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Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective stress and Capillarity

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay In-place densification of granular soils

Blasting or by Explosives

The range of soil grain sizes suitable for compacting by blasting method is the same as for Vibroflotation. In this method, the compaction is achieved by successive detonations of small explosive charges in saturated soils. Relative densities of 70 to 80 % upto a depth of 20 to 25 m can be achieved.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Blasting or by Explosives Explosive charges (60 % dynamite, 30% special gelatin dynamite, and ammonite are most commonly used) are placed at about 2/3 times the thickness of the stratum to be densified. The spacings of the charges vary from 3 to 8 m. Three to five successive detonations of several spaced charges are usually required to achieve the desired compaction. The shock waves due to blasting cause liquefaction of the saturated sand, followed by densification. Practically no compaction is achieved in the top 1 m and so this zone usually needs recompaction by rollers.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Blasting or by Explosives

The relation for the weight of charge and the sphere of influence for compaction can be given by: W = CR3

Where W = Weight of charge R = Sphere of influence C = Constant (0.0025 for 60 % dynamite) If blasting is used in dry or partially saturated soils, preflooding is desirable. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Compaction by Pounding, Dynamic compaction or High energy impact

 Used for improving surface and near surface zones of soil and fill material whose existing condition is considered marginal or inadequate foundation support…

 The method consists of dropping a heavy weight from a relatively great height; Weights ranging: 2 tons to 15 tons, and drops have ranged from 10 to 30 m. Pounding– Repeated heavy blows

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Dynamic compaction

 Usually, a closely spaced grid pattern is selected for the pounding locations, and the multiple poundings are required at each drop location (typically 5 to 10 drops).

 Can densify loose cohesion-less soils, fracture and densify buried building rubble such as that which exists at old building sites, consolidate fine grained soils, and compact buried garbage fills.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay  The pounding creates a depression at each drop location and also produces an areal settlement.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Water table

Air in irregular spaces between soil particles

Water surrounding particles and at points of contact between particles, and filling small void spaces

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay A soil can be visualized as a skeleton of solid particles enclosing continuous voids which contain water and / or air.

The volume of the soil skeleton as a whole can change due to rearrangement of the soil particles into new positions, mainly by rolling and sliding, with a corresponding change in the forces acting between the particles.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay  In a fully saturated soil, since water is considered to be incompressible, a reduction in volume is possible only if some of the water can escape from the voids.

 In a dry or a partially saturated soil a reduction in volume is always possible due to compression of the air in the voids, provided there is a scope for particle rearrangement.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Vertical subsurface stress resulting from the soil mass

Ground surface z σv γt = unit weight of soil, homogeneous from ground surface to depth z Unit area σv = γt z

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Pore pressure  Pore water pressure (PWP) is the pressure in the water in the void spaces or pores which exist between and around the mineral grains. • u = pore pressure pore water u grains u u u u

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Pore pressure

 Pore water pressure under no flow conditions is given by the hydrostatic pressure.

ground surface

u = γw h WT

pore water h

grains

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Pore Water Pressure As the name implies, is the pressure which exists in the water which is present in the pores of the soil. The soil pores are normally interconnected and they may be visualized as being a highly intricate and complex collection of irregular tubes.

z

γw z

Soil having interconnected voids which are similar to irregular tubes… Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective stress principle (Karl Terzaghi in 1936)

Valid only for Saturated soils

Effective stress σ´ , at a point in a soil mass is equal to the total stress σ, at that point minus the pore water pressure u, at that location. σ ′ = σ − uw Both total stress σ and pore water pressure u are physically meaningful parameters; stresses that can actually be measured in the field.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Terzaghi’s Effective Stress Principle

• Terzaghi (1936) proposed the relationship for effective stress.

• “All measurable effects of a change of stress, such as compression, distortion, and a change of shearing resistance are due to changes in effective stress”. • Certain aspect of the engineering behaviour of soil, especially, compression and shear strength are functions of effective stress.

First important equation in Geotechnical Engineering… Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Nature of effective stress

Effective stress σ´, by definition, can be determined only by arithmetic manipulation: σ - uw

Unlike σ and uw, σ´ is thus not a physical parameter. It is thus only a mathematical concept but obviously a useful parameter since it has empirically been observed to be the determinant of the engineering behaviour of soil.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective stress concept through an idealized saturated soil element under stress σ A grains σ

A′′ A′′ ’′ ′ A A F′ uw A Pore water w Ac An idealized saturated soil element in equilibrium A′′A′′ is stretched view of plane A′A′ • Wavy plane A´A´ passes through particle to particle points – almost entire plane passes through pore water Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective stress concept through an idealized saturated soil element under stress A σ Since the soil element is in equilibrium the algebraic ′′ A′′ sum of the forces must be A equal to zero. F′ uw

Aw Ac σA The total stress on account of overburden, σ, multiplied by the area of plane A

uwAw The pore water pressure multiplied by the area of the plane which passes through pore water Aw F´ The summation of forces which act at particle to particle contacts through which the plane passes. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective Stress Effective stress is not • Applying laws of statics to the stress at particle to soil element in equilibrium particle contact. Stress at particle • Ac + Aw = A contact is a physical • σA = F′ + uw (Aw) stress equal to F′/(Ac) • σ = (F′/A) + [uw (A-Ac)/A] Where a = contact area • σ = σ′ + (1-A /A) u c w between particles per unit • σ = σ′ + (1-a) uw gross area of the soil. In granular materials a → 0, σ ′ = σ − u [After Lambe and Whitman, 1969] w Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective stress concept At point O

σ = γh1 + γ sat h2

Point O a) Gross area A uw = γ wh2 Area of contact b) soil solid Total Area of contact soil solid = A σ ′ = γh1 + γ subh2 c c)

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective stress is sometimes used interchangeably with intergranular stress. Although the terms are approximately same, there is some difference.

Total vertical force F at the level of O is the sum of the following forces:

1)Forces carried by soil solids at their point of contact Fs

Fs = F1(v) + F2(v) + F3(v)+…. Vertical components of F1, F2,..

2)Force carried by water Fw = uw(A-Ac) 3)Electrical attractive force between solid particles

at the level of O, FA 4) Electrical repulsive force between solid particles

at the level of O, FR

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective stress concept

Total Vertical force F = Fs+ Fw - FA+ FR

 A  σ = σ + u 1− c  − A′ + R′ ig w  A 

σ = σ ig + uw (1− a)− A′ + R′

Where σig = intergranular stress; a = Ac/A ; A´ = Electrical attractive force per unit area of cross-section of soil; R´ = Electrical repulsive force per unit area of cross-section of soil.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Intergranular Stress

Hence

σ ig = σ − uw (1− a)+ A′ − R′

The value of a is very small in the working stress range.. a 0

σ ig = σ − uw + A′ − R′

 For granular soils, silts, and clays of low plasticity, the magnitudes of A´ and R´ are small; For all practical purposes, the intergranular stress becomes:

σ ig ≈ σ − uw

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Intergranular Stress

In highly plastic and dispersed clays, A´ - R´ is large, such situations: σ ig ≠ σ − uw

 In clay soils mineral crystals are not in direct contact since they are surrounded by adsorbed layers of water. clay platelets  It is assumed that inter- granular forces can be adsorbed water transmitted through the adsorbed water.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective stress in a partially saturated soil

Partially saturated soils exist in a three phase state. The water in the voids is not continuous. Pore air occupies considerable volume in the system. Total stress at any point = (effective stress + pore air + pore water pressure) pore air

solid particle pore water

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective stress in partially saturated soil • According to Bishop (1960), ´ • σ = σ + ua – Ψ (ua – uw) • Ψ is the fraction of unit cross sectional area of soil occupied by water.

• For Dry soil Ψ = 0 (Sr = 0)

• For Saturated soil Ψ = 1 (Sr = 100%)

• For intermediate values of Sr , Ψ is read from chart.

Bishop (1960) determined the nature of the variation of ψ

with Sr for several soils, based on their triaxial tests for unsaturated soil specimens.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective stress in partially saturated soil

1

0.8

0.6 ψ 0.4

0.2

0 0 20 40 60 80 100 Degree of saturation (%)

Redrawn after Bishop (1960) Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effect of fluctuations of water table on effective stress

2 2 Ground h1 surface 1 1

h Saturated soil

σv σv´

1 – 1 Initial water location (at ground surface) 2 – 2 Water level (during rain) - Water level rise

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effect of fluctuations of water table on effective stress 1 – 1 Initial water level 2 – 2 water level location location (before rain) (during rain)

σ v = γ sat h σ v = γ sat h + γ wh1 = γ + uw = γ wh uw w (h1 h) σ ′ = γ σ v′ = γ subh v subh The rise of water level above ground surface increased both uw and σ by the same amount, and consequently effective stress remains unchanged.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effect of fluctuations of water table on effective stress Ground 1 1 surface

h1 2 γ h d 2

Saturated soil

σv σv´

1 – 1 Initial water location (at ground surface) 2 – 2 Water level (after rain) – water table depletion

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effect of fluctuations of water table on effective stress 2 – 2 water level location 1 – 1 Initial water level location (before rain) (after rain)

σ v = γ sat h σ v = γ d h1 + γ sat (h − h1) = γ − uw = γ wh uw w (h h1) σ ′ > γ h σ v′ = γ subh v sub Sudden depletion of water table causes increase in effective stress  could lead to crushing of grains settlement of structure.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effect of fluctuations of water table on effective stress

1) With a shift in the water table there is a change in the distribution of PWP with depth. (occurs over a finite time interval)

2) Time interval is long in soils like clays in which water flows slowly and almost instantaneous in soils like sand in which water flows very fast.

3) When PWP are adjusting to the new location of GWT, the condition of water can be described as being TRANSIENT HYDRODYNAMIC. ---After achieving equilibrium condition changes to hydrostatic.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effect of fluctuations of water table on effective stress

The effect of fluctuation of water table on the distribution of effective stress with depth can be summarized as follows: For water table below ground surface, a rise of water table causes a reduction in the effective stress and a fall in the water table produces an increase in effective stress.

For water table above ground surface, a fluctuation in the exposed water level does not alter the effective stress in the soil.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effect of fluctuations of water table on effective stress Let us consider some facts noted each year during monsoon through personal observation or news paper reports: -During monsoon the GWT is known to rise and hence effective stress reduces.  so does shear strength. When shear strength reduces below the magnitude of shear stresses in soil slides /collapses occur.

Increase in σ occurs instantaneously whereas an increase in effective stress is not instantaneous, since particle adjustment and readjustment is not instantaneous.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Example 1 Plot the variation of total and effective vertical stresses, and pore water pressure with depth for the soil profile shown below.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Solution for problem 1 At 10 m depth, σv = (4)(17.8) + (2)(18.5) + (4)(19.5) = 186.2 kPa u = (6)(9.81) = 58.9 kPa

σv’ = 186.2 – 58.9 = 127.3 kPa

Variation of σv, u, σ′v with depth 

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Neutral stress Void ratio changes lead balls from e0 to e1. e0 to e1, produces a Surface before σ change in other placing lead balls mechanical properties of soil. Surface after For this reason it is soil placing lead balls called ‘effective stress’.

Only effective stresses can induce changes in volume in a soil mass and can produce frictional resistance. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Neutral stress WT • The increase in pressure due to the weight of water does not have a h w hw= σ/γw measurable influence on the void ratio or any other mechanical property.

• Therefore, the pressure Sat. soil produced by water is also called as Neutral Pressure • or Neutral stress. Neutral stresses can not by themselves cause volume change or produce frictional resistance. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillarity

Ground Water Table ( or Phreatic surface) is the level to which underground water will rise in an observation well, pit or other open excavation into the earth.  In addition, Every soil in the field is completely saturated up to some height above the water table and partially up to some more height. This is attributed to the phenomenon of CAPILLARITY in soils.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillarity

Capillarity arises from a fluid property known as surface tension, which is a phenomenon that occurs at the interface between different materials.

For soils: Surface of water, mineral grains and air

DEFINITION of Surface tension: Caused by each portion of the liquid surface exerting tension (due to molecular attraction) on adjacent portions of the surface or on objects that are in contact with the liquid surface.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillary rise

The phenomenon in which water rises above the GWT against the pull of gravity but is in contact with the water table as its source is referred to as CAPILLARY RISE.

Water is sucked up into the pores of the soil in this zone on account of the surface tension of water, a manifestation referred to as the Capillary phenomenon.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillary water system Zone of capillary saturation: Closest to GWT Zone of partial saturation: Above the zone of saturation is the zone of capillary saturation and above is the zone of partial capillary saturation. In this zone water is connected through the smaller pores, but more of the larger pores are filled with air. Zone of contact water:

The water in this zone surrounds the points of contact between soil particles and also surrounds soil particles, but is disconnected through pores.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillarity

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillary Rise

DEFINITION: A rise in a liquid above the level of zero pressure due to a net upward force produced by the attraction of the water molecules to a solid surface, e.g. glass, soil (for those cases where the adhesion of the liquid to the solid is greater than the cohesion of the liquid to itself)

Immersing a glass tube of small diameter into a vessel containing water. Rise of water in tube = f (d of tube and cleanliness of its inner surface).

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillary rise

hc

It is reasonable to assume that pore spaces between soil particles of various diameters, behaves in much the same manner as that of a capillary tube.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillary rise

In soils, shapes of void spaces between solid particles are unlike those in capillary tubes. The voids are of irregular and varying shape and size, and interconnected in all directions. ⇒ Hence, accurate prediction of the height of capillary rise in soil is next to impossible.

However, the features of capillarity rise in tubes are applicable to soils as they facilitate an understanding of factors affecting capillarity.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Microscopic view of soil

The tube containing water exhibits positive capillary rise, where the water adheres to the sides of the tube causing the fluid to rise slightly.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillary pressure F T o⋅π ⋅d⋅cos(α) F ( ) To F π ⋅d⋅T o⋅cos α α α u c A  2   π ⋅d  d  4 

4⋅T o⋅cos(α) u c d

For chemically clean glass tube α = 0

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillarity and soil water energy

Soil water exists in small spaces in soil as a film around soil particles.

The small pores can act as capillaries. A capillary is a very thin tube in which a liquid can move against the force of gravity.

Water is attracted to the glass tube by adhesion so a thin film flows up the side of the tube, while cohesion drags more water along.

The liquid rises to the point where gravity balances the adhesive and cohesive forces. The narrower the tube the higher the water column can rise.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillary rise hc ∑ F v F − W y F F W

π 2 hc T o⋅π ⋅d ⋅d ⋅h c⋅γ w 4

W At equilibrium hc is at a maximum, therefore Solving for hcmax yields:

4⋅T o −0.3 h cmax d⋅γ w d⋅γ w

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Pore size d Capillary rise hc

hc1 hc2 hc3 hc4 Height of capillary rise is a function of diameter of capillary tube. D 10 For soils d 5

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillarity and Soil water energy ● Surface tension: the greater attraction of water molecules for each other than the air above at liquid-air interfaces primarily due to cohesion.

● Adhesion and surface tension together cause the phenomenon called capillarity--the movement of water up a wick made of hydrophilic solid materials.

● Capillary movement takes place in any direction.

● The height of capillary rise in a tube is directly proportional to the liquid's surface tension and adhesion to the solid surface, but inversely proportional to the tube radius and the density of the liquid. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillary rise

4TCosα hc = γ wd

This estimate may be improved to allow for the effect of grading and grain shape characteristics, such as irregularity and flakiness:

C hc = eD10

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillary rise hc

Rough approximation to maximum height hc to which water can rise by capillarity in a given soil is:

Where C = constant (0.1 – 0.5 cm2) C f( grain shape, surface impurities) hc = eD10 e = void ratio

Capillary action holds soil water in small pores against the force of gravity. The smaller the pores, the greater the movement can be.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillary rise in soil

Soil Type D10 Size Capillary Head (mm) (cm) Coarse Gravel 0.82 6 Fine Gravel 0.3 20 Silty Gravel 0.06 68 Medium Sand 0.02 120 Silt 0.006 180 Clay < 2 mm Meters

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Approximate relationship between capillary rise and soil type

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Relationship between grain size of uniform quartz powder and height of capillary rise

hc is greatest for fine grained soils, but rate of rise is slow because of their low permeability.

Maximum for silts and very fine sand size particles After Atterberg (1908)

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillarity

• Coarse grained soils are only partially saturated even at ground surface elevations close to the u=0 dry soil water level, whereas fine -u grained soils may be WT saturated for a u

saturated zone above water table saturated considerable distance soil above it. u = γwhw

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillary rise in soil (stress profile)

-hcγw

hc

uc hcγw

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Capillary rise in soil

Surface Tension air/water surface Interface u Sr

Discontinuous Water

Capillary Fringe -hcγw

hc Capillary Saturation

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Effective Stresses Due to Capillarity

In the capillary zone: σ′ = σ - (-uc) = σ + uc

Ground surface. σT u σ´

γdry γdry -hcγw

γsat - γw γsat

γw

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Angle of repose

• Dry unconsolidated grains will form a pile with a slope angle determined by the angle of repose. • • The angle of repose is the steepest angle at which a pile of unconsolidated grains remains stable, and is controlled by the frictional contact between the grains. •  In general, for dry materials the angle of repose increases with increasing grain size, but usually lies between about 30 and 37o.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Angle of repose

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay The role of water

Think about building a sand castle on the beach. If the sand is totally dry, it is impossible to build a pile of sand with a steep face like a castle wall.

If the sand is somewhat wet, however, one can build a vertical wall.

If the sand is too wet, then it flows like a fluid and cannot remain in position as a wall.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay The role of water

Slightly wet unconsolidated materials exhibit a very high angle of repose because surface tension between the water and the solid grains tends to hold the grains in place.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay The role of water

When the material becomes saturated with water, the angle of repose is reduced to very small values and the material tends to flow like a fluid. This is because the water gets between the grains and eliminates grain to grain frictional contact.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay The role of water (clays)

Soils containing smectites or montmorillonites expand when they become wet as water enters the crystal structure and increases the volume of the mineral. When such clays dry out, the loss of water causes the volume to decrease and the clays to shrink or compact (This process is referred to as hydrocompaction).

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Physical examples of capillarity phenomena Poor Poor Good strength strength strength Absence of capillary pressure

Capillary zone

GWT Confining pressure results from the columns of water hanging on the different menisci at the surface of the beach.  RD is more or less same only change is the presence of capillary moisture or its absence.  When sea water breaks capillary menisci gets washed off and temporarily induced shear strength is lost. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Physical examples of capillarity phenomena

Two soil grains held together by a capillary film. 

 Bulking structure in sand is due to capillary action.

Strength gain in a granular soil due to partial saturation and surface tension is termed as apparent cohesion.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Example 2

A 3.5m thick silt layer underlain by a 3m thick clay layer is shown in Figure. Calculate the total stress, pore water pressure, and effective stress at points A, B, C, D, and E. The water table is located 2.5 m below the ground surface. The capillary rise in the silt layer is 1.5m. Assume that the silt layer has a degree of saturation Sr = 60% in the zone of capillary rise.

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Solution for problem 2 After Helwany (2007)

= - 0.6 x 1.5 x 9.81 = -8.82 kPa

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay