1. OverviewIn the earlier reports, a brief introduction on Piled –Raft foundation was given. A review of literature relevant to the said subject was also presented. A numerical example on raft foundation was manually solved. The same problem was modelled and analysed in SAFE software. The present report further extends the literature survey. Also the raft foundation in third report is provided with piles and is analysed in this report.

2. Literature Review

Prakoso and Kulhawy (2001) proposed a displacement based design methodology. The author

conducted a parametric study to examine the effects of system geometry elements on the

performance of piled rafts. The key results he proposed: a) the pile group to raft width ratio

(Bg/Br) and pile depth are the most influential elements of system geometry. To minimize

settlement, an optimum pile depth should accompany an optimum (Bg/Br) ratio. b) A width ratio

of about 1 is the most effective to minimize the average displacement. While a width ratio of

about 0.5 is the most effective to minimize the differential displacement. c) For the given pile

group geometry, raft thickness apparently had little effect on differential settlement of piled rafts

with 0.2 ≤ (Bg /Br )≤ 0.8, but it had a more significant effect on different settlement of fully piled

rafts. Thus optimizing the pile group width is more effective than thickening the raft for reducing

the differential displacement. d) The displacements of the piled rafts are more controlled by their

system geometry than by their compression capacity.

Reul and Randolph (2004) analysed different piled raft configurations by means of three-

dimensional elastoplastic finite element analyses. In the study, the pile positions, the pile number,

the pile length, and the raft-soil stiffness ratio as well as the load distribution on the raft had been

varied. The key results of parametric study are: a) For the same total pile length, smaller average

settlements are achieved with longer piles rather than with a higher number of piles. b) For a raft

under uniform loading or core-edge loading, the differential settlements can be most efficiently

reduced by installation of piles only under the central area of the raft. c) For a raft subjected to

uniform loading, the installation of piles does not seem to reduce the bending moments compared

to the unpiled raft. d) The installation of piles under the loaded areas together with non-uniform

pile lengths, yield the minimum total pile length.

Noh et al (2008) carried out analysis of un-piled and piled raft foundations with sandy soil conditions. Based on the geotechnical parameters, a finite element analysis was conducted on un-piled and piled raft foundations. The authors concluded that the raft thickness affects differential settlement and bending moments, but has little effect on load sharing or maximum settlement. Piles spacing plays an important role on the performance of piled raft foundation. It affects greatly the maximum settlement, the differential settlement, the bending moment in the raft, and the load shared by the piles. To reduce the maximum settlement of piled raft foundation, optimum

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performance is likely to be achieved by increasing the length of the piles involved. Whereas the differential settlement, the maximum bending moment and the load sharing are not affected much by increasing the pile lengths.

Singh B. and Singh N. (2008) analysed a raft of 16 m x 16 m in plan with 16 square piles of 0.4

m x 0.4 m cross-sectional area and 12 m length using the finite element software ANSYS. First

only the raft part of the foundation was analysed, and then piles were added to form a piled raft.

The analysis was carried out for different raft thicknesses and soil modulus. The analysis gave

non-linear load-settlement curves. Axial load distribution on individual piles was also analysed.

Conclusive remarks made by the author are: a) The raft thickness has little effect on maximum

settlement in soft cohesive soils. Greater raft thickness is not generally advantageous in reducing

overall settlement. The optimum raft thickness can be determined from a parametric analysis. b)

A thin raft (0.5 m thickness) in a soft soil (soil modulus= 25kN/m2) shows rigid behaviour. The

same raft behaves flexible in a soil with high modulus. The raft can regain its rigid behaviour if its

thickness is increased. d) In the piled raft, the centre pile carries the maximum load, followed by

the edge pile and then the corner pile, which carries the minimum load. e) Addition of piles

increases the load carrying capacity of raft foundation. Restricting the number of piles to make

them reach their ultimate capacity earlier than the raft is more beneficial.

