Soil Mechanics and Foundation Engineering Notes for SSC JE Civil

Soil mechanics and foundation engineering is a high-weightage subject of the SSC JE Civil paper. Every year, 5 to 8 questions come on the phase relations, the Atterberg limits, the classification of the soil, the compaction, the permeability, the shear strength and the bearing capacity. These soil mechanics notes for SSC JE Civil give you all the formulas, the tests and the standard values in simple tables, followed by 20 practice questions. Read them with the Surveying Notes for SSC JE, Concrete Technology Notes for SSC JE and Strength of Materials and Structural Analysis Notes for SSC JE Civil notes.

Soil and the Three-Phase Diagram

Soil is a natural, unconsolidated material made of the solid particles, water and air. The three-phase diagram shows the solids (volume Vs, weight Ws), the water (Vw, Ww) and the air (Va, with no weight). The volume of the voids is Vv = Vw + Va and the total volume is V = Vs + Vv.

• Residual soils are formed and stay at the same place; transported soils are carried by water (alluvial), wind (aeolian), glaciers (glacial) and gravity (colluvial).
• The mineral kaolinite is the least active clay mineral; montmorillonite is the most active and makes the swelling soil (the black cotton soil); illite is in between.
• Specific gravity of the soil solids G is about 2.65 for sand, 2.6 to 2.8 for clays and 2.65 to 2.7 for most soils.

Phase Relationships (Important Formulas)

• gamma_w = 9.81 kN per cubic metre (about 10 kN per cubic metre).
• Order of the unit weights: gamma_sat > gamma > gamma_d > gamma' (submerged).
• The relative density (density index) of the sand Dr = (emax - e) / (emax - emin); the sand is loose if Dr is less than 33 percent and dense if it is more than 66 percent.

Index Properties: Grain Size and Atterberg Limits

• Sieve analysis is used for the particles coarser than 0.075 mm (the 75 micron sieve); hydrometer or pipette analysis is used for the finer particles (based on Stokes' law).
• Coefficient of uniformity Cu = D60 / D10 and coefficient of curvature Cc = (D30 squared) / (D10 x D60). A well-graded gravel has Cu more than 4 and Cc between 1 and 3; a well-graded sand has Cu more than 6 and Cc between 1 and 3.
• D10 is called the effective size.

Classification of Soils (Indian Standard)

• Examples: GW (well-graded gravel), SP (poorly graded sand), CL (clay of low plasticity), CH (clay of high plasticity), ML (silt of low plasticity).
• A soil is coarse-grained if more than 50 percent is retained on the 75 micron sieve and fine-grained if more than 50 percent passes it.
• The A-line of the plasticity chart: PI = 0.73 (LL - 20). A soil above the A-line is clay and below it is silt or organic soil.

Compaction

• Compaction is the quick reduction of the air voids by the mechanical energy; consolidation is the slow reduction of the water from the voids under a steady load.
• The curve between the dry density and the water content has a peak: the peak is the Maximum Dry Density (MDD) at the Optimum Moisture Content (OMC).
• The zero air voids line (the saturation line) is the upper limit; the compaction curve always lies below it.
• Field rollers: smooth-wheeled (for gravel and sand), sheep-foot (for clays), pneumatic tyred (for most soils) and vibratory (for granular soils).
• The field density is checked by the sand replacement method or the core cutter method.

Permeability, Seepage and Effective Stress

• Darcy's law: v = k i, where v is the discharge velocity, k is the coefficient of permeability (m per second) and i is the hydraulic gradient (head loss per unit length). Discharge Q = k i A.
• Seepage velocity vs = v / n (n is the porosity), which is always more than the discharge velocity.
• Constant head test is for the coarse soils (sand and gravel); the falling head test is for the fine soils (silt and clay). Hazen's formula: k = C (D10 squared), with D10 in cm and C about 100.
• The permeability depends on the grain size, the void ratio, the temperature and the degree of saturation; it is the highest in the gravel and the lowest in the clay.
• Effective stress principle (Terzaghi): sigma' = sigma - u, where sigma is the total stress and u is the pore water pressure. The soil behaviour (strength and settlement) depends on the effective stress.
• Quick sand condition (boiling): the upward seepage makes the effective stress zero; the critical hydraulic gradient ic = (G - 1) / (1 + e), which is about 1.
• Piping is the removal of the soil by the seepage under the dams; the flow net is made of the flow lines and the equipotential lines, which cut each other at 90 degrees.

Consolidation and Settlement

• Consolidation is the slow decrease in the volume of a saturated clay under a steady load because the water is squeezed out. Terzaghi's one-dimensional theory explains it.
• The load is first taken by the pore water, and then it is shifted slowly to the soil skeleton, so the excess pore pressure becomes zero at the end.
• Compression index Cc is the slope of the e versus log sigma' curve; the coefficient of consolidation Cv decides the rate; the time factor Tv = Cv t / (Hdr squared), where Hdr is the drainage path (half the thickness for the double drainage).
• Settlement of a clay layer: S = [Cc H / (1 + e0)] log10 [(sigma0 + delta sigma) / sigma0].
• Normally consolidated clay: the present stress is the maximum stress it has felt. Over-consolidated clay: it has felt a higher stress earlier. Over-consolidation ratio OCR = the preconsolidation pressure / the present effective pressure.
• Types of settlement: immediate (elastic), primary consolidation and secondary consolidation (creep).

Shear Strength of Soil

Earth Pressure and Retaining Walls

• Ka x Kp = 1, and Kp is much more than Ka.
• The active pressure on a wall of height H in the cohesionless soil is Pa = 0.5 Ka gamma H squared acting at H / 3 from the base.
• Rankine's theory (a smooth, vertical wall) and Coulomb's theory (the wall friction is considered) are the main theories.
• A retaining wall is checked for the overturning (factor of safety 1.5 or more), sliding (1.5 or more) and the bearing pressure.
• Types: gravity, cantilever, counterfort and buttress walls.

Bearing Capacity and Foundations

• Shallow foundations: isolated (spread) footing, combined footing, strip footing, strap footing and the raft (mat) foundation, used when the soil is weak or the loads are heavy.
• Deep foundations: piles (end-bearing and friction piles), piers and wells (caissons). A pile is used when the strong layer is at a depth.
• Negative skin friction (down drag) acts on a pile in a settling soil. The group efficiency of the pile group is generally less than 1.
• The water table within the depth B below the footing reduces the bearing capacity by about 50 percent.
• Black cotton soil (expansive soil) has montmorillonite and swells and shrinks; the foundation should be below the zone of the moisture change, or the under-reamed piles are used.
• Soil exploration: the borings (auger, wash boring and percussion), and the samples: disturbed and undisturbed. The area ratio of a good sampler is less than 10 to 12 percent. The depth of the exploration should be about 1.5 times the width of the foundation.
• Slope stability: the factor of safety of a slope = resisting force / driving force; the methods are the Swedish slip circle and the Fellenius method; the Taylor stability number is used for the cohesive soil.

Important Questions Explained

Question 1: What is the relation between e, S, w and G?
Answer: e S = w G.

Question 2: What is the plasticity index of a soil with a liquid limit of 60 percent and a plastic limit of 25 percent?
Answer: PI = LL - PL = 60 - 25 = 35 percent.

Question 3: What is the coefficient of uniformity of a soil with D60 = 0.6 mm and D10 = 0.1 mm?
Answer: Cu = D60 / D10 = 0.6 / 0.1 = 6.

Question 4: Which test is used to find the OMC and the MDD of a soil?
Answer: The Proctor compaction test (standard or modified).

Question 5: What is the critical hydraulic gradient for a soil with G = 2.65 and e = 0.65?
Answer: ic = (G - 1) / (1 + e) = 1.65 / 1.65 = 1.

Question 6: What is the coefficient of active earth pressure for a soil with phi = 30 degrees?
Answer: Ka = (1 - 0.5) / (1 + 0.5) = 1/3.

Question 7: What is the shear strength of a saturated clay of unconfined compressive strength 100 kPa?
Answer: c = qu / 2 = 50 kPa (phi = 0).

Quick Tips to Remember

• Learn the phase relations in one line: e S = w G, n = e / (1 + e), gamma_d = gamma / (1 + w).
• For the Atterberg limits, remember the order LL, PL, SL (the water content falls from the liquid to the solid state).
• Remember that PI = LL - PL and that the clay is above the A-line.
• Remember Ka = 1/3 for phi = 30 degrees and that Kp = 3.
• Remember the SPT numbers: 63.5 kg, 750 mm and the last 300 mm.
• Remember that the effective stress controls the strength and the settlement of the soil.

Common Mistakes to Avoid

• Confusing the porosity (less than 1) and the void ratio (can be more than 1).
• Writing the Proctor test energy values wrongly (2.6 kg and 310 mm for the standard test).
• Mixing the compaction (air voids) and the consolidation (water squeezed out).
• Using the total stress instead of the effective stress.
• Writing the shear strength of the sand with a cohesion.

Quick Revision Points

• e S = w G; n = e / (1 + e); PI = LL - PL; LI = (w - PL) / PI.
• Cu = D60 / D10; Cc = D30 squared / (D10 D60).
• Darcy: v = k i; vs = v / n; ic = (G - 1) / (1 + e).
• Shear strength: tau = c + sigma' tan phi; clay: phi = 0, c = qu / 2.
• Ka = (1 - sin phi) / (1 + sin phi); Kp = 1 / Ka.
• Terzaghi: qu = c Nc + gamma Df Nq + 0.5 gamma B N_gamma (strip).
• SPT: 63.5 kg hammer, 750 mm fall; the N value.

Practice Questions With Answers

1. What is the formula of the void ratio?
   Answer: e = Vv / Vs (Volume of voids to solids).
2. What is the relation between n and e?
   Answer: n = e / (1 + e) (Porosity).
3. What is the relation of the degree of saturation?
   Answer: e S = w G (Basic relation).
4. What is the formula of the plasticity index?
   Answer: PI = LL - PL (Atterberg limits).
5. Which test gives the liquid limit?
   Answer: Casagrande test (25 blows) (12 mm closure).
6. What is the diameter of the thread in the plastic limit test?
   Answer: 3 mm (Plastic limit).
7. What is the IS classification symbol of a clay of high plasticity?
   Answer: CH (Above the A-line).
8. What is the weight of the rammer in the standard Proctor test?
   Answer: 2.6 kg (Fall 310 mm).
9. What is the weight of the rammer in the modified Proctor test?
   Answer: 4.9 kg (Fall 450 mm).
10. Which roller is the best for the clay?
    Answer: Sheep-foot roller (Kneading).
11. State Darcy's law.
    Answer: v = k i (Velocity = k x gradient).
12. Which test is used for the permeability of the sand?
    Answer: Constant head test (Coarse soils).
13. What is the formula of the effective stress?
    Answer: sigma' = sigma - u (Terzaghi).
14. What is the value of phi for a saturated clay in the undrained test?
    Answer: Zero (Cohesion only).
15. Which test is for the cohesive soil only?
    Answer: Unconfined compression test (qu).
16. What is Ka for phi = 30 degrees?
    Answer: 1/3 (Active earth pressure).
17. What is the value of Ka x Kp?
    Answer: 1 (Rankine).
18. Which theory gives the bearing capacity equation for a strip footing?
    Answer: Terzaghi's theory (Nc, Nq, N_gamma).
19. What is the weight of the hammer in the SPT?
    Answer: 63.5 kg (Fall 750 mm).
20. Which clay mineral causes the swelling in the black cotton soil?
    Answer: Montmorillonite (Expansive soil).

How to Practise This Topic

1. Write the phase relations and the Atterberg limits on one page and learn them.
2. Solve five numerical problems of the phase relations by yourself.
3. Revise the tests, the standard values and the earth pressure the next day.
4. Attempt the practice questions without looking at the answers.
5. Solve the SSC practice papers and the previous year papers to practise the JE pattern.

Related Notes and Practice

• Surveying Notes for SSC JE
• Concrete Technology Notes for SSC JE
• Strength of Materials Notes for SSC JE
• Fluid Mechanics and Hydraulics Notes for SSC JE
• Civil Engineering (SSC JE) Notes
• SSC practice papers

Frequently Asked Questions

What is soil mechanics?

Soil mechanics is the branch of civil engineering that studies the behaviour of the soil under the loads, its strength, the settlement and the flow of the water.

What are the Atterberg limits?

The Atterberg limits are the liquid limit, the plastic limit and the shrinkage limit, which are the water contents at which the soil changes its state.

What is the plasticity index?

The plasticity index is the difference between the liquid limit and the plastic limit of a soil (PI = LL - PL).

What is the difference between compaction and consolidation?

Compaction is the reduction of the air voids by the mechanical energy, while consolidation is the slow reduction of the volume of a saturated soil due to the squeezing out of the water.

What are OMC and MDD?

The optimum moisture content (OMC) is the water content at which the soil gets the maximum dry density (MDD) for the given compaction energy.

What is Darcy's law?

Darcy's law says that the velocity of the flow of water through the soil is directly proportional to the hydraulic gradient (v = k i).

What is the effective stress?

The effective stress is the total stress minus the pore water pressure; it controls the strength and the settlement of the soil.

What is the Mohr-Coulomb equation?

The Mohr-Coulomb equation is tau = c + sigma' tan phi, which gives the shear strength of the soil.

What is the SPT?

The Standard Penetration Test is a field test in which a 63.5 kg hammer falls 750 mm to drive a split spoon sampler, and the number of blows for the last 300 mm is the N value.

What is the bearing capacity of a soil?

The bearing capacity is the maximum load per unit area that a soil can take without a shear failure or too much settlement.

How many questions come from soil mechanics in the SSC JE exam?

Usually 5 to 8 questions come from soil mechanics and the foundation engineering in the SSC JE Civil paper.

How can I prepare soil mechanics for SSC JE?

Learn the formulas and the standard values in tables, solve the numerical problems and the previous year questions, and revise the tests.