Bridge Substructure Analysis & Design

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ABSTRACT

The analysis and design of all the components of even the most simple bridge type can be a fairly laborious and cumbersome job especially with respect to the various elements of the bridge substructure. For bridges located on major perennial rivers, resort will have to be made to deep foundations like wells or pile foundations, the design of which involves lengthy computational effort. The bridge engineer should be equipped with a handy computational tool with the help of which he can quickly and reliably determine the suitability of various layouts and configuration of the sub-structure before finalizing the most optimum design of the substructure. In this thesis and attempt has been made to develop a P.C. based software on VB.Net platform for the analysis and design of substructure for bridges with simply-supported spans. The computer programme includes the analysis and of wall-type and circular piers and includes the option for the complete analysis and design of two-types of deep foundations on the basis of the relevant IS Codes of Practice: Well foundations and pile foundations. The pile foundations can be analyzed and designed for both river and non-river bridge crossings and the user is presented the option of two types of piles for use in the foundations: under-reamed piles particularly for non-river bridge foundations and bored cast-in-situ circular piles. A noteworthy feature of the program is that lateral load analysis of both free and fixed-head piles can be carried out by the user in line with the recommendations of the relevant IS Codes. The user friendly and interactive program assists the user in the selection of preliminary dimensions of the well foundation, the safety of which is checked of the elastic state of the soil surrounding the well and at ultimate loads. Structural design of the critical well components like well curb, steining and well cap is incorporated in the software. The results for foundation design obtained from the program have been validated with long-hand calculations present in the Appendix.

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LIST OF TABLES

Table.

No. Title Pg.No.

2.1 Value of constant K for Pressure Intensity due to Water Current 7

2.2 Permissible Stresses in Concrete 9

3.1 Silt factors for Sandy beds, IRC: 78-20008 15

3.2 Values of the constant Q for square or rectangular wells 20

4.1 Bearing Capacity Factor, 33

4.2 Value of coefficient of horizontal soil stress ( 33

4.3 Safe loads for under-reamed piles 35

4.4 Values of the constant (kN/m3) 41

4.5 Values of the constant K (kN/m2) 41

A-1 Calculation of Maximum Shear forces bearings 141

A-2 Stresses due to horizontal shear force at bearings 141

A-3 Summary of Stresses due to various forces acting on the Pier 142 A-4 Resultant Compressive Stresses at Point “A” & “B” on Pier 143 A-5 Resultant Tensile Stresses at Point “A” & “B” on Pier 143 A-6 Horizontal shear force at bearings & moments at the base of foundation 148 A-7 Seismic moment due of mass of bridge components & Live load 148

B-1 Calculation of Maximum Shear forces at bearings 168

B-2 Stresses due to horizontal shear force at bearings 169

B-3 Summary of Stresses due to various forces acting on the Pier 169 B-4 Resultant Compressive Stresses at “A” & “B” on Pier 170

B-5 Resultant Tensile Stresses at “A” & “B” on Pier 170

B-6 Moment about longitudinal axis in pile cap from the critical section 182

B-7 Calculation of two-way shear force 184

B-8 Calculation of one-way shear force at critical section along L-L axis of bridge

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LIST OF FIGURES

Fig.

No. Title Pg. No.

2.1 Typical Shapes of Piers 5

3.1 Different Shapes of Well 11

3.2 Typical Section of Well Foundation 12

4.1 Piles Classification on the basis of load transfer mechanism 26

4.2 Uplift Piles 27

4.3 Use of piles in scourable beds 27

4.4 Piles in expansive soils can control seasonal movements 28

4.5 Free Standing Pile Group 29

4.6 Piled Foundation 29

4.7 Load resisting mechanism in a pile 31

4.8 Bearing Capacity Factor, for bored piles 32

4.9 Adhesion factor for cohesive soils 34

4.10 Typical arrangement of piles in a group 36

4.11 Determination of the depth of fixity of the pile 42

4.12 Reduction factors for free-head and fixed-head piles 43

4.13 Computation of Settlements for End Bearing Piles & Friction Piles 45

4.14 Critical section for moment & one-way shear 47

4.15 Critical section for two-way shear 47

4.16 Typical detailing of reinforcement in a pile cap 47

5.1 Flow Chart of preliminary dimensioning of pier 51

5.2 Flow Chart for Analysis of Pier 52

5.3 Flow Chart for calculation of Maximum Scour Depth 54

5.4 Flow Chart for calculation of soil resistance 56

5.5 Flow Chart for calculation of soil resistance at ultimate loads 58

5.6 Flow Chart for design of Well curb 59

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5.8 Flow Chart for design of Well Cap 61

5.9 Flow Chart for soil details 63

5.10 Flow Chart for calculating safe bearing Capacity of bored cast-in-situ pile 65 5.11 _{Flow Chart for calculating safe bearing Capacity of an under-reamed Pile} 66 5.12 Flow Chart for calculation of SBC of group of bored cast-in-situ piles 68 5.13 Flow Chart for calculation of SBC of group of under-reamed piles 69

5.14 Lateral load capacity of Under-reamed Pile 70

5.15 Lateral load capacity of Bored Cast-in-situ pile 71

5.16 Design of Pile Cap 72

6.1 Details of Soil layers in Ground 104

A-1 _{Pier Section in longitudinal direction of bridge} 133

A-2 Water Pressure Details 137

A-3 Location of “A” & “B” on pier 142

A-4 Diagram of a Well Foundation 145

A-5 Diagram of Well curb 146

A-6 Diagram of Bottom Plug 146

A-7 Load dispersion area in well cap 158

A-8 _{Moments in well-cap when freely supported} 160

A-9 Moments in well-cap when fully clamped 161

A-10 Reinforcement Details of Well Cap 163

B-1 Pier Section in transverse direction of bridge 164

B-2 Location of “A” & “B” on Pier 170

B-3 Effective overburden pressure on pile 172

B-4 Arrangement of Piles in Foundation 174

B-5 Settlement of End bearing piles 180

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CHAPTER 1 INTRODUCTION

1.1 INTRODUCTION

Thomas B. Macaulay once said: “Of all inventions, the alphabet and the printing press alone, excepted, those inventions which abridge distance have done the most for the civilization of our species”. Since ancient times, bridges have been the most visible testimony to the contribution of engineers. Bridges have always figured prominently in human history. They enhance the vitalities of the cities and aid the social, cultural and economic improvements of the locations around them.

Bridge is a structure providing passage over an obstacle without closing the way beneath. The required passage may be for a road, a railway, pedestrians, a canal or a pipeline and the obstacle to be crossed may be a river, a road, railways or a valley. The portion of the bridge structure below the level of the bearing and above the founding level is generally referred to as the substructure. The design of bridge substructure is an important part of the overall design for a bridge and affects to a considerable extent the aesthetics, the safety and the economy of the bridge. Bridge substructure are a very important part of a bridge as it safely transfers the loads from the superstructure to the earth in such a manner that the stresses on the soil are not excessive & the resulting deformations are within the acceptable limits.

The selection of the foundation system for a particular site depends on many considerations, including the nature of subsoil, location where a bridge is proposed to be constructed i.e. over a river, road, or a valley, etc. & the scour depth. A bridge may have either have the following types of foundations:

1. Well foundations: It is the most common type of foundation in India for both road & railway bridges. Such foundation can be sunk to great depths and can carry very heavy vertical and lateral loads. Well foundations can also be installed in a boulder stratum. It is a massive structure and is relatively rigid in its structural behavior.

2. Pile foundations: It consist of relatively long and slender members, called piles which are used to transfer loads through weak soil or water to deeper soil or rock strata having a high bearing capacity. They are also used in normal ground conditions for elevated road ways.

The analysis and the design of all the components of a bridge particularly with reference to the bridge substructure can become a very lengthy and laborious task if the calculations are attempted manually. A design engineer would like to try various

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configurations, shapes and sizes of the principal components of a bridge before finalizing the most optimum combination on the basis of safety, economics and aesthetics of the elements of the super-structure and the sub-structure. At the same time, in spite of the best efforts during sub-soil investigations, many uncertainties always exist with respect to the sub-soil conditions which may be encountered at pier and foundation locations. Unexpected sub-soil conditions may require a significant redesign of the foundation or in extreme cases the

foundation type may have to be changed from for example an open-footing to a pile or a well foundation. For the above eventualities, it is desirable that a quick, handy and reliable

computational tool should be available to the design engineer for the analyses and design of bridge sub-structure in general and well and pile foundations in particular.

In this thesis an attempt has been made to develop P.C. software package in the VB.Net platform for the analysis and design of sub-structures for concrete bridges with simply supported spans.

Analysis of the super-structure for loads transferred to the sub-structure is included in the software. Two IRC loading categories: Class AA and Class A are considered for super-structure analysis. The option for single lane and two lanes of traffic is included. The user is provided with the option of two types of concrete piers: wall-type and hammer-head type with a circular shaft. The analysis and design of both these types of piers is included in the software. In the software, the option is provided for two types of deep foundations: well and piles. Well foundations are essentially meant for river-bridge crossings where as the option for pile foundations take care of pile analysis and design for both non-river and river bridge crossings. The analysis of the well foundation is carried out as per the relevant IRC code for the resultant axial, lateral loads and moments transferred from the super-structure for the following two conditions: (1) The soil surrounding the well is in an elastic state (2) At

ultimate load conditions. The program includes check on thickness of the bottom plug and the analysis and design of the critical components of a well viz. well curb, well steining and well cap. Practical considerations related to construction of wells are examined through a check on the sinking effort developed in the well. Two types of piles are available for design of pile foundations: (1) Under-reamed piles and (2) Bored cast-in-situ circular piles. Under-reamed piles are essentially meant for non-river bridge crossings and their design for vertical and lateral loads has been carried out as per recommendations of IS: 2911. The software includes the analysis and design of both free-head and fixed-head bored cast-in-situ circular piles in cohesion less as well as cohesive soils. A noteworthy feature of the software is the lateral load analysis of the pile as per the relevant IS Code. The design of the pile foundation

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concludes with check on group behavior including settlement analysis and structural