This document discusses the bearing capacity of bedrock and soil deposits on slopes. It provides definitions of key terms like ultimate and allowable bearing capacity. It describes various methods for calculating bearing capacity, including equations that account for factors like rock mass quality, joint spacing, slope angle, and soil type. Failure modes like general shear, local shear, and punching shear are also outlined. The document notes how soil deposits form on slopes and factors affecting the stability of soils on steep slopes, both natural and human-related.

1. BEARING CAPACITY OF BED
ROCK AND SOIL DEPOSITS ON
SLOPES
Submitted by:
Saurav Poudel
Roll No: 11
Second Semester, Engineering
Geology
Submitted to:
Central Department
of Geology, TU
Kirtipur

2. INTRODUCTION
 The term "bearing capacity" refers to a foundation's soil or rock's
ability to support and transmit loads from a structure.
 Due to complex load distribution phenomena and the ensuing
response, building a structure on any sloped surface is more difficult
than building one on a flat level.
 Terzaghi was the first to discuss the ultimate bearing capacity of soil
while taking into account its shear strength characteristics.
 Later, Meyerhof and Vesic both proposed various footing shapes.

3. BEARING CAPACITY
Goodman (1980) suggests the following equation for determining the
ultimate bearing capacity qu.
qu = qur (Nɸ+1)
where Nɸ= tan2(450 + ɸ/2),
Where, qur=unconfined compressive strength of rock.
The ratio of joint spacing to foundation width, as well as intact and rock
mass characteristics including joint orientation, joint condition (open or
closed), rock type, and intact and mass rock strengths, all affect the bearing
capacity of foundations built on rock masses.

4. BEARING CAPACITY
 Ultimate bearing capacity
Theoretical maximum pressure which can be supported without
failure.
Least gross pressure which will cause shear failure of the supporting soil
immediately below the footing.
 Allowable bearing capacity
Ultimate bearing capacity divided by a factor of safety.
Sometimes, on soft soil sites, large settlements may occur under loaded
foundations without actual shear failure occurring; in such cases, the
allowable bearing capacity is based on the maximum allowable
settlement.

5. ULTIMATE BEARING CAPACITY
The ultimate bearing capacity (the load per unit area of the foundation at
which shear failure/sliding in rock mass occurs) was governed by old US
construction regulations as,

6. ALLOWABLE BEARING CAPACITY
FOR PILE FOUNDATIONS
The allowable bearing capacity of socketed piles is given by:
qa= qc.Nj.Nd
where, Nd = 0.8 + 0.2 h/d
h = depth of socket in rock
D = diameter of socket
Determination of Net Allowable Bearing Pressure from pressure
meter Test
qa=
𝟏
𝟑
[𝜸𝑫𝒇 + 𝑲𝒅 𝑷𝒍 − 𝜸𝑫𝒇 ]
where qa= allowable bearing pressure in t/m2
Pl= limit pressure determined by the pressuremeter in t/m2
𝛾𝐷𝑓 = overburden pressure in t/m2

7. CONTINUED…
 Shallow foundations on slope bedrock must meet two requirements in
order to function correctly.
i. They must be protected from general shear failure in the mass of rock
that supports them.
ii. They cannot experience significant settlement or relocation.
 Settlement and sliding and Shear Failure are the two design criteria.
 The rock bearing capacity numbers listed in various building codes are
essentially estimates, hence it is advised to choose the bearing capacity
determined by measurements of specific characteristics made in-situ and
in laboratories.

8. ROCK MASS WITH FAVORABLE
DISCONTINUITIES
The net allowable bearing pressure can be estimated from;
qa = qc X Nj
where qc = average uniaxial compressive strength of rock cores
Nj= empirical coefficient depending on the spacing of the discontinuities.
𝟑+
𝑺
𝑩
𝟏𝟎 [𝟏+𝟑𝟎𝟎

𝒔
]
)
= thickness of discontinuity
S = spacing of discontinuities
B = width of footing
The above relationship is valid for a rock mass with spacing of continuities >
0.3 m ,  < 10mm (15mm if filled with soil) and B > 0.3m.

