Assumptions of Westergaard' s Theory of stress distribution

Hi,

Westergaard developed a solution to determine distribution of stress due to point load in soils composed of thin layer of granular material that partially prevent lateral deformation of the soil.

Assumptions:

(1) The soil is elastic and semi-infinite.

(2) Soil is composed of numerous closely spaced horizontal layers of negligible thickness of an infinite rigid material.

(3) The rigid material permits only the downward deformation of mass in which horizontal deformation is zero.

Thanks!

Reference: 

Classification of Soil based on Grain Size

Hi, here is the classification of the soil on the basis of the particle size.
Soil classification on the basis of their color, smell, porosity,  place of origin, strength etc. is either not easy, or is not of much relevance to the soil engineer. Classification on the basis of the grain size and the plasticity of the soil is of much relevance to a soil engineer.

• Based on the grain size:

Below 0.002 mm are the Clay sizes
Between 0.002 and 0.075 mm are the Silt sizes
Between 0.075 mm and 4.75 mm are the Sand sizes
and between 4.75 mm and 80 mm are the Gravel sizes.

Part- 2 Soil Mechanics and foundation Engineering- GATE 2014 exam preparation

1. For a clay slope of height 10 m, if stability number is 0.05, bulk density is 20 kN/m^2, cohesion is 25 kN/m^2, then critical height of the slope in the soil is 25.0 m.

2. A strip footing of width 1.0 m is resting on a soft clay strata at a depth of 1.0 m. The angle of internal friction is zero, and cohesion is 20 kN/m^2. The water table is at a great depth. The ultimate bearing capacity of soil according to Terzaghi's equation is 114 kN/m^2.

3. Gross bearing capacity of a footing is 450 kN/m^2. If footing is 1.5 m wide at a depth of 1 m in clayey soil with unit weight of 20 kN/m^3, then net bearing capacitywill be 430 kN/m^3.

4. A 30 cm diameter friction pile is embedded 10 m into a homogeneous consolidated deposit. Unit adhesion developed between clay and pile shaft is 4 t/m^2 and adhesion factor is 0.7. The safe load for factor of safety 2.5 will be 10.55 t.

5. A single acting steam hammer weighing 82.5 kN and falling through a height of 1.2 m drives a pile. If final set is 12.5 mm, then according to Engineering News formula. [ P= WH/ 6(s+0.25)]

6. If bearing capacity of a strip footing on a saturated clay is 120 kN/m^2, then bearing capacity of a circular footing(diameter = width) will be more than 120 kN/m2.

7. Following data is obtained from a void ratio- pressure diagram, e1= 0.6;  e2 = 0.7; S1 = 17; S2 = 17.5, then the co-efficient of compressibility is 0.2 m^2/t

to be continued to part -3....

GATE 2014 - Soil mechanics - one liners- Part 1

1. A soil sample is having a specific gravity of 2.60 and a void ratio of 0.78. The water content in percentage required to fully saturate the soil at that void ratio would be 30%.

2. A loose uniform sand with rounded grains has effective grain size of 0.05 cm. Co-efficient of permeability of the sand is 0.25 cm/sec

3. If flow net of a coffer dam foundation had 6 numbers of flow channels and 16 numbers of equipotential drops, with the head of water lost during seepage being 6 m through foundation having k= 4*10^(-5) m/min, then seepage loss (in m^3/day) per meter length of the dam will be 12.96 * 10^(-2)

4. Properties of flow net are: Flow lines are perpendicular to equipotential lines, No two flow lines or equipotential lines start from the same point and no two flow lines cross each other.

5. Flownet drawn for a weir; total head loss is 6 m, number of potential drops is 10 and length of the flow path for the last square is 1 m. The exit gradient is 0.6.

6. In a saturated soil deposit having a density of 22 kN/m^3, the effective normal stress on a horizontal plane at 5 m depth will be 60 kN/m^2

7. Average pore water pressure in a fully saturated clay specimen, which was subjected to a pressure of 20 N/cm^2 initially, was measured to be 7 N/cm^2 after a period of time. Degree of consolidation reached at that time is 65%.