Rabiei (2009) presented a parametric study on the effect of pile configuration, pile number, pile

length and raft thickness on piled raft foundation behaviour using computer program ELPLA

(Elastic Plates). In the parametric study four basic pile configurations were investigated. Pile

configuration 1 had the piles uniformly distributed under whole raft area. In pile configuration 2,

the piles were placed only in the central area of the raft. Pile configuration 3 had piles under

central area of the raft as well as under the edges of the raft. In pile configuration 4, the piles were

placed only under the edges of the raft. The conclusions put forward by the author are as follows:

a) for a particular pile configuration, increase in number of piles decreased the maximum positive

bending moment except in configuration 4. By increasing the number of piles, maximum negative

bending moment decreased. b) In configuration 3, for constant outer pile length and increasing

central pile length, maximum positive moment, differential settlement and central settlement

decreased and percentage of load on piles increased. c) Except for thin rafts, the maximum

settlement was not greatly affected by raft thickness. d) The differential settlement decreases

significantly with increasing raft thickness.

Gowri (2011) analyzed raft foundation using FEM. They carried out the study in two phases, viz; first phase consisting of validation of ANSYS results and second phase consisting of parametric study. They varied MAT size and thickness to measure settlement and ultimate load carrying

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capacity. They observed that there is increase in load carrying capacity with the increase in thickness up to 1.25m and later load carrying capacity remains more or less the same. Also the load carrying capacity increased up to 3m x 3m size raft and later load carrying capacity decreased with increase in raft size and finally became constant. Lastly they observed that there was a linear increase in settlement with increase in raft size. The authors concluded that a raft of size 3m x 3m with 1.25m thickness relatively gives higher load carrying capacity with permissible settlements.

Shukla et al (2011) studied different parameters like size of the raft, thickness of the raft, diameter of the piles, length of piles, configuration of piles, stiffness of raft and piles etc., which affect the behavior of piled raft foundation. Their interdependency was also reviewed. They found that increase in raft thickness increases settlement whereas increase in pile diameter reduces the settlement.

Cho et at (2012) performed a nonlinear three-dimensional finite element analysis with pile–soil

slip interface model for different pile configurations. Collusions put forward by the author are: a)

The average settlement could be reduced effectively with wider spaced pile groups with the same

number of piles. Furthermore, the efficiency of piles in a piled raft had maximized when the

magnitude of the applied load of the piled raft was similar to the ultimate capacity of pile groups

in the piled raft. b) The differential settlement had minimized by the centre area being supported

by piles. c) The loading type (uniform or point load) greatly influenced the differential settlement

rather than the average settlement

3. Numerical Studies The foundation is designed for a storage 5 story building. The bearing stress is around 100 kN/m 2. The raft is designed as flat plate, which has a uniform thickness and without any beams or pedestals. The raft is modelled in SAFE software. All analysis and design are based on the ACI code. Raft foundation can be design using several methods. Here, “the Conventional Rigid Method” is used for design. All design parameters are shown in table 1.

Parameter Notation ValueYield strength of steel Fy 400 MPaStrength of concrete fc 30 MPaYoung modules of elasticity of concrete Ec 2E+06 kN/m2

Dead load factor D.L.F D.L.F 1.2Live load factor L.L .F L.L .F 1.6Soil Unit weight γ soil γ soil 15 kN/m3

Allowable Bearing stress qa qa 100 kN/m2

Concrete Unit weight γ concrete γ concrete 25 kN/m3

Table 1, Parameters used in Raft Design

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3.1 Raft Modeling and Analysis:

Figure 1, Raft layout and column notation

Raft foundation is modelled in SAFE software. The raft has x side spacing of 7 meters and y-side spacing of 6 meters with one meter edge distance around the edges columns. The plan of the raft is shown in figure 1.

The total area of the raft = (3 7 + 1 + 1) + (3 6 + 1 + 1) =23 20 = 460 ∗ ∗ ∗ 𝑚2

3.2 Columns loads in Raft

Assumed design loads are tabulated below.

Load type Load case Load value (kN/m2)

Services Dead 2.5 kN/m2

Slab own weight assumed Dead (25kN/m3)(0.2m) =5 kN/m2

Flooring Dead 1 kN/m2

Live loads Live 7 kN/m2

Table 2, Design loads

Columns loadsAxial Dead Load = Stress per unit area kN/m * Turbidity area

Sample calculation:Column type C1 Axial unfactored Dead load = 42.5 kN/m2 ∗ 4 ∗ 4.5 m = 765 kN

Axial unfactored Live load = 35 kN/m2 ∗ 4 ∗ 4.5 m = 630 kN Total Sevice Axial load = 765 + 630 kN = 1395 kN Ultimate axial load = 1.2 (765) + 1.6 (630) = 1926 kN

Extra Column loadsThese columns cause moments around x-axis and y-axis. The axial loads of the original columns and extra columns are shown in the table

Column no.Dead load

(kN)Live load

(kN)Total service

load (kN)

Total factored load

(kN)C1 765 630 1395 1926C2 1190 980 2170 2996C3 1148 945 2093 2889

C4 (maximum) 1785 1470 3255 4494

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C5 (extra) 500 300 800 1080C6 (extra) 450 250 700 940C7 (extra) 400 200 600 800C8 (extra) 350 150 500 660

Table 3, Column Loads

3.3 Selection of foundation typeThe foundation is assumed to rest on loose sand soil. The properties used in the analysis and the design of this raft foundation are shown in table 4.

Soil type Loose sand

Effective bearing stress for the soil qe= 100 kN/m2

Sub-grade modules 20,000 kN/m3

Concrete strength of raft 30 MPa

Reinforcement Steel strength 400 MPaTable 4, Properties taken in Raft Design

qe = 100 kN/m2

Total Maximum Service Axial load = 1785 + 1470 kN = 3255 kN

Area of single square footing = 1.1 (3255 )100

= 35.8 m

B X B = 35.8−→ B = √ 35.8 = 6 m by 6 mThus area to be excavated under one column is considerably large and as such a raft foundation will be much efficient and more economical.

3.4 Raft thickness: In Raft foundation, the thickness can be determined by checking the diagonal tension shear that will be imposed in the raft. The maximum ultimate column load will be used in the calculation. 𝑈 = 𝑏𝑜.𝑑. (0.34) √∅ 𝑓𝑐′ …. ACI 318 C11.12.2.1Where, U = factored column load

= Reduction factor = 0.85 ∅𝑏𝑜 = the perimeter of the sheared area d = effective depth of raft 𝑓𝑐′ = Compressive strength of concrete

In this Raft, 𝑈 = 4494 kN = 4.494 MN𝑏𝑜 = 4(0.4 + 𝑑) = 1.6 + 4𝑑And by using the equation above, the required depth of the raft can be determined.𝑈 = 𝑏𝑜.𝑑. (0.34) ∅ 𝑓𝑐′

4.494 = (1.6 + 4𝑑) (𝑑) (0.75) (0.34) √30

4.494 = (1.6𝑑 + 4𝑑2) (1.397)

3.2169 = 1.6𝑑 + 4𝑑2

0 = 4𝑑2 + 1.6𝑑 − 3.2169

0 = 4𝑑2 + 1.6𝑑 − 3.2169Solving equation for d

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d = 0.689 m = 689 mm = 700 mm Thickness of the raft = 700 + 75 + 25 (assumed bar diameter) Thickness = 800 mm For this thickness, raft is found to be safe in one way and two way shear checks.3.6 Soil Pressure Check:The net soil pressure is checked at each point of the raft foundation. The raft foundation is neither symmetric about x-axis nor y-axis due to difference in the columns positions and loads. Moments effects on the raft are checked to assure that the stresses in the raft under all columns are less than the net allowable stress i.e. 100 kN/m2.

Figure 3, Total service loads on columns (DL+LL)

q = (QA )±( MyX

Iy )±( MxYIx

)

A = Area of mat = ( (7∗3 )+1+1 )∗¿ = 23 * 20 = 460 m2.

Ix= b h3

12 = 23∗203

12 = 15333.3 m4

Iy=h b3

12=20∗233

12 = 20278.3 m4

𝑄 = 𝑠𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑠𝑒𝑟𝑣𝑖𝑐𝑒 𝑐𝑜𝑙𝑢𝑚𝑠 𝑙𝑜𝑎𝑑𝑠𝑄 = 4 𝐶1 + 4 𝐶2 + 4 𝐶3 + 4 𝐶4 + 𝑒𝑥𝑡𝑟𝑎 𝑐𝑜𝑙𝑢𝑚𝑛 𝑙𝑜𝑎𝑑𝑠𝑄 = 4 1395 + 4 2170 + 4 2093 + 4 3225 + 800 + 700 + 600 + 500𝑄 = 38252 𝑘𝑁𝑒𝑥 = X’− 10.5

X’ = 10.976 𝑚𝑒𝑥 = 10.976 − 10.5 = 0.4758 𝑚𝑀𝑦 = 𝑄.𝑒𝑥= 38252 0.4758 = 18200 ∗ 𝑘𝑁. 𝑚𝑒𝑦 = 𝑌′− 9𝑌’ = 9.07843 𝑚𝑒𝑦 = 9.07843 − 9 = 0.07843 𝑚𝑀𝑥 = 𝑄𝑒𝑦 = 38252 ∗ 0.07843 = 3000 𝑘𝑁. 𝑚Calculate Soil pressure due to total service axial loads and moments:

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qi = −(QA )± (MyX

Iy )±( MxYIx

) , i = 1, 2, 3, 4.

where (-) minus signs refers to compression stress.Soil pressure will be checked in the four corners of the raft. Soil pressure should not be more than the allowable stress of the soil and not less than 0 kN/m2 to make sure that no tension occurs in any part of the raft.

q1 = −(QA )−(MyX

Iy )−( MxYIx

) = −96 𝑘𝑁/𝑚2 < 𝑞𝑛𝑒𝑡 = 100 𝑘𝑁/𝑚2 ok

q2 = −(QA )+( MyX

Iy )−( MxYIx

) = -75 𝑘𝑁/𝑚2 < 𝑞𝑛𝑒𝑡 = 100 𝑘𝑁/𝑚2 ok

q3 = −(QA )+( MyX

Iy )+( MxYIx

) = -71 𝑘𝑁/𝑚2 < 𝑞𝑛𝑒𝑡 = 100 𝑘𝑁/𝑚2 ok

q4 = −(QA )−(MyX

Iy )+( MxYIx

) = -91 𝑘𝑁/𝑚2 < 𝑞𝑛𝑒𝑡 = 100 𝑘𝑁/𝑚2 ok

All pressure values are in compression and they are less than the net bearing stress of the soil

which is equal to 100 𝑘𝑁/𝑚2.

3.7 Raft deformation analysis3.7.1 Unpiled-raft: The following table show effect of raft thickness on raft deformation, and differential settlement.

RAFT THICKNESS (m) DIFFERENTIAL SETTLEMENT ( mm)200 29.44300 18.98500 10.85800 6.621000 5.421200 4.61500 3.692000 2.71

Table 5, Differential settlement of unpiled raft foundation

0 500 1000 1500 2000 250005

101520253035

RAFT THICKNESS (mm)

DIFF

ERET

IAL

SETT

LEM

ENT

(mm

)

Graph 1, Raft Thickness V/S Diff Settlement

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Figure 4, Unpiled - Raft deformation contours

3.7.2 Piled- Raft:With the introduction of piles under the raft, the differential settlement decreased considerably. Piles of diameter 600 mm and length 3 m are introduced below the raft foundation. Different pile configuration analysed in SAFE are shown below.

a) 12 piles b) 9 piles c) 13 piles A

e ) 21 piles f ) 13 piles BFig 6, Pile Configuration

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The deformation contours for raft foundation with 21 piles in shown below.

Figure 6, Piled - Raft deformation contours (21 piles)

9 PILES 12 PILES 13 PILES A

13 PILES B 21 PILES02468

101214

PILE CONFIG

DIFF

. SET

TLEM

ENT

MM

Graph 2, Pile Config and Diff. Settlement

3.8 ConclusionIncrease in raft thickness beyond a particular limit has little or no effect on settlement of foundation. The increase in raft thickness reduces differential settlement but causes more settlement of foundation. Thus a better solution is to provide piles raft foundation to check differential settlement and total settlement. The position on piles under the raft plays important role in reducing settlement. A parametric study should always be done so as to find out the optimum pile number and position.

4. Analysis of Raft and Piled Raft in SAP2000

Problem : Figure given below shows a raft subjected to loading also shown in figure. Input Values: Ec = 5000√20 = 22360000 N/sq.mmν = 0.2Subgrade Modulus = 10,000 kN/cu.m

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4.1 Total and Differential Settlements in Raft :

1 2 3 4 5 6 7 8 9 100

102030405060708090

100

Total Settlement in Raft In X direction

Tota

l Sett

lem

ent

1 2 3 4 5 6 7 8 902468

1012141618

Diff Settlement In Raft In X direction

Diffe

renti

al S

ettle

men

t

10

1 2 3 4 5 6 7 8 9 100

102030405060708090

100

Total Settlement in Raft In Y direction

Tota

l Sett

lem

ent

1 2 3 4 5 6 7 8 902468

1012141618

Diff Settlement In Raft In Y direc-tion

Diffe

renti

al S

ettle

men

t

4.2 Pile Position Configurations

4.3 Total and differential Settlements in Piled Raft for different pile position configuratons

1 2 3 4 5 6 7 8 9 1005

101520253035

Total settlement in Piled Raft in X dirn

Tota

l Set

lem

ent

1 2 3 4 5 6 7 8 9 100

0.51

1.52

2.53

3.5

Differential settlement in Piled Raft in X dirn

Diffe

renti

al se

ttlem

ent

1 2 3 4 5 6 7 8 9 100

5

10

15

20

25

30

35

Total settlement in Piled Raft in Y dirn

Tota

l Set

lem

ent

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5

Differential settlement in Piled Raft in Y dirn

Diffe

renti

al se

ttlem

ent

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5. Work to be done1. Parametric studies of for position of piles under a raft foundation.2. Parametric studies of for to find out optimum L/d ratio.3. Study of effect of pile configuration on max. BM4. Study of effect of varying pile length, etc.

References

Cho, J., Lee, J. H., Jeong, S., and Lee, J. (2012). “The settlement behaviour of piled raft in

clay soils.” Ocean Eng., 53, 153-16.

Chow, H. (2007). Analysis of piled-raft foundations with piles of different lengths and

diameters. Ph. D. Thesis, School of Civil Engineering, University of Sydney, Sydney,

Australia.

Gowri, S. (2011) “Analysis of Mat foundation using finite element method”, J. Earth Science

and Eng., 04, 113-115.

IS 2950. (Part I) (1981). Code of practice for design and construction of raft foundations

(second revision), BIS, New Delhi, India.

Kurian, N. P. (2005). Design of foundation systems - Principles and practice. Narosa

Publishing house, New Delhi, India.

Noh, E. Y., Huang, M., Surarak, C., Adamec, R. and Balasurbamaniam, A. S. (2008).

“Finite element modeling for piled raft foundation in sand.” Proc., 11th East Asia-Pacific

Conference on Structural Engineering and Construction (11EASEC-2008),

Taipei,Taiwan,19-21.

Prakoso, W. A. and Kulhawy, F. H. (2001). “Contribution to the raft foundation design.” J.

Geotech. and Geoenviron. Eng., ASCE, 127(1), 17-24.

Rabiei, M. (2009). Parametric study for piled raft foundations. World Wide Web of Geotechnical Engineers.< http://www.ejge.com/2009/Ppr0906/Abs0906.htm > (June 30,2012).

Reul, O., and Randolph, M. F., (2004). “Design strategies for piled rafts subjected to non-

uniform vertical loading.” J. Geotech. and Geoenviron. Eng., ASCE, 130(1), 1-13.

Singh, N. T., and Singh, B. (2008). “Interaction analysis for piled rafts in cohesive soils.”

Proc., 12th International conference of International Association for Computer Methods

and Advances in Geomechanics. (IACMAG-2008),Goa, India, 3289-3296.

Shukla, S. J., Desai, A. K. and Solanki, C. H. (2011). “Behavioral study of piled raft

foundation in layered soil deposits.” J. Advanced Eng. Tech., 2(4), 191-195.

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