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Soil mechanics
Soil mechanics is a branch of SOIL PHYSICS and APPLIED MECHANICS that describes the behavior of SOILS. It differs from fluid mechanics and solid mechanics in the sense that soils consist of a heterogeneous mixture of fluids (usually air and water) and particles (usually CLAY,SILT ,SAND, and GRAVEL) but soil may also contain organic solids and other matter. Along with ROCK MECHANIC’S, soil mechanics provides the theoretical basis for analysis in GEOTECNICAL ENGINEERING & in subdiscipline of CIVIL ENGINEERING,ENGINEERING GEOLOGY, a subdiscipline of GEOLOGY. Soil mechanics is used to analyze the deformations of and flow of fluids within natural and man-made structures that are supported on or made of soil, or structures that are buried in soils.] Example applications are building and bridge foundations, retaining walls, dams, and buried pipeline systems. Principles of soil mechanics are also used in related disciplines such as
Genesis and composition of soils
Soil composition
Soil mineralogy
Grain size distribution
SOIL GRADATIONS[Sieve analysis}
Soil mechanics
Atterberg and shrinkage limits liquid & plastic limits
Objective: To determine the range of water content which exhibits consistency of a given soil sample at liquid limit, plastic limit and shrinkage limit.
Theory: Liquid limit (LL): It is the water content at which a 2 mm wide groove in a soil pat will close for a distance of 12.5mm when dropped 25 times in a standard liquid limit device (casagrade apparatus).
Plastic limit (PL): It is the water content at which a thread of soil just begins to crack and crumble when rolled to a diameter of 3mm.
Shrinkage limit (SL): It is the maximum water content at which no change in volume of the soil mass occurs when the water content is further reduced.
Plasticity index (PI): The plasticity index (PI) is defined as;
PI=LL–PL
Liquidity index (LI): This index is defined as;
LI = (w - PL) / (LL – PL)
Apparatus
Liquid limit device and grooving toolShrinkage limit set consisting of shrinkage dish, glass plate with prongs, mercury and evaporating dishLarge glass plate for plastic limitDistilled waterOvenBalance of 0.01g accuracyDessicatorWater canSpatula, cotton waste, duster and grease Procedure:
Liquid LimitTake about 120g of dry soil passing 425µ IS sieve and mix it thoroughly with distilled water using spatula until the soil mass becomes homogenous paste.
Adjust the liquid limit device with the aid of the gauge on the grooving tool to obtain the fall of cup equal to 1cm above the base. Turn the handle and practice to obtain a speed of 2 blows per second.
Place the soil paste in the cup, level up to a depth of 1cm at the point, which comes in contact with the base. Divide this paste by drawing the grooving tool through the sample along the symmetrical axis of the cup, holding the tool perpendicular to the cup at the point of contact.
Turn the handle at the rate of two revolutions per seconds and count the blows necessary to close the groove in the soil for a distance of 12mm.
Take the sample of the soil paste from near the closed groove and keep in the water can to determine the water content.
Repeat the above process three or four times by adding some distilled water each time. Adjust the amount of water by visual judgment so that two readings are above 25 and two below 25 blows. However, the blows should not be lower than 15 nor greater than 35.
Preserve this soil for shrinkage limit test.
Draw the flow curve, and determine the liquid limit.
Plastic limitTake about 20g of soil passing through the sieve of size 425Pm and place it on a glass plate. Mix it thoroughly with distilled water until it is plastic enough to be rolled.
Roll the soil between the hand and the glass plate so as to form a thread of 3mm diameter.
Knead the soil together and roll again until a 3mm diameter thread shows sign of crumbling.
Take some of the crumbling material obtained in step 3 for water content determination. This defines the plastic limit.
Repeat steps 2 to 4 three times so as to obtain average plastic limit.
Shrinkage Limit
Place about 30g of the soil fraction passing 425Pm IS sieve in a porcelain dish and thoroughly mix it with distilled water. The water should be added to make the soil slightly flowing.
Note: The amount of required water could be about the liquid limit in low plastic (friable) soils; otherwise it could be about 1.1 to 1.2 times the liquid limit in medium to high plastic soils.
Apply a thin coat of grease to the inside of the shrinkage dish and measure its empty weight.
Place the soil paste in the shrinkage dish, simultaneously tapping it so that it fills completely the dish without entrapping any air bubbles. Weigh the dish with soil paste inside.
Keep the dish in the oven set at 105 to 1100C for 24 hours. Take the dry weight of the soil pat.
Determine the volume of the dry soil pat by mercury displacement method *
Determine the volume of the dish by filling it with mercury.