8. Water is flowing at the rate of 0.1 cc/sec in an upward direction through a sand sample with k = 2*10^(-3) cm/sec. Thickness of sand sample is 10 m and sectional area is 50 cm^2. The effective stress at middle of sample if Ysat = 2 t/m^3 is

9. In a drained tri-axial compression test, a saturated specimen of a cohesion-less sand fails under a deviating stress of 3 kgf/cm^2 when cell pressure is 1 kgf/cm^2. The effective angle of shearing resistance of sand is about  45 degrees + friction angle.

10. A un-drained tri-axial compression test is carried out on a saturated clay sample under a cell pressure of 100 kN/m^2. If sample failed at a deviator stress of 200 kN/m^2, then cohesion of the given sample of clay is 100 kN/m^2.

Reference : GK publishers

Factors affecting co-efficient of permeability of soil

Hello

There is an equation known as Poiseuille's equation, which when compared with the Darcy's law gives the value of coefficient of permeability,

  k = C.Yw/U * Ds^2 * e^3/ (1+e)

 In above equation, the factor k depends on:

(1) Grain Size: Allen Hazen found that the co-efficient of permeability can be expressed as 

                                k(in cm) = c.(D10)^2

  where, D10= effective diameter(cm)

              C = constant, approximately equal to 100.

(2) Properties of pore fluid: 

  viscosity of the fluid affects the flow, more the viscosity less is the fluidity so it is inversely proportional to the viscosity.

 k1/k2 = n2/n1

(3) Void ratio: 

Based on the mean hydraulic radius it can be written that,

k1/k2 = (e1/e2)^2

(4) Structural arrangements: Depending upon the method of compaction and condition existing during deposition, the structural arrangement of soil mass may vary at the same void ratio and consequently permeability also varies. it is defined by the factor C is the above equation.

For stratified deposits the flow is different for flow parallel and perpendicular or stratification.

(5) Degree of saturation and other foreign matter:

The permeability is affected by the partial saturation of the soil, when it has entrapped the air inside. Other foreign matter has the general tendency to flow towards the critical flow channel and thus choking it.

(6) Adsorbed water: The adsorbed water held on the surface of colloidal particles are highly cohesive and is immobile to normal hydrodynamic forces. Because of this the area of effective void space is reduced and thus permeability is reduced.

Thanks!

Limitations of Rankine's Theory

There are the following limitations in the Rankine's Theory
(i) As the retaining walls are usually constructed of masonry or cement concrete, the back of the wall is never smooth, and hence friction develops.
(ii)due to assumption that wall back is smooth, the resultant pressure must act parallel to the surface but due to frictional forces, the active earth pressure gets inclined in the wall at an angle equal to angle of friction.
(iii) The wall back may not always be vertical. In practice a batter is given to the wall back.
(iv) The retained soil may not be always cohesion-less.

Reference: GK Publishers, GATE

Flow Lines and Flow net of soil

Hello

Flow Lines 

-are the paths which water particle follow in the course of seepage. Water flows from the point of higher head to low head.

Equipotential lines 

-are the lines formed by joining the points of same head or potential on the flow lines.

FLOW NETS: 

If we draw the flow lines and the equipotential lines for a given flow of water through a given soil we get a net like sketch which is known as flow net. Flow lines are always at 90 degrees to  the equal potential lines.

Properties of Flow net:

1. Flow lines and equal potential lines intersect each other at 90 degrees.
2. The areas bounded by the flow lines and equal potential lines form approximate squares.
3.  Flow nets must satisfy the boundary conditions of flow field.
4.  Quantity of water flowing through each flow channel is the same.
5.  The potential drop in any two consecutive equal potential lines is same/constant.
6. Flow lines and equal potential lines are smooth curves.
7. Flow lines do show refraction at the interface between two soils having different coefficient of permeability.

Application of Flow Net:

(i) Determination of seepage: For the seepage through a flow net for isotropic condition                   Total Discharge, q = k.h.Nf/Nd

       where,  k = co-efficient of permeability

                    h= head causing flow

                  Nf= Total numbers of flow channels

                  Nd= Total numbers of potential drops.

(ii) Determination of seepage pressure: The change in the effective pressure due to flow of water is known as seepage pressure. The seepage pressure at any point can be determined by

                                  Ps= H.Yw

 where, H= hydraulic potential at any point

                = h - n.h/Nd = (Nd-n).h/Nd

                n = numbers of potential drops.

Thanks!

Reference: