Soil exploration, earth pressure and retaining structures

Before a structure is designed, the ground must be investigated, and where soil must be held back — in hill roads, basements and bridge abutments — the lateral earth pressure on walls must be calculated. Stone masonry, gabion and RCC retaining walls line Nepal's hill roads. This note covers soil exploration (methods, planning, sampling, field tests, reports), Rankine and Coulomb earth pressure theories and stability checks of retaining walls.

Key concepts

Soil exploration — purpose and planning

• Purpose: determine soil profile, groundwater level, engineering properties, bearing stratum, and likely problems (landslide, liquefaction, expansive soils).
• Stages: reconnaissance (site visit, geology maps) → preliminary exploration → detailed exploration.
• Planning: number and spacing of boreholes depend on structure type and variability (e.g. 3–5 holes for a building; along a line for roads/canals). Depth of exploration ≈ depth where added stress drops to about 10% of the applied stress (≈ 1.5–2 × footing width for isolated footings), or to firm stratum/rock.

Methods of exploration

Method	Use
Open pits / trial pits	Shallow depths (≤ 3–4 m), direct visual inspection, undisturbed block samples
Auger boring	Soft to stiff soils, shallow depths
Wash boring	Fast, but samples disturbed
Rotary/percussion drilling	Hard soils, rock coring
Geophysical (seismic refraction, electrical resistivity)	Large areas, depth to rock, water table

Soil sampling and samplers

• Disturbed samples: structure destroyed; used for classification, Atterberg limits, grain size.
• Undisturbed samples: structure and water content preserved; for strength, consolidation tests.
• Area ratio $A_r = \dfrac{D_o^2 - D_i^2}{D_i^2}\times100$ — should be ≤ 10% for undisturbed sampling (thin-walled tubes).
• Other quality indices: inside clearance (1–3%), outside clearance (0–2%), recovery ratio.
• Samplers: split-spoon (SPT, disturbed, $A_r$ ≈ 110%), Shelby/thin-walled tube, piston sampler (soft clays), Denison (stiff soils), core barrels for rock.

Field tests

• Standard Penetration Test (SPT): 63.5 kg hammer, 750 mm drop; record blows for three 150 mm increments; N = blows for last 300 mm. Corrections for overburden and dilatancy (submerged fine sand if N > 15: $N' = 15 + 0.5(N-15)$).
• Cone penetration test (static/dynamic), plate load test (bearing capacity and settlement), vane shear, pressuremeter, field permeability (pumping) tests.

Site investigation report

Includes introduction and scope, site description and geology, exploration methods, borehole logs, groundwater observations, laboratory and field test results, interpretation of soil profile, recommendations on foundation type, depth, allowable bearing capacity and expected settlement, and special precautions.

Earth pressure theories

• At-rest ($K_0$): no wall movement. Jaky: $K_0 = 1 - \sin\phi$.
• Active ($K_a$): wall moves away from soil; minimum pressure (basement walls that can yield, retaining walls).
• Passive ($K_p$): wall pushed into soil; maximum resistance (anchor blocks, toe of wall).
• Order: $K_a < K_0 < K_p$.

Rankine's theory (smooth vertical wall, horizontal backfill; $K_a$, $K_p$ under Formulas):

• Active pressure at depth $z$: $p_a = K_a\gamma z - 2c\sqrt{K_a}$.
• Resultant (cohesionless): $P_a = \tfrac12 K_a\gamma H^2$ acting at $H/3$ above base.
• Surcharge $q$: adds $K_a q$ uniformly (resultant at $H/2$).
• Submerged backfill: use $\gamma'$ plus full water pressure $\tfrac12\gamma_w H^2$.
• Tension crack depth in cohesive soil: $z_c = \dfrac{2c}{\gamma\sqrt{K_a}}$; unsupported vertical cut height $H_c = 2z_c = \dfrac{4c}{\gamma\sqrt{K_a}}$.

Coulomb's wedge theory: considers wall friction $\delta$, inclined back and sloping backfill; solved graphically by Culmann's or Rebhann's construction.

Stability analysis of retaining walls

Checks (typical minimum FS):

1. Overturning about toe: $FS = \dfrac{\sum M_R}{\sum M_O} \ge 2.0$ (1.5 for some codes).
2. Sliding: $FS = \dfrac{\mu\sum W + P_p}{P_a} \ge 1.5$.
3. Bearing pressure: $q_{max,min} = \dfrac{\sum W}{B}\left(1\pm\dfrac{6e}{B}\right)$ ≤ allowable bearing capacity; resultant within middle third ($e \le B/6$) to avoid tension at heel.
4. Overall (deep-seated) slope stability.

Techniques to increase stability

• Provide shear key below base (sliding), widen base or extend heel (overturning, sliding).
• Weep holes and back drains / filter to relieve water pressure (most failures in monsoon are due to water).
• Use granular backfill, reduce surcharge, add counterforts or buttresses, tie-backs/anchors, soil nailing, reinforced earth.
• Batter the wall face toward the backfill.

High-yield points

• $K_a < K_0 < K_p$; for $\phi = 30^\circ$: 1/3, 0.5 and 3.
• SPT: 63.5 kg hammer, 750 mm drop; N = blows for the last 300 mm.
• Undisturbed sampling needs area ratio ≤ 10%; split spoon ≈ 110%.
• Keep the resultant in the middle third ($e \le B/6$).
• Typical FS: overturning ≈ 2, sliding ≈ 1.5.

Formulas

$K_a = \frac{1-\sin\phi}{1+\sin\phi} = \tan^2\!\left(45^\circ - \frac{\phi}{2}\right),\qquad K_p = \frac{1}{K_a},\qquad K_0 = 1 - \sin\phi$ $P_a = \tfrac12K_a\gamma H^2$ at $H/3$; $z_c = 2c/(\gamma\sqrt{K_a})$.

Worked example

A 6 m smooth vertical wall retains dry sand ($\gamma = 18$ kN/m³, $\phi = 30^\circ$). Find active thrust and its point of action.

• $K_a = (1 - 0.5)/(1 + 0.5) = 1/3$
• $P_a = \tfrac12\times\tfrac13\times18\times6^2 = 108$ kN/m
• Acts at 6/3 = 2 m above base. ($K_p = 3$ would give 972 kN/m if the wall moved into the soil.)

Exam tips

• $K_a < K_0 < K_p$; for $\phi = 30^\circ$: $K_a = 1/3$, $K_0 = 0.5$, $K_p = 3$.
• Active pressure needs only a small movement; passive needs much larger movement.
• Area ratio ≤ 10% for undisturbed samples; split spoon gives disturbed samples.
• SPT N = blows for the last 300 mm of 450 mm penetration.
• Keep resultant within middle third ($e \le B/6$); weep holes reduce hydrostatic pressure.

Exam-style questions

From Calmon's question bank, which has 25 questions on this topic.

1. Compared with Rankine's theory, Coulomb's wedge theory of earth pressure

• A. Is applicable only to cohesive soils
• B. Assumes the back of the wall to be perfectly smooth
• C. Assumes the soil to be in a state of plastic equilibrium throughout
• D. Takes into account the friction between the wall and the backfill

Answer: D. Coulomb considers the equilibrium of a sliding soil wedge and includes the wall friction angle $\delta$, whereas Rankine assumes a smooth wall.

2. A sampling tube has an outside diameter of 50 mm and an inside diameter of 48 mm at the cutting edge. Its area ratio is about

• A. 7.8%
• B. 17.0%
• C. 8.5%
• D. 4.0%

Answer: C. $A_r = \dfrac{D_o^2 - D_i^2}{D_i^2} \times 100 = \dfrac{2500 - 2304}{2304} \times 100 \approx 8.5\%$.

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