Enter the observation in the record sheet and compute the shrinkage limit
*****Important: Every precaution should be taken while handling mercury (e.g. your finger nails should be trimmed). For detailed safety requirements, you are advised to refer to the web page http://www.ilpi.com/safety/mercury.html
References:
IS 2720 (Part 5): Determination of liquid and plastic limit
IS 2720(Part 6): Determination of shrinkage factors
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Soil mechanics
TYPES OF SOILS
TYPES OF SOILS
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Technical practical’s viva Field Work
Boring – Types of Boring
The types of boring methods commonly adopted for soil exploration are as under :-
(a) Auger boring
(b) Shell and Auger boring
(c) Wash boring
(d) Percussion boring
(e) Rotary boring
(a) Auger boring
SUB SOIL EXPLORATION
The process of collection soil data for the assessment soil properties at a site through series of laboratory and field investigation is collectively called Sub-soil Exploration
Enables the engineers to draw soil profile indicating the sequence of soil strata and the properties of soil involved.
COMMON STAGES IN SITE INVESTIGATION
Desk Study
Site Recognition
Field Investigations
a) Preliminary Ground Investigation
b) Detailed Ground Investigation
Laboratory Testing
Report Writing
Follow up Investigations during design & construction
Appraisal of performance
METHOD OF EXPLORATIONS
1. DIRECT METHOD
2. SEMI DIRECT METHOD
3. INDIRECT METHODS
PURPOSE OF SOIL INVESTIGATION
Site investigation provides first hand information for
• Selection of foundation type.
Design of foundations.
Contractors to quote realistic and competitive tenders.
Planning construction techniques.
Selection of appropriate construction equipment (especially for excavation and foundations).
Feasibility studies of the site.
Estimating development cost for the site.
Study of environmental impacts of the proposed construction.
METHODS OF INVESTIGATION
The methods to determine the sequence, thickness and lateral extent of the soil strata and where appropriate the level of bedrock.
The common methods include
Test pits
Shafts and audits
Boring or drilling
TEST PITS
The excavation of test pits is a simple and reliable method.
The depth is limited to 4-5m only.
The in-situ conditions are examined visually
It is easy to obtain disturbed and undisturbed samples
Block samples can be cut by hand tools and tube samples can be taken from the bottom of the pit.
BORING OR DRILLING
Boring refers to advancing a hole in the ground.
Boring is required for the following
• To obtain representative soil and rock samples for laboratory tests.
• Performance of in-situ tests to assess appropriate soil characteristics. Some of the common types of boring are as follows
• Auger boring
Wash boring
• Rotary drilling
• Core drilling
• Percussion drilling
AUGER BORING
Hand Auger
Mechanical Auger
It is the simplest method of boring used for small projects in soft cohesive soils.
For hard soil and soil containing gravels boring with hand auger becomes difficult.
Hand-auger holes can be made up to about 20m depth, although depth greater than about 8-10m is usually not practical.
In the realm of commercial construction, augers attached to heavy machinery are used to bore holes deep into the ground. Augers attach to foundation drilling rigs, which create drilled shafts in the ground.
HAND AUGER
• The length of the auger blade varies from 0.3-0.5m.
• The auger is rotated until it is full of soil, then it is with drawn to remove the soil and the soil type present at various depths is noted.
Repeated with drawl of auger for soil removal makes boring difficult below 8-10m depth.
• The soil samples collected in this manner are disturbed samples and can be used for classification test.
Auger boring may not be possible in very soft clay or coarse and because the hole tends to collapse when auger is removed
Mechanical Auger
In the realm of commercial construction, augers attached to heavy machinery are used to bore holes deep into the ground. Augers attach to foundation drilling rigs, which create drilled shafts in the ground.
auger, tool (or bit) used with a carpenter's brace for drilling holes in wood. It looks like a corkscrew and has six parts: screw, spurs, cutting edges, twist, shank, and tang
Auger drill bits are sharp points available in sizes ranging from 2 to 18 inches, with intermediate sizes as well. There are also several types of augers. You can get handheld augers, or you can find models that can attach to excavators, cranes, skid steers, or other motorized equipment for bigger jobs
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IMAGES OF DIFFERENT TYPES OF AUGER'S
MORE DETAIL'S WILL BE AVAILABLE IF YOU DEMAND IT OTHERWISE SHORT DESCPIPTIONS WILL BE FOLLOWED BY VIDEO'S & SHORT NOTES ON THIS TOPIC OF AUGER'S
.Bearing capacity
The ultimate load which a foundation can support may be calculated using bearing capacity theory. For preliminary design, presumed bearing values can be used to indicate the pressures which would normally result in an adequate factor of safety. Alternatively, there is a range of empirical methods based on in situ test results.
The ultimate bearing capacity (qf) is the value of bearing stress which causes a sudden catastrophic settlement of the foundation (due to shear failure).
The allowable bearing capacity (qa) is the maximum bearing stress that can be applied to the foundation such that it is safe against instability due to shear failure and the maximum tolerable settlement is not exceeded. The allowable bearing capacity is normally calculated from the ultimate bearing capacity using a factor of safety (Fs).
When excavating for a foundation, the stress at founding level is relieved by the removal of the weight of soil. The net bearing pressure (qn) is the increase in stress on the soil.
qn = q - qo
qo = g D
where D is the founding depth and g is the unit weight of the soil removed.
Failure mechanisms and derivation of equations
A relatively undeformed wedge of soil below the foundation forms an active Rankine zone with angles (45º + f'/2).
The wedge pushes soil outwards, causing passive Rankine zones to form with angles (45º - f'/2).
The transition zones take the form of log spiral fans.
For purely cohesive soils (f = 0) the transition zones become circular for which Prandtl had shown in 1920 that the solution is
qf = (2 + p) su = 5.14 su
This equation is based on a weightless soil. Therefore if the soil is non-cohesive (c=0) the bearing capacity depends on the surcharge qo. For a footing founded at depth D below the surface, the surcharge qo = gD. Normally for a shallow foundation (D<B), the shear strength of the soil between the surface and the founding depth D is neglected.
radius of the fan r = r0 .exp[q.tanf'].
q is the fan angle in radians (between 0 and p/2)
f' is the angle of friction of the soil
ro = B/[2 cos(45+f'/2)]
Upper and lower bound solutions
Failure mechanisms and derivation of equations
The bearing capacity of a soil can be investigated using the limit theorems of ideal rigid-perfectly-plastic materials.
The ultimate load capacity of a footing can be estimated by assuming a failure mechanism and then applying the laws of statics to that mechanism. As the mechanisms considered in an upper bound solution are progressively refined, the calculated collapse load decreases.
As more stress regions are considered in a lower bound solution, the calculated collapse load increases.
Therefore, by progressive refinement of the upper and lower bound solutions, the exact solution can be approached. For example, Terzaghi's mechanism gives the exact solution for a strip footing.
Semi-circular slip mechanism
Failure mechanisms and derivation of equations
Suppose the mechanism is assumed to have a semi-circular slip surface. In this case, failure will cause a rotation about point O. Any surcharge qo will resist rotation, so the net pressure (q - qo) is used. Using the equations of statics:
Moment causing rotation
= load x lever arm
= [(q - qo) x B] x [½B]
Moment resisting rotation
= shear strength x length of arc x lever arm
= [s] x [p.B] x [B]
At failure these are equal:
(q - qo ) x B x ½B = s x p.B x B
Net pressure (q - qo ) at failure
= 2 p x shear strength of the soil
This is an upper-bound solution.
Circular arc slip mechanism
Failure mechanisms and derivation of equations
Consider a slip surface which is an arc in cross section, centred above one edge of the base. Failure will cause a rotation about point O. Any surcharge qo will resist rotation so the net pressure (q - qo) is used. Using the equations of statics:
Moment causing rotation
= load x lever arm
= [ (q - qo) x B ] x [B/2]
Moment resisting rotation
= shear strength x length of arc x lever arm
= [s] x [2a R] x [R]
At failure these are equal:
(q - qo) x B x B/2 = s x 2 a R x R
Since R = B / sin a :
(q - qo ) = s x 4a /(sin a)²
The worst case is when
tana=2a at a = 1.1656 rad = 66.8 deg
The net pressure (q - qo) at failure
= 5.52 x shear strength of soil
Bearing capacity of shallow foundations
The ultimate bearing capacity of a foundation is calculated from an equation that incorporates appropriate soil parameters (e.g. shear strength, unit weight) and details about the size, shape and founding depth of the footing. Terzaghi (1943) stated the ultimate bearing capacity of a strip footing as a three-term expression incorporating the bearing capacity factors: Nc, Nq and Ng, which are related to the angle of friction (f´).
For drained loading, calculations are in terms of effective stresses; f´ is > 0 and N c, Nq and Ng are all > 0.
For undrained loading, calculations are in terms of total stresses; the undrained shear strength (su); Nq = 1.0 and Ng = 0
c = apparent cohesion intercept
qo = g . D (i.e. density x depth)
D = founding depth
B = breadth of foundation
g = unit weight of the soil removed.
Bearing capacity equation (undrained)
Bearing capacity of shallow foundations
Skempton's equation is widely used for undrained clay soils:
qf = su .Ncu + qo
where Ncu = Skempton's bearing capacity factor, which can be obtained from a chart or by using the following expression:
Ncu = Nc.sc.dc
where sc is a shape factor and dc is a depth factor.
Nq = 1, Ng = 0, Nc = 5.14
sc = 1 + 0.2 (B/L) for B<=L
dc = 1+ Ö(0.053 D/B ) for D/B < 4
Bearing capacity equation (drained)
Bearing capacity of shallow foundations
Terzaghi (1943) stated the bearing capacity of a foundation as a three-term expression incorporating the bearing capacity factors
Nc, Nq and Ng.
He proposed the following equation for the ultimate bearing capacity of a long strip footing:
This equation is applicable only for shallow footings carrying vertical non-eccentric loading.
For rectangular and circular foundations, shape factors are introduced.
qf = c .Nc .sc + qo .Nq .sq + ½ g .B .Ng .sg
Other factors can be used to accommodate depth, inclination of loading, eccentricity of loading, inclination of base and ground. Depth is only significant if it exceeds the breadth.
Bearing capacity factors
Bearing capacity equation (drained)
The bearing capacity factors relate to the drained angle of friction (f'). The c.Nc term is the contribution from soil shear strength, the qo.Nq term is the contribution from the surcharge pressure above the founding level, the ½.B.g.Ng term is the contribution from the self weight of the soil. Terzaghi's analysis was based on an active wedge with angles f' rather than (45+f'/2), and his bearing capacity factors are in error, particularly for low values of f'. Commonly used values for Nq and Nc are derived from the Prandtl-Reissner expression giving
Exact values for Ng are not directly obtainable; values have been proposed by Brinch Hansen (1968), which are widely used in Europe, and also by Meyerhof (1963), which have been adopted in North America.
Brinch Hansen:
Ng = 1.8 (Nq - 1) tanf'
Meyerhof:
Ng = (Nq - 1) tan(1.4 f')
Shape factors
Bearing capacity equation (drained)
Terzaghi presented modified versions of his bearing capacity equation for shapes of foundation other than a long strip, and these have since been expressed as shape factors. Brinch Hansen and Vesic (1963) have suggested shape factors which depend on f'. However, modified versions of the Terzaghi factors are usually considered sufficiently accurate for most purposes.
sc
sq
sg
square
1.3
1.2
0.8
circle
1.3
1.2
0.6
rectangle (B<L)
1+ 0.2(B/L)
1+ 0.2(B/L)
1 - 0.4(B/L)
B = breadth, L = length
Depth factors
Bearing capacity equation (drained)
It is usual to assume an increase in bearing capacity when the depth (D) of a foundation is greater than the breadth (B). The general bearing capacity equation can be modified by the inclusion of depth factors.
qf = c.Nc.dc + qo.Nq.dq + ½ B.gNg.dg
for D>B:
dc = 1 + 0.4 arctan(D/B)
dq = 1 + 2 tan(f'(1-sinf')² arctan(B/D)
dg = 1.0
for D=<B:
dc = 1 + 0.4(D/B)
dq = 1 + 2 tan(f'(1-sinf')² (B/D)
dg = 1.0
Factor of safety
Bearing capacity of shallow foundations
A factor of safety Fs is used to calculate the allowable bearing capacity qa from the ultimate bearing pressure qf. The value of Fs is usually taken to be 2.5 - 3.0.
The factor of safety should be applied only to the increase in stress, i.e. the net bearing pressure qn. Calculating qa from qf only satisfies the criterion of safety against shear failure. However, a value for Fs of 2.5 - 3.0 is sufficiently high to empirically limit settlement. It is for this reason that the factors of safety used in foundation design are higher than in other areas of geotechnical design. (For slopes, the factor of safety would typically be 1.3 - 1.4).
Experience has shown that the settlement of a typical foundation on soft clay is likely to be acceptable if a factor of 2.5 is used. Settlements on stiff clay may be quite large even though ultimate bearing capacity is relatively high, and so it may be appropriate to use a factor nearer 3.0.
Presumed bearing values
For preliminary design purposes, BS 8004 gives presumed bearing values which are the pressures which would normally result in an adequate factor of safety against shear failure for particular soil types, but without consideration of settlement.
Category
Types of rocks and soils
Presumed bearing value
Non-cohesive soils
Dense gravel or dense sand and gravel
>600 kN/m²
Medium dense gravel,
or medium dense sand and gravel
<200 to 600 kN/m²
Loose gravel, or loose sand and gravel
<200 kN/m²
Compact sand
>300 kN/m²
Medium dense sand
100 to 300 kN/m²
Loose sand
<100 kN/m² depends on
degree of looseness
Cohesive soils
Very stiff bolder clays & hard clays
300 to 600 kN/m²
Stiff clays
150 to 300 kN/m²
Firm clay
75 to 150 kN/m²
Soft clays and silts
< 75 kN/m²
Very soft clay
Not applicable
Peat
Not applicable
Made ground
Not applicable
Presumed bearing values for Keuper Marl
Weathering
Zone
Description
Presumed bearing value
Fully weathered
IVb
Matrix only
as cohesive soil
Partially weathered
IVa
Matrix with occasional pellets less than 3mm
125 to 250 kN/m²
III
Matrix with lithorelitics up to 25mm
250 to 500 kN/m²
II
Angular blocks of unweathered marl with virtually no matrix
500 to 750 kN/m²
Unweathered
1
Mudstone (often not fissured)
750 to 1000 kN/m²
Bearing capacity of piles
The ultimate bearing capacity of a pile used in design may be one three values:
the maximum load Qmax, at which further penetration occurs without the load increasing;
a calculated value Qf given by the sum of the end-bearing and shaft resistances;
or the load at which a settlement of 0.1 diameter occurs (when Qmax is not clear).
For large-diameter piles, settlement can be large, therefore a safety factor of 2-2.5 is usually used on the working load.
A pile loaded axially will carry the load:
partly by shear stresses (ts) generated along the shaft of the pile and
partly by normal stresses (qb) generated at the base.
The ultimate capacity Qf of a pile is equal to the base capacity Qb plus the shaft capacity Qs.
Qf = Qb + Qs = Ab . qb + S(As . ts)
where Ab is the area of the base and As is the surface area of the shaft within a soil layer.
Full shaft capacity is mobilised at much smaller displacements than those related to full base resistance. This is important when determining the settlement response of a pile. The same overall bearing capacity may be achieved with a variety of combinations of pile diameter and length. However, a long slender pile may be shown to be more efficient than a short stubby pile. Longer piles generate a larger proportion of their full capacity by skin friction and so their full capacity can be mobilised at much lower settlements.
The proportions of capacity contributed by skin friction and end bearing do not just depend on the geometry of the pile. The type of construction and the sequence of soil layers are important factors.
Driven piles in non-cohesive soil
Driving a pile has different effects on the soil surrounding it depending on the relative density of the soil. In loose soils, the soil is compacted, forming a depression in the ground around the pile. In dense soils, any further compaction is small, and the soil is displaced upward causing ground heave. In loose soils, driving is preferable to boring since compaction increases the end-bearing capacity.
In non-cohesive soils, skin friction is low because a low friction 'shell' forms around the pile. Tapered piles overcome this problem since the soil is recompacted on each blow and this gap cannot develop.
Pile capacity can be calculated using soil properties obtained from standard penetration tests or cone penetration tests. The ultimate load must then be divided by a factor of safety to obtain a working load. This factor of safety depends on the maximum tolerable settlement, which in turn depends on both the pile diameter and soil compressibility. For example, a safety factor of 2.5 will usually ensure a pile of diameter less than 600mm in a non-cohesive soil will not settle by more than 15mm.
Although the method of installing a pile has a significant effect on failure load, there are no reliable calculation methods available for quantifying any effect. Judgement is therefore left to the experience of the engineer.
Ultimate pile capacity
Driven piles in non-cohesive soil
The ultimate carrying capacity of a pile is:
Qf = Qb + Qs
The base resistance, Qb can be found from Terzaghi's equation for bearing capacity,
qf = 1.3 c Nc + qo Nq + 0.4 g B Ng
The 0.4 g B Ng term may be ignored, since the diameter is considerably less than the depth of the pile.
The 1.3 c Nc term is zero, since the soil is non-cohesive.
The net unit base resistance is therefore
qnf = qf - qo = qo (Nq -1)
and the net total base resistance is
Qb = qo (Nq -1) Ab
The ultimate unit skin friction (shaft) resistance can be found from
qs = Ks .s'v .tand
where s'v = average vertical effective stress in a given layer
d = angle of wall friction, based on pile material and f´
Ks = earth pressure coefficient
Therefore, the total skin friction resistance is given by the sum of the layer resistances:
Qs = S(Ks .s'v .tand .As)
The self-weight of the pile may be ignored, since the weight of the concrete is almost equal to the weight of the soil displaced.
Therefore, the ultimate pile capacity is:
Qf = Ab qo Nq + S(Ks .s'v .tand .As)
Values of Ks and d can be related to the angle of internal friction (f´) using the following table according to Broms.
Material
d
Ks
low density
high density
steel
20°
0.5
1.0
concrete
3/4 f´
1.0
2.0
timber
2/3 f´
1.5
4.0
It must be noted that, like much of pile design, this is an empirical relationship. Also, from empirical methods it is clear that Qs and Qb both reach peak values somewhere at a depth between 10 and 20 diameters.
It is usually assumed that skin friction never exceeds 110 kN/m² and base resistance will not exceed 11000 kN/m².
Standard penetration test
Driven piles in non-cohesive soil
The standard penetration test is a simple in-situ test in which the N-value is the mumber of blows taken to drive a 50mm diameter bar 300mm into the base of a bore hole.
Schmertmann (1975) has correlated N-values obtained from SPT tests against effective overburden stress as shown in the figure.
The effective overburden stress = the weight of material above the base of the borehole - the wight of water
e.g. depth of soil = 5m, depth of water = 4m, unit weight of soil = 20kN/m³, s'v = 5m x 20kN/m³ - 4m x 9.81kN/m³ » 60 kN/m²
Once a value for f´ has been estimated, bearing capacity factors can be determined and used in the usual way.
Meyerhof (1976) produced correlations between base and frictional resistances and N-values. It is recommended that N-values first be normalised with respect to effective overburden stress:
Normalised N = Nmeasured x 0.77 log(1920/s´v)
Pile type
Soil type
Ultimate base resistance
qb (kPa)
Ultimate shaft resistance
qs (kPa)
Driven
Gravelly sand
Sand
40(L/d) N
but < 400 N
2 Navg
Sandy silt
Silt
20(L/d) N
but < 300 N
Bored
Gravel and sands
13(L/d) N
but < 300 N
Navg
Sandy silt
Silt
13(L/d) N
but < 300 N
L = embedded length
d = shaft diameter
Navg = average value along shaft
Cone penetration test
Driven piles in non-cohesive soil
End-bearing resistance
The end-bearing capacity of the pile is assumed to be equal to the unit cone resistance (qc). However, due to normally occurring variations in measured cone resistance, Van der Veen's averaging method is used:
qb = average cone resistance calculated over a depth equal to three pile diameters above to one pile diameter below the base level of the pile.
Shaft resistance
The skin friction can also be calculated from the cone penetration test from values of local side friction or from the cone resistance value using an empirical relationship:
At a given depth, qs = Sp. qc
where Sp = a coefficient dependent on the type of pile
Type of pile
Sp
Solid timber )
Pre-cast concrete )
Solid steel driven )
0.005 - 0.012
Open-ended steel
0.003 - 0.008
Bored piles in non-cohesive soil
The design process for bored piles in granular soils is essentially the same as that for driven piles. It must be assumed that boring loosens the soil and therefore, however dense the soil, the value of the angle of friction used for calculating Nq values for end bearing and d values for skin friction must be those assumed for loose soil. However, if rotary drilling is carried out under a bentonite slurry f' can be taken as that for the undisturbed soil.
Driven piles in cohesive soil
Driving piles into clays alters the physical characteristics of the soil. In soft clays, driving piles results in an increase in pore water pressure, causing a reduction in effective stress;.a degree of ground heave also occurs. As the pore water pressure dissipates with time and the ground subsides, the effective stress in the soil will increase. The increase in s'v leads to an increase in the bearing capacity of the pile with time. In most cases, 75% of the ultimate bearing capacity is achieved within 30 days of driving.
For piles driven into stiff clays, a little consolidation takes place, the soil cracks and is heaved up. Lateral vibration of the shaft from each blow of the hammer forms an enlarged hole, which can then fill with groundwater or extruded porewater. This, and 'strain softening', which occurs due to the large strains in the clay as the pile is advanced, lead to a considerable reduction in skin friction compared with the undisturbed shear strength (su) of the clay. To account for this in design calculations an adhesion factor, a, is introduced. Values of a can be found from empirical data previously recorded. A maximum value (for stiff clays) of 0.45 is recommended.
The ultimate bearing capacity Qf of a driven pile in cohesive soil can be calculated from:
Qf = Qb + Qs
where the skin friction term is a summation of layer resistances
Qs = S( a .su(avg) .As)
and the end bearing term is
Qb = su .Nc .Ab
Nc = 9.0 for clays and silty clays.
Bored piles in cohesive soil
Following research into bored cast-in-place piles in London clay, calculation of the ultimate bearing capacity for bored piles can be done the same way as for driven piles. The adhesion factor should be taken as 0.45. It is thought that only half the undisturbed shear strength is mobilised by the pile due to the combined effect of swelling, and hence softening, of the clay in the walls of the borehole. Softening results from seepage of water from fissures in the clay and from the un-set concrete, and also from 'work softening' during the boring operation.
The mobilisation of full end-bearing capacity by large-diameter piles requires much larger displacements than are required to mobilise full skin-friction, and therefore safety factors of 2.5 to 3.0 may be required to avoid excessive settlement at working load.
Carrying capacity of piles in layered soil
When a pile extends through a number of different layers of soil with different properties, these have to be taken into account when calculating the ultimate carrying capacity of the pile. The skin friction capacity is calculated by simply summing the amounts of resistance each layer exerts on the pile. The end bearing capacity is calculated just in the layer where the pile toe terminates. If the pile toe terminates in a layer of dense sand or stiff clay overlying a layer of soft clay or loose sand there is a danger of it punching through to the weaker layer. To account for this, Meyerhof's equation is used.
The base resistance at the pile toe is
qp = q2 + (q1 -q2)H / 10B but £ q1
where B is the diameter of the pile, H is the thickness between the base of the pile and the top of the weaker layer, q2 is the ultimate base resistance in the weak layer, q1 is the ultimate base resistance in the strong layer.
Effects of groundwater\
The presence and movement of groundwater affects the carrying capacity of piles, the processes of construction and sometimes the durability of piles in service.
Effect on bearing capacity
In cohesive soils, the permeability is so low that any movement of water is very slow. They do not suffer any reduction in bearing capacity in the presence of groundwater.
In granular soils, the position of the water table is important. Effective stresses in saturated sands can be as much as 50% lower than in dry sand; this affects both the end-bearing and skin-friction capacity of the pile.
Effects on construction
When a concrete cast-in-place pile is being installed and the bottom of the borehole is below the water table, and there is water in the borehole, a 'tremie' is used.
With its lower end lowered to the bottom of the borehole, the tremmie is filled with concrete and then slowly raised, allowing concrete to flow from the bottom. As the tremie is raised during the concreting it must be kept below the surface of the concrete in the pile. Before the tremie is withdrawn completely sufficient concrete should be placed to displace all the free water and watery cement. If a tremie is not used and more than a few centimetres of water lie in the bottom of the borehole, separation of the concrete can take place within the pile, leading to a significant reduction in capacity.
A problem can also arise when boring takes place through clays. Site investigations may show that a pile should terminate in a layer of clay. However, due to natural variations in bed levels, there is a risk of boring extending into underlying strata. Unlike the clay, the underlying beds may be permeable and will probably be under a considerable head of water. The 'tapping' of such aquifers can be the cause of difficulties during construction.
Effects on piles in service
The presence of groundwater may lead to corrosion or deterioration of the pile's fabric.
In the case of steel piles, a mixture of water and air in the soil provides conditions in which oxidation corrosion of steel can occur; the presence of normally occurring salts in groundwater may accelerate the process.
In the case of concrete piles, the presence of salts such as sulphates or chlorides can result in corrosion of reinforcement, with possible consequential bursting of the concrete. Therefore, adequate cover must be provided to the reinforcement, or the reinforcement itself must be protected in some way. Sulphate attack on the cement compounds in concrete may lead to the expansion and subsequent cracking. Corrosion problems are minimised if the concrete has a high cement/aggregate ratio and is well compacted during placement.
.Bearing capacity असर क्षमता
• विफलता तंत्र और समीकरणों की व्युत्पत्ति
• उथली नींव की असर क्षमता
• अनुमानित असर मूल्य
• ढेर की असर क्षमता
अंतिम भार जिसे नींव सहन कर सकती है, असर क्षमता सिद्धांत का उपयोग करके गणना की जा सकती है। प्रारंभिक डिजाइन के लिए, अनुमानित असर मूल्यों का उपयोग उन दबावों को इंगित करने के लिए किया जा सकता है जो सामान्य रूप से सुरक्षा के पर्याप्त कारक के परिणामस्वरूप होंगे। वैकल्पिक रूप से, इन सीटू परीक्षण परिणामों के आधार पर कई अनुभवजन्य विधियाँ हैं।
अंतिम असर क्षमता (qf) असर तनाव का मूल्य है जो नींव के अचानक भयावह निपटान (कतरनी विफलता के कारण) का कारण बनता है।
स्वीकार्य असर क्षमता (qa) अधिकतम असर तनाव है जिसे नींव पर लागू किया जा सकता है ताकि यह कतरनी विफलता के कारण अस्थिरता के खिलाफ सुरक्षित हो और अधिकतम सहनीय निपटान पार न हो। स्वीकार्य असर क्षमता की गणना आम तौर पर सुरक्षा के कारक (Fs) का उपयोग करके अंतिम असर क्षमता से की जाती है।
नींव के लिए खुदाई करते समय, मिट्टी के वजन को हटाने से नींव के स्तर पर तनाव कम हो जाता है। शुद्ध असर दबाव (qn) मिट्टी पर तनाव में वृद्धि है। qn = q - qo qo = D जहाँ D नींव की गहराई है और हटाई गई मिट्टी का इकाई भार है। ________________________________________ विफलता तंत्र और समीकरणों की व्युत्पत्ति असर क्षमता ऊपरी और निचली सीमा समाधान अर्ध-वृत्ताकार फिसलन तंत्र वृत्ताकार चाप फिसलन तंत्र नींव के नीचे मिट्टी की एक अपेक्षाकृत अपरिवर्तित कील (45º + '/2) के कोण के साथ एक सक्रिय रैंकिन क्षेत्र बनाती है। कील मिट्टी को बाहर की ओर धकेलती है, जिससे निष्क्रिय रैंकिन क्षेत्र (45º - '/2) के कोण के साथ बनते हैं। संक्रमण क्षेत्र लॉग सर्पिल पंखे का रूप लेते हैं। पूरी तरह से चिपकने वाली मिट्टी ( = 0) के लिए संक्रमण क्षेत्र गोलाकार हो जाते हैं जिसके लिए प्रांटल ने 1920 में दिखाया था कि इसका हल है
qf = (2 + ) su = 5.14 su
यह समीकरण भारहीन मिट्टी पर आधारित है। इसलिए यदि मिट्टी गैर-चिपकने वाली है (c = 0) तो असर क्षमता अधिभार qo पर निर्भर करती है। सतह के नीचे गहराई D पर स्थापित फ़ुटिंग के लिए, अधिभार qo = है। आम तौर पर उथली नींव (D<B) के लिए, सतह और नींव की गहराई D के बीच मिट्टी की कतरनी ताकत की उपेक्षा की जाती है।
पंखे की त्रिज्या r = r0 .exp[.tan'].
रेडियन में फैन कोण है (0 और /2 के बीच)
' मिट्टी का घर्षण कोण है
ro = B/[2 cos(45+'/2)]
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ऊपरी और निचली सीमा समाधान विफलता तंत्र और समीकरणों की व्युत्पत्ति
आदर्श कठोर-पूर्णतया प्लास्टिक सामग्री के सीमा प्रमेयों का उपयोग करके मिट्टी की वहन क्षमता की जांच की जा सकती है।
किसी विफलता तंत्र को मानकर और फिर उस तंत्र पर स्थैतिकी के नियमों को लागू करके फ़ुटिंग की अंतिम भार क्षमता का अनुमान लगाया जा सकता है। जैसे-जैसे ऊपरी सीमा समाधान में विचार किए गए तंत्रों को उत्तरोत्तर परिष्कृत किया जाता है, गणना की गई पतन भार कम हो जाती है।
जैसे-जैसे निचली सीमा समाधान में अधिक तनाव क्षेत्रों पर विचार किया जाता है, गणना की गई पतन भार बढ़ जाती है।
इसलिए, ऊपरी और निचली सीमा समाधानों के उत्तरोत्तर परिशोधन द्वारा, सटीक समाधान तक पहुँचा जा सकता है। उदाहरण के लिए, टेरज़ागी का तंत्र स्ट्रिप फ़ुटिंग के लिए सटीक समाधान देता है।
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अर्ध-वृत्ताकार फिसलन तंत्र विफलता तंत्र और समीकरणों की व्युत्पत्ति
मान लीजिए कि तंत्र में अर्ध-वृत्ताकार फिसलन सतह है। इस मामले में, विफलता बिंदु O के चारों ओर घूमने का कारण बनेगी। कोई भी अधिभार qo घूर्णन का विरोध करेगा, इसलिए शुद्ध दबाव (q - qo) का उपयोग किया जाता है। स्थैतिकी के समीकरणों का उपयोग करते हुए:
घूर्णन का कारण बनने वाला क्षण
= भार x लीवर आर्म
= [(q - qo) x B] x [½B]
घूर्णन का विरोध करने वाला क्षण
= कतरनी शक्ति x चाप की लंबाई x लीवर आर्म
= [s] x [.B] x [B]
विफलता पर ये बराबर हैं:
(q - qo ) x B x ½B = s x .B x B
विफलता पर शुद्ध दबाव (q - qo )
= 2 x मिट्टी की कतरनी शक्ति
यह एक ऊपरी सीमा समाधान है।
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वृत्ताकार चाप स्लिप तंत्र विफलता तंत्र और समीकरणों की व्युत्पत्ति
एक स्लिप सतह पर विचार करें जो क्रॉस सेक्शन में एक चाप है, जो आधार के एक किनारे के ऊपर केंद्रित है। विफलता बिंदु O के बारे में एक घूर्णन का कारण बनेगी। कोई भी अधिभार qo घूर्णन का विरोध करेगा इसलिए शुद्ध दबाव (q - qo) का उपयोग किया जाता है। स्थैतिकी के समीकरणों का उपयोग करते हुए:
घूर्णन का कारण बनने वाला आघूर्ण
= भार x लीवर आर्म
= [ (q - qo) x B ] x [B/2]
घूर्णन का प्रतिरोध करने वाला आघूर्ण
= कतरनी शक्ति x चाप की लंबाई x लीवर आर्म
= [s] x [2R] x [R]
विफलता पर ये बराबर हैं:
(q - qo) x B x B/2 = s x 2 R x R
चूँकि R = B / sin :
(q - qo ) = s x 4 /(sin )²
सबसे खराब स्थिति तब होती है जब
tan=2 at = 1.1656 rad = 66.8 deg
विफलता पर शुद्ध दबाव (q - qo)
= 5.52 x मिट्टी की कतरनी शक्ति
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उथली नींव की वहन क्षमता वहन क्षमता
• असर क्षमता समीकरण (अनियंत्रित)
• असर क्षमता समीकरण (नियंत्रित)
• सुरक्षा कारक
एक नींव की अंतिम असर क्षमता की गणना एक समीकरण से की जाती है जिसमें उपयुक्त शामिल होता है
Esther Bryce
Founder / Interior designer
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Architect
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