Soil Mechanics-II Bearing Capacity of Soils

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Soil Mechanics-IIBearing Capacity of Soils

• Dr. Attaullah Shah

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Selection of Foundation .

• Shallow foundations
• Where the ratio of embedment depth to min plan
  dimension is less or equal to 2.5
• Embedment depth is the depth below the ground
  surface where the base of foundation rests.
• a. plain concrete foundation,
• b. stepped reinforced concrete foundation,
• c. reinforced concrete rectangular foundation,
• d. reinforced concrete wall foundation.

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Steps in selection of Foundation types

• 1 Obtain the required information concerning the
  nature of the superstructure and the loads to be
  transmitted to the foundation.
• 2. Obtain the subsurface soil conditions.
• 3. Explore the possibility of constructing any
  one of the types of foundation under the existing
  conditions by taking into account (i) the
  bearing capacity of the soil to carry the
  required load, and (ii) the adverse effects
  on the structure due to differential settlements.
  Eliminate in this way, the unsuitable types.
• 4. Once one or two types of foundation are
  selected on the basis of preliminary studies,
  make more detailed studies. These studies may
  require more accurate determination of loads,
  subsurface conditions and footing sizes. It may
  also be necessary to make more refined estimates
  of settlement in order to predict the behavior of
  the structure.
• 5. Estimate the cost of each of the promising
  types of foundation, and choose the type that
  represents the most acceptable compromise between
  performance and cost.

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Some basic definitions

• Total Overburden Pressure q0
• qo is the intensity of total overburden pressure
  due to the weight of both soil and water at the
  base level of the foundation.
• Effective Overburden Pressure q'0
• q'0 is the effective overburden pressure at the
  base level of the foundation.
• The Ultimate Bearing Capacity of Soil, qu
• qu is the maximum bearing capacity of soil at
  which the soil fails by shear.
• The Net Ultimate Bearing Capacity, qnu
• qnu is the bearing capacity in excess of the
  effective overburden pressure q'0 expressed as

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• Gross Allowable Bearing Pressure, qa is
  expressed as
• where Fs factor of safety.
• Net Allowable Bearing Pressure, qna
• Safe Bearing Pressure, qs
• qs is defined as the net safe bearing pressure
  which produces a settlement of the foundation
  which does not exceed a permissible limit.
• Note In the design of foundations, one has to
  use the least of the two values of qna and qs.

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BEARING CAPACITY THEORIES

• The determination of bearing capacity of soil
  based on the classical earth pressure theory of
  Rankine (1857) began with Pauker, a Russian
  military engineer (1889).
• It was modified by Bell (1915). Pauker's theory
  was applicable only for sandy soils but the
  theory of Bell took into account cohesion also.
• The methods of calculating the ultimate bearing
  capacity of shallow strip footings by plastic
  theory developed considerably over the years
  since Terzaghi (1943). Terzaghi extended the
  theory of Prandtl (1921).
• Taylor (1948) extended the equation of Prandtl by
  taking into account the surcharge e Terzaghi
  (1943) first proposed a semi-empirical equation
  for computing the ultimate bearing capacity of
  strip footings by taking into account cohesion,
  friction and weight of soil, and replacing the
  overburden pressure with an equivalent surcharge
  load at the base level of the foundation effect
  of the overburden soil at the foundation level.

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Methods of bearing capacity determination

• 1. Terzaghi's bearing capacity theory
• 2. The general bearing capacity equation
• 3. Field tests
• TERZAGHI'S BEARING CAPACITY THEORY
• Terzaghi made the following assumptions for
  developing an equation for determining qu for a
  c-? soil.
• The soil is semi-infinite, homogeneous and
  isotropic,
• The problem is two-dimensional,
• The base of the footing is rough,
• The failure is by general shear,
• the load is vertical and symmetrical,
• The ground surface is horizontal,
• the overburden pressure at foundation level is
  equivalent to a surcharge load
• the principle of superposition is valid,
• Coulomb's law is strictly valid, that is,

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Mechanism of Failure

• The shapes of the failure surfaces under ultimate
  loading conditions are given in Fig.
• The zones of plastic equilibrium represented in
  this figure by the area gedcf may be subdivided
  into three zones
• 1 . Zone I of elastic equilibrium
• 2. Zones II of radial shear state
• 3. Zones III of Rankine passive state
• When load qu per unit area acting on the base of
  the footing of width B with a rough base is
  transmitted into the soil, the tendency of the
  soil located within zone I is to spread but this
  is counteracted by friction and adhesion between
  the soil and the base of the footing.
• Due to the existence of this resistance against
  lateral spreading, the soil located immediately
  beneath the base remains permanently in a state
  of elastic equilibrium, and the soil located
  within this central Zone I behaves as if it were
  a part of the footing and sinks with the footing
  under the superimposed load.

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• The depth of this wedge shaped body of soil abc
  remains practically unchanged, yet the footing
  sinks.
• This process is only conceivable if the soil
  located just below point c moves vertically
  downwards. This type of movement requires that
  the surface of sliding cd (Fig.) through point c
  should start from a vertical tangent. The
  boundary be of the zone of radial shear bed (Zone
  II) is also the surface of sliding.
• As per the theory of plasticity, the potential
  surfaces of sliding in an ideal plastic material
  intersect each other in every point of the zone
  of plastic equilibrium at an angle (90 - ?).
  Therefore the boundary be must rise at an angle ?
  to the horizontal provided the friction and
  adhesion between the soil and the base of the
  footing suffice to prevent a sliding motion at
  the base.
• The sinking of Zone I creates two zones of
  plastic equilibrium, II and III, on either side
  of the footing. Zone II is the radial shear zone
  whose remote boundaries bd and af meet the
  horizontal surface at angles (45 - ?/2), whereas
  Zone III is a passive Rankine zone. The
  boundaries de and fg of these zones are straight
  lines and they meet the surface at angles of
  (45 - ?/2). The curved parts cd and cf in Zone
  II are parts of logarithmic spirals whose centers
  are located at b and a respectively.

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• Ultimate Bearing Capacity of Soil Strip Footings
• Terzaghi developed his bearing capacity equation
  for strip footings by analyzing the forces acting
  on the wedge abc in Fig.
• where Qult ultimate load per unit length of
  footing, c unit cohesion, /the effective unit
  weight of soil, B width of footing, D, depth
  of foundation, Nc, Nq and N? are the bearing
  capacity factors. They are functions of the angle
  of friction ?.
• where Kp passive earth pressure coefficient

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Bearing capacity factors of Terzaghi
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Terzaghi's bearing capacity factors for general
shear failure
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Equations for Square, Circular, and Rectangular
Foundations

• Terzaghi's bearing capacity Eq. has been modified
  for other types of foundations by introducing the
  shape factors. The equations are
• Square Foundations
• Circular Foundations
• Rectangular Foundations
• Ultimate Bearing Capacity qu in Purely
  Cohesion-less and Cohesive Soils Under General
  Shear Failure
• For cohesion-less soil (for c 0) and cohesive
  soils (for ? 0) as follows.
• Strip Footing
• Square Footing
  
• Circular Footing
• Rectangular Footing

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EFFECT OF WATER TABLE ON BEARING CAPACITY

• In case the water table lies at any intermediate
  depth less than the depth (Df B), the bearing
  capacity equations are affected due to the
  presence of the water table.
• Case 1. When the water table lies above the base
  of the foundation.

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Solved Example

• A strip footing of width 3 m is founded at a
  depth of 2 m below the ground surface in a (c -
  ?) soil having a cohesion c 30 kN/m2 and angle
  of shearing resistance ? 35. The water table
  is at a depth of 5 m below ground level. The
  moist weight of soil above the water table is
  17.25 kN/m3.
• Determine (a) the ultimate bearing capacity of
  the soil, (b) the net bearing capacity, and (c)
  the net allowable bearing pressure and the load/m
  for a factor of safety of 3. Use the general
  shear failure theory of Terzaghi.

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• If the water table in Ex. 12.1 rises to the
  ground level, determine the net safe bearing
  pressure of the footing. All the other data given
  in Ex. 12.1 remain the same. Assume the saturated
  unit weight of the soil ?sat 18.5 kN/m3.

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Home Assignment

• A rectangular footing of size 10 x 20 ft is
  founded at a depth of 6 ft below the ground
  surface in a homogeneous cohesionless soil having
  an angle of shearing resistance ? 35. The
  water table is at a great depth. The unit weight
  of soil 7 114 lb/ft3. Determine (1) the net
  ultimate bearing capacity, (2) the net allowable
  bearing pressure for Fs 3, and (3) the
  allowable load Qa the footing can carry. Use
  Terzaghi's theory.
• A rectangular footing of size 10 x 20 ft is
  founded at a depth of 6 ft below the ground level
  in a cohesive soil (? 0) which fails by general
  shear. Given ?sat 114 lb/ft3, c 945 lb/ft2.
  The water table is close to the ground surface.
  Determine qu , qnu and qna by Terzaghi's method,

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THE GENERAL BEARING CAPACITY EQUATION

• Meyerhof (1963) presented a general bearing
  capacity equation which takes into account the
  shape and the inclination of load. The general
  form of equation suggested by Meyerhof for
  bearing capacity is

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Validity of the Bearing Capacity Equations

• There is currently no method of obtaining the
  ultimate bearing capacity of a foundation other
  than as an estimate (Bowles, 1996).
• There has been little experimental verification
  of any of the methods except by using model
  footings. Up to a depth of Df B the Meyerhof qu
  is not greatly different from the Terzaghi value
  (Bowles, 1996). The Terzaghi equations, being the
  first proposed, have been quite popular with
  designers.
• Both the Meyerhof and Hansen methods are widely
  used. The Vesic method has not been much used. It
  is a good practice to use at least two methods
  and compare the computed values of qu. If the two
  values do not compare well, use a third method.

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STANDARD PENETRATION TEST

• The method has been standardized as ASTM D-1586
  (1997) with periodic revision since 1958. The
  method of carrying out this test is as follows
• 1. The split spoon sampler is connected to a
  string of drill rods and is lowered into the
  bottom of the bore hole which was drilled and
  cleaned in advance.
• 2. The sampler is driven into the soil strata to
  a maximum depth of 18 in by making use of a 140
  Ib weight falling freely from a height of 30 in
  on to an anvil fixed on the top of drill rod. The
  weight is guided to fall along a guide rod. The
  weight is raised and allowed to fall by means of
  a manila rope, one end tied to the weight and the
  other end passing over a pulley on to a hand
  operated winch or a motor driven cathead.
• 3. The number of blows required to penetrate each
  of the successive 6 in depths is counted to
  produce a total penetration of 18 in.
• 4. To avoid seating errors, the blows required
  for the first 6 in of penetration are not taken
  into account those required to increase the
  penetration from 6 in to 18 in constitute the
  N-value.
• The SPT is conducted normally at 2.5 to 5 ft
  intervals. The intervals may be increased at
  greater depths if necessary.

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ULTIMATE BEARING CAPACITY OF FOOTINGS BASED ON
SPT VALUES (N

• Standard Energy Ratio Res Applicable to N Value
• The empirical correlations established in the USA
  between N and soil properties indicate the value
  of N conforms to certain standard energy ratios.
  Some suggest 70 (Bowles, 1996) and others 60
  (Terzaghi et al., 1996).
• The relation between Ncor and ? established by
  Peck et al., (1974) is given in a graphical form
  in Fig. The value of Ncor to be used for getting
  ? is the corrected value for standard energy. The
  angle ? obtained by this method can be used for
  obtaining the bearing capacity factors, and hence
  the ultimate bearing capacity of soil.
• Cohesive Soils
• Relationship Between Ncor and qu (Unconfined
  Compressive Strength) Relationships have been
  developed between Ncor and qu (the undrained
  compressive strength) for the ? 0 condition.
  This relationship gives the value of cu for any
  known value of Ncor. The relationship may be
  expressed as Eq.
• where the value of the coefficient may vary
  from a minimum of 12 to a maximum of 25

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