeder entries, (4) inter-panel barrier pil-
lars, (5) room and pillar mines, (6) shafts, and (7) “tunnels”
(Pariseau 2022).
PROBLEM DEFINITION
The problem is to compute displacements and related
strains induced by ramp excavation and the stresses that
result, given ramp geometry, geology including rock prop-
erties, and pre-ramp stress. The combination of pre-ramp
stress and stress change induced by ramp excavation allows
for computation of elastic and yielding zone extents about
the ramp section and beyond. This information provides
useful guidance to safe ramp design in the form of element
safety factor distributions.
A local element safety factor concept defined as the ratio
of strength to stress requires definitions of suitable measures
of strengths and stress for analysis. Both arise in the con-
text of stress-strain relations. Strength may be defined as
stress at the elastic limit, so in case of the famous Mohr-
Coulomb criterion one has fs =tm(strength)/tm(stress)
which reduces to fs =Co/sc in unconfined compression and
to fs =To/st in uniaxial tension where Co and To are uncon-
fined compressive and tensile strengths, respectively. Here
tm is the maximum shear stress at failure. Alternatively, fs
=J N/2
2 (strength)/tm (stress) where J2 is the second invari-
ant of deviatoric stress (a measure of shear strength) and
N is an exponent determined by testing, usually between
one and two. This alternative also reduces to the uncon-
fined compression and tension cases and has the advantage
of including the effect of the intermediate principal stress
on strength. When the formation is isotropic and N=1,
this definition reduces to the well-known Drucker-Prager
criterion.
PROBLEM APPROACH
Approach to the problem is by the finite element method
and is easy as one-two-three. Step one requires specification
of rock properties in the region of interest including elas-
tic moduli and strengths. An elastic response to an initial
application load followed by inelastic behavior is illustrated
in Figure 1.
24-088
Underground Mine Ramp Design for Beginners
William G. Pariseau
University of Utah, Salt Lake City, Utah
INTRODUCTION
Safety of mine ramps begins with an analysis of stress that
almost certainly must be done numerically to take into
account ramp geometry, route geology, rock properties, and
pre-ramp stresses. The popular finite element method serves
analysis purposes quite well. As a practical matter several
obstacles to implementation need to be addressed includ-
ing collection of rock and joint properties along the pro-
posed ramp route, selection of ramp type, and specification
of cross-section shape, size, and route grade. Additionally,
stresses along the proposed route must be specified, prefer-
ably from in situ measurements.
One need not be an expert in numerical methods to
proceed to ramp design, although a background in mechan-
ics of materials and rock mechanics is essential, and a first
course in numerical methods is quite helpful. The necessary
software is easily brought to the design task, more accu-
rately, to the task of design evaluation. This software also
addresses other important mine design problems including
design of safe (1) main entries in stratified ground, (2) bar-
rier pillars, (3) bleeder entries, (4) inter-panel barrier pil-
lars, (5) room and pillar mines, (6) shafts, and (7) “tunnels”
(Pariseau 2022).
PROBLEM DEFINITION
The problem is to compute displacements and related
strains induced by ramp excavation and the stresses that
result, given ramp geometry, geology including rock prop-
erties, and pre-ramp stress. The combination of pre-ramp
stress and stress change induced by ramp excavation allows
for computation of elastic and yielding zone extents about
the ramp section and beyond. This information provides
useful guidance to safe ramp design in the form of element
safety factor distributions.
A local element safety factor concept defined as the ratio
of strength to stress requires definitions of suitable measures
of strengths and stress for analysis. Both arise in the con-
text of stress-strain relations. Strength may be defined as
stress at the elastic limit, so in case of the famous Mohr-
Coulomb criterion one has fs =tm(strength)/tm(stress)
which reduces to fs =Co/sc in unconfined compression and
to fs =To/st in uniaxial tension where Co and To are uncon-
fined compressive and tensile strengths, respectively. Here
tm is the maximum shear stress at failure. Alternatively, fs
=J N/2
2 (strength)/tm (stress) where J2 is the second invari-
ant of deviatoric stress (a measure of shear strength) and
N is an exponent determined by testing, usually between
one and two. This alternative also reduces to the uncon-
fined compression and tension cases and has the advantage
of including the effect of the intermediate principal stress
on strength. When the formation is isotropic and N=1,
this definition reduces to the well-known Drucker-Prager
criterion.
PROBLEM APPROACH
Approach to the problem is by the finite element method
and is easy as one-two-three. Step one requires specification
of rock properties in the region of interest including elas-
tic moduli and strengths. An elastic response to an initial
application load followed by inelastic behavior is illustrated
in Figure 1.