9. BEARING CAPACITY USING RQD
Effect of fracture intensity on bearing capacity can be estimated using
RQD,
• No reduction
RQD >90%
• Reduce by a factor 0.27-0.7
%50 <RQD< 90%
• Reduce by a factor 0.25-0.1
RQD <50%

10. CONTINUED…
 In the rock formation where bedding planes, joints and other planes of
weakness exist, the practice that is normally followed is to classify the rock
according to RQD.
 Peck et al (1974) have related the RQD to the allowable bearing pressure qa
as given in the table below; RQD qa ton/ft2 qa Mpa
100 300 29
90 200 19
75 120 12
50 65 6.25
25 30 3
0 10 0.96

11. Soil
Type
Soil Description Safe bearing
Capacity, kpa
1 Soft Rock or Shale 440
2 Gravel, sandy gravel, silty sandy gravel; very dense and offer high
resistance to penetration during excavation (soil shall include the groups
GW, GP, GM, GC)
400
3 Sand (other than fine sand), gravelly sand, silty sand; dry (soil
shall include the groups SW, SP, SM, SC
200
4 Fine sand; loose & dry (soil shall include the groups SW, SP 100
5 Silt, clayey silt, clayey sand; dry lumps which can be easily crushed by
finger (soil shall include the groups ML,, SC, & MH)
150
6 Clay, sandy clay; can be indented with strong thumb pressure (soil shall
include the groups CL, & CH)
150
7 Soft clay; can be indented with modest thumb pressure (soil shall include
the groups CL, & CH)
100
8 Very soft clay; can be penetrated several centimeters with thumb pressure
(soil shall include the groups CL & CH)
50

12. FACTORS AFFECTING BEARING
CAPACITY
i. Nature of soil and its physical and engineering properties.
ii. Nature of the foundation and other details such as the size,
shape, depth below the ground surface, and the rigidity of the
structure.
iii. Total and differential settlements that the structure can
withstand without functional failure
iv. Location of the groundwater table relative to the level of the
foundation.
v. Initial stresses, if any.

13. DIFFERENT MODES OF FAILURE
• A footing on rock could fail in a variety of ways.
• If the rock mass is largely unfractured, cracking
occurs.
• After a fracture begins, further loading causes it to
spread, and at still higher loads, the cracks combine
and start to interfere, eventually crushing under the
added load.
• The fractured and crushed rock beneath the loaded
area extends outward as a result of the dilatancy
effect, eventually leading to certain radial networks
of cracks (wedges) that spread up to the surface. Fig: Different modes of failure

14. a) General Shear Failure
When the settlement reaches around 7% of
the foundation width, the foundations on
dense sand with a relative density more
than 70% fail quickly with pronounced
peak resistance. Failure surfaces and a
significant bulging of a sheared mass of
sand both accompany the failure.
BEARING CAPACITY FAILURE
MODES

15. BEARING CAPACITY FAILURE
MODES
b. Local Shear Failure
• Foundations built on sand with a
relative density of 35 to 70 percent
do not suddenly fail.
• Sand begins to bulge at the surface
as soon as the settlement exceeds
8% of the foundation width.
• A boundary of sheared zones can
be seen at the surface at
settlements of around 15% of the
foundation width.
• The apex of base resistance might
not ever be reached, though.

16. BEARING CAPACITY FAILURE
MODES
c. Punching Shear Failure
• Foundation on relatively loose sand with a
relative density less than 35% into the soil
without any bulging of the sand surface.
• The base resistance gradually increases as
settlement progresses.
• The failure surface, which is vertical or
slightly inclined and follows the perimeter
of the base, never reaches the sand
surface.

17. MEYERHOF’S METHOD OF COMPUTING
ULTIMATE BEARING CAPACITY OF
FOUNDATIONS ON SLOPE
There are occasions where structure are required to be built on slopes or
near the edges of slopes.
Since full formations of shear zones under ultimate loading conditions
are not possible on the sides close to the slopes or edges, the supporting
capacity of soil on that side get considerably reduced.
Meyerhof (1957) has extended his theories to include the effect of
slopes on the stability of foundations.
Strip Foundations on Slopes
The zones of plastic flow is less than that of a similar foundation on a
level ground.

18. The region above the failure surface of a
shallow strip foundation is assumed to be
divided into a central elastic zone abc, a
radial shear zone bcd and a mixed shear
zone bden.
The stresses in the zones of plastic
equilibrium can be found out as for a
horizontal ground surface (Meyerhof,
1951), replacing the weight of soil wedge
ben by the equivalent stresses, p0 and s0
normal and tangential respectively, to the
plane be inclined at angle  to the
horizontal.
Bearing Capacity is given by;
qu = cNc + p0Nq + ½ BN ----(i)

19. The same equation (i) may also be expressed
as
qu = cNcq + ½  BNq ----(ii)
The bearing capacity factors Ncq and Nq for
foundations on slope may be obtained from
figure beside (Meyerhof. 1957),
For purely cohesive soils (ɸ=0) and
cohensionless soils (c=0).
It can be seen from the figures that the N
factors decrease with grater inclination of
slope.
For inclination of slopes used in practice (
300), the decrease in bearing capacity is small
in the case of clays and but is considerable
for sand and gravel slopes.

20. The effect of flowing water on the bearing
capacity may require to be analyzed if the
foundation is submerged with flowing water.
If the foundation soil is cohesive with a small
or no angle of shearing resistance, the stability
of foundation will have to be analyzed by taking
into account the stability of the slope.
Slopes of purely cohesive soil of great depth
may fail either by toe or base failures. The upper
limit of the bearing capacity of a foundation in a
purely cohesive soil may be estimated from the
expression.
qu= cNcq + Df -----(iii)
where the factor Ncq is given in the upper part.

21. BEARING CAPACITY OF
FOUNDATIONS ON TOP OF A SLOPE
The stability of the foundation depends on the
distance ƀ of the top edge of the slope from the face
of foundation.
The form of ultimate bearing capacity equation for a
strip footing may be expressed as (Meyerhof, 1957)
qu = cNcq + ½  BNq ----(iv)
The upper limit of the bearing capacity of a
foundation in a purely cohesive soil may be
estimated from;
qu = cNcq + Df ------ (v)
The resultant bearing capacity factors Ncq and Nq
depends on the distance ƀ, , ɸ and the Df/B ratio.

22. SOIL DEPOSITS ON SLOPE
• The slope provides the energy (potential energy) of the rockfall; the
soil determines the strength, permeability coefficient, and porosity
of the soil, which affects the pore water pressure of the soil; rainfall
is the trigger factor.
• In general, its amount determines the scale of the rockfall and
rockfall quantity.
• The thickness and composition of soil horizons vary with position
on a hillslope and with water drainage.
• For example: on the upper slopes of poorly drained profiles,
underlying rock may be exposed by surface erosion, and nutrient-
rich soils (A horizon) may accumulate at the toe slope.
• In well-drained profiles under forest cover, the leached layers (E
horizon) may be relatively thick.

23. SOIL DEPOSITS ON SLOPE
• Because of mechanical weathering brought on by
precipitation, temperature changes, etc., soils are created.
• Gravitational forces acting on disaggregated particles
lead them to flow down the slopes and accumulate as
discrete deposits along the bottom regions of slopes, in
topographic depressions, and especially at the bases of
cliffs in sites with appropriate topographic relief.
• Deposits moved by gravitational forces are referred to as
colluvium or colluvial materials.
• Large numbers of fragments ranging in size from small
to very large are commonly produced by the relatively
quick physical disintegration of bedrock exposed on
cliffs: after falling from the cliff, they gather near the
base as talus.

24. SOIL DEPOSITS ON SLOPE
• Naturally occurring and man-made factors both contribute to the instability of soils
on steep slopes.
• The gradient and contour of the slope, the geology, the soil, the vegetation, and the
temperature are natural characteristics of steep slopes that make them prone to
failures and mass movement.
• Shallow, loose soils on impermeable surfaces, steeper slopes, and during severe
storms are more prone to mass movement.
• Development, habitation, shifting farming, deforestation, forest fires, soil mining,
and other slope disturbances are examples of human activities that cause soils on
steep slopes to become unstable.
• Gravity, water saturation, and water movement can cause mass movement or
landslides, which can take the following different forms: falls, crawls, slumps, and
earthflows; debris avalanches and debris flows; debris torrents; and bedrock
failures.

25. THANK YOU !!!