Kuliah PSB 09-1

Sipil Itenas 2013 –

SI-224PERANCANGAN STRUKTUR BAWAH

DOSEN:Dr. techn. INDRA NOER HAMDHAN, ST., MT.

JURUSAN TEKNIK SIPILINSTITUT TEKNOLOGI NASIONALBANDUNG 2013

Shallow Foundation


Shallow FoundationsShallow Foundations vs Deep Foundations


Shallow FoundationsShallow Foundations vs Deep Foundations

Shallow foundation:A type of foundation that is used when

the earth directly beneath a structure has sufficient bearing capacity to sustain

the loads from the structure

Deep foundation:A type of foundation that is used when the soil near the ground surface is weak.


Shallow FoundationsShallow Foundations vs Deep FoundationsShallow foundation: Deep foundation:

1) Light, flexible structure: older residential construction, residential construction which include a basement, and in many commercial structures,

1) Heavy, rigid structure: other uncommon building, such as large bridge, tower, and the empire state building.

2) Nice soil condition: hard, uniform soil.

2) Poor soil condition: liquefaction, soft clay and sands.

3) Cheaper than deep foundation 3) Typically more expansive4) Easier construction 4) More complex to construct and

more time than shallow foundation.5) Typically types: spreading

footing foundation, slab-on-grade foundation, pad foundation, strip foundation, and raft foundation.

5) Typically types: battered piles, bearing piles, caissons, and friction piles.


Shallow Foundations

Pondasi telapak (spread footing)Pondasi telapak

Pondasi batukali


Introductions

Two main characteristics:1) The foundations have to be safe against overall

shear failure in the soil that supports them.2) The foundations cannot undergo excessive

displacement or settlement

The load per unit area of the foundations at which shear failure in soil occurs is called the ultimate bearing capacity.

Shallow Foundations


Ultimate Bearing Capacity

General concepts:1) A strip foundation with a width of B resting on the surface of

a dense sand or stiff cohesive soil.

If a load gradually applied to the foundations, settlement will increase.

At a certain point – when the load per unit are equals qu – a sudden failure in the soil supporting the foundation will take place, and the failure surface in the surface in the soil will extend to the ground surface.

The load per unit are, qu, is usually referred to as the ultimate bearing capacity of the foundation. When such sudden failure in soil takes place, it is called general shear failure.

Shallow Foundations



2) If the foundation under consideration rests on sand or clayey soil of medium compaction, an increase in the load foundation will also be accompanied by an increase in settlement.

The failure surface in the soil will gradually extend outward from the foundation. When the load per unit area on the foundation equal qu(1), movement of the foundation will be accompanied by sudden jerks.

A considerable movement of the foundation is then required for the failure surface in soil to extend to the ground surface. The load per nit area at which this happens is the ultimate bearing capacity, qu.

Shallow Foundations



Beyond that point, an increase in load will accompanied by a large increase in foundation settlement. The load per unit area of the foundation, qu(1), is referred to as the first failure load. A peak value of q is not realized in this type of failure, which is called the local shear failure in soil.

3) If the foundation supported by a fairly loose soil, the failure surface in soil will not extend to the ground surface.Beyond the ultimate failure load, qu, the load-settlement plot will be steep and practically linear.

This type of failure in soil is called the punching shear failure.

Shallow Foundations



Vesic (1973) proposed a relationship for the mode of bearing capacity failure of foundations resting on sands.

For square foundations, B=L; for circular foundations, B = L = diameter, so B* = B Modes of foundation failure in sand.

Shallow Foundations


Terzaghi’s Bearing Capacity Theory

Terzaghi (1943) was the first to present a comprehensive theory for the evaluation of the ultimate bearing capacity of rough shallow foundation.

Terzaghi suggested that for a continuous or strip foundation, the failure surface in soil at ultimate load may be assumed: general shear failure.

Bearing capacity failure in soil under a rough rigid continuous foundations.

Shallow Foundations



The failure zone under the foundation can be separated into three parts:

1) The triangular zone ACD immediately under the foundation.2) The radial shear zones ADF and CDE, with the curves DE and

DF being arcs of a logarithmic spiral.3) Two triangular Rankine passive zones AFH and CEG.

The angles CAD and ACD are assumed to be equal to the soil friction angle f’. With the replacement of the soil above the bottom of the foundation by an equivalend surcharge q, the shear resistance of the soil along the failure surfaces GI and HJ was neglected.

Shallow Foundations



Using equilibrium analysis, Terzaghi expressed the ultimate bearing capacity in the form:

B = width/diameter of foundation.

Assumed: general shear failure

Shallow Foundations



Terzaghi’s bearing capacity factor:

Shallow Foundations



For foundations that exhibit the local shear failure mode in soils, Terzaghi suggested the following modification:

Nc’, Nq’ and N’, the modified bearing capacity factors, can be calculated by using the bearing capacity equations (for Nc, Nq, and N, respectively) by replacing ’ by ’ = tan-1 (⅔ tan ’)

Shallow Foundations



Terzaghi’s modified bearing capacity factor:

Shallow Foundations


Factor of Safety (FS)

Calculating the gross allowable load bearing capacity of shallow foundation requires the application of a factor of safety (FS) to the gross ultimate bearing capacity, or:

The net ultimate bearing capacity is defined as the ultimate pressure per unit are of the foundation that can be supported by the soil in excess of the pressure cause by the surrounding soil at the foundation level.

So,

Shallow Foundations



Example #1A square foundation is 1.5 m x 1.5 m in plan. The soil supporting the foundation has a friction angle ’=20o, and c’ = 15.2 KPa. The unit weigh of soil, , is 17.8 KN/m3. Determine the allowable gross load on the foundation with a factor of safety (FS) of 4. Assume that the depth of the foundation (Df) is 1 meter and that general shear failure occurs in soil.

Answer:

From table:

Allowable gross load:

Shallow Foundations



Example #2Repeat example #1, asssuming that local shear failure occurs in the soil supporting the foundation.

Answer:

From table:

Allowable gross load:

Shallow Foundations


Modification of Bearing Capacity Equations for Water TableIf the water table is close to the foundation, some modification of the bearing capacity equations will be necessary:

Case I: If the water table is located so that 0 ≤ D1 ≤ Df, the factor q in the bearing capacity equations take the form:

The value of in the last term of the equations has to be replaced by ’Case II: If the water table is located so that 0 ≤ d ≤ B:

The value of in the last term of the equations has to be replaced by where

Case III: If the water table is located so that d ≥ B, the water will no effect on the ultimate bearing capacity.

Shallow Foundations


Meyerhof’s Bearing Capacity Theory

Meyerhof (1963) suggested the following form of the general bearing capacity equation:

for the case of rectangular foundation (0 < B/L < 1) and account the shearing resistance along the failure surface in soil above the bottom the foundation.

Where:

Shallow Foundations


Meyerhof’s Bearing Capacity TheoryShallow Foundations



Nq Nc N

0 1 5.14 0.00

1 1.09 5.38 0.00

2 1.20 5.63 0.01

3 1.31 5.90 0.02

4 1.43 6.19 0.04

5 1.57 6.49 0.07

6 1.72 6.81 0.11

7 1.88 7.16 0.15

8 2.06 7.53 0.21

9 2.25 7.92 0.28

10 2.47 8.34 0.37

11 2.71 8.80 0.47

12 2.97 9.28 0.60

13 3.26 9.81 0.74

14 3.59 10.37 0.92

15 3.94 10.98 1.13

Nq Nc N

16 4.34 11.63 1.37

17 4.77 12.34 1.66

18 5.26 13.10 2.00

19 5.80 13.93 2.40

20 6.40 14.83 2.87

21 7.07 15.81 3.42

22 7.82 16.88 4.07

23 8.66 18.05 4.82

24 9.60 19.32 5.72

25 10.66 20.72 6.77

26 11.85 22.25 8.00

27 13.20 23.94 9.46

28 14.72 25.80 11.19

29 16.44 27.86 13.24

30 18.40 30.14 15.67

Shallow Foundations



Example #3A square foundation has to carry a gross allowable total mass of 15.290 kg. The depth of foundation is 0.7m. The load is inclined at an angle of 20o to vertical. Determine the width of the foundation, B. Use Meyerhof’s Bearing Capacity theory and a factor of safety of 3.Answer: From table:

Nc = 30.14, Nq = 18.40, N = 15.67

q = Df = 18 * 0.7 = 12.6 kN/m2

Fqs = Fs = 1+0.1 (B/L) tan2 (45+’/2)

Shallow Foundations


Eccentrically Loaded Foundations

In several cases, foundation are subjected to moments in addition to the vertical load.

The nominal distribution of pressure:

Where:Q = total vertical loadM = moment on the foundation

Shallow Foundations



The distance: is the eccentricity. So:

When the eccentricity e becomes B/6, qmin is zero. For e > B/6, qminwill be negative, which means that tension will develop. Because soil cannot take any tension, there will then be a separation between the foundation and the soil underlying it.

The value of qmax:

Shallow Foundations



The factor of safety for such types of loading against bearing capacity failure can be evaluated by using the procedure suggested by Meyerhoff (1953), which is generally referred to as the effective area method.The following is Meyerhof’s step-by-step procedure for determining the ultimate load that soil can support and the factor of safety against bearing capacity failure:

1) Determine the effective dimensions of the foundation:B’ = effective width = B – 2eL’ = effective length = L(if the eccentricity were in the direction of the length of the foundation, the value of L’ = L – 2e and B’ = B.

Shallow Foundations



2) The ultimate bearing capacity:

To evaluate of shape factor with effective length and effective width dimension instead of L and B, respectively. To determine depth factor do not replace B with B’.

3) The total ultimate load that the foundation can sustain is:

4) The factor of safety against bearing capacity failure is:

5) Check the factor of safety againts qmax or FS = qu’/qmax

Shallow Foundations



Example #4A continuous foundation is shown in figure. If the load eccentricity is 0.5ft, determine the ultimate load, Qult per unit length of the foundationAnswer:

AND THEN ….?

Shallow Foundations



Example #5

A square foundation is shown in figure. Q = 10 ton and M= 1 ton m. Use FS = 4 and determine the size of the footing.Use bearing capacity, shape, and depth factors from Meyerhof.

Answer:

1 m

B

= 1.6 t/m3

sat = 1.8 t/m3

Q

M

Shallow Foundations


Vertical Stress Increase in A Soil Mass

Stress Due To A Concentrated LoadIn 1885, Boussinesq developed the mathematical relationships for determining the normal and shear stress at any point inside homogeneus, elastic, and isotropic medium due to a concentrated load located at the surface.

Shallow Foundations



Stress Due To A Circularly Loaded AreaBoussinesq’s equation can also be used to determine the vertical stress below the centre of a flexible circularly loaded area. Let the radius of the loaded area B/2, and let qo be the uniformly distributed load per unit area.

Shallow Foundations



Stress Below A Rectangular Area

The integration technique of Boussinesq’s equation also allows the vertical stress at any point below the corner of a flexible rectangular load area to be evaluated.

Shallow Foundations



Stress Below A Rectangular Area ( 2 : 1 Method)Based on assumption that the stress from the foundation spreads out along lines with a vertical-to-horizontal slope of 2 : 1.

Shallow Foundations



Stress Increase Under An EmbankmentFigure shows the cross section of an embankment of height H. For this two dimensional loading condition, the vertical stress increase may be expressed as:

Shallow Foundations



ExerciseFind average increase in pressure (av) at clay layer caused by load of foundation.

Shallow Foundations


Elastic Settlement

Elastic Settlement Based on The Theory of ElasticityThe elastic settlement of a shallow foundation can be estimated by using the theory of elasticity. From Hook’s law:

Where:

Shallow Foundations


Elastic Settlement

Elastic Settlement Based on The Theory of ElasticityTheoretically, if the foundation is perfectly flexible, the settlement may be expressed as:

Where:

Shallow Foundations


Elastic SettlementElastic Settlement Based on The Theory of Elasticity

Center of foundation:

Corner of foundation:

Shallow Foundations


Elastic SettlementElastic Settlement Based on The Theory of ElasticityDue to the nonhomogeneous nature of soil deposits, the magnitude of Es may vary with depth. For that reason, Bowles (1987) recommended using a weighted average of Es:

Shallow Foundations


Elastic Settlement

Elastic Settlement Based on The Theory of ElasticityExample #6

Answers:

Shallow Foundations


Elastic Settlement

Elastic Settlement Based on The Theory of ElasticityExample #6

Shallow Foundations


Primary Consolidation SettlementConsolidation settlement occurs over time in saturated clayey soils subjected to an increased load caused by construction of the foundation.On the basis of the one-dimensional consolidation settlement equations:

Shallow Foundations


Primary Consolidation Settlement

Shallow Foundations


Primary Consolidation SettlementNote that the increase in effective pressure, ’, on the clay layer is not constant with depth. The magnitude of ’ will decrease with the increase in depth measured from the bottom of the foundation. The average increase may be approximated by:

Where t’, m’, and b’ are respectively, the effective pressure increases at the up, middle, and bottom of the clay layer that are caused by the construction of the foundation.

Shallow Foundations


Primary Consolidation Settlement

Example #7

Shallow Foundations


Primary Consolidation SettlementExample #7

Shallow Foundations


Bearing Capacity Based On SPT DataDikembangkan oleh Terzaghi & Peck (1967) dan Meyerhof (1974). Kemudian Bowles (1982) menganjurkan kenaikan 50% dari kapasitas daya dukung izin yang dianjurkan Meyerhof.

Shallow Foundations

qall = kapasitas daya ukung ijin (kPa).Kd = faktor kedalaman = 1 + 0.33 Df/BB = lebar fundasiF = faktor koreksi (berperan sebagai faktor keamanan).N = nilai NSPT rata-rata yang sudah dikoreksi


Bearing Capacity Based On SPT DataFaktor Koreksi (F):

Shallow Foundations

Harga Ni untuk i = 55, 60, dan 70 adalah jumlah tumbukan yang telah dikoreksi berdasarkan perbandingan energi standard.


Shallow FoundationsKoreksi NSPT:

Catatan: Ein yang umum digunakan di Indonesia adalah koreksi Seed yaitu 60%

N160 = N standard = NSPT CN CB CR CS


B x B

Df

Bearing Capacity Based On SPT DataNilai NSPT Rata-Rata: nilai rata-rata (secara statistik) antara 0.5 Df di atas dasar fundasi sampai dengan 2B di bawah dasar fundasi.

Shallow Foundations

0.5Df

2B

Nilai NSPT Rata-Rata


Bearing Capacity Based On CPT DataDikembangkan oleh Schmertmann (1978) untuk Df/B ≤ 1.5:

Shallow Foundations


B x B

Df

Bearing Capacity Based On CPT DataNilai qc Rata-Rata: nilai rata-rata antara 0.5 B di atas dasar fundasi sampai dengan 1.1B di bawah dasar fundasi.

Shallow Foundations

0.5B

1.1B

Nilai qc Rata-Rata


Bearing Capacity Based On CPT DataDikembangkan oleh Meyerhof (1965) untuk tanah pada umumnya (c – soils) dengan asumsi penurunan yang terjadi sebesar 25mm:

Shallow Foundations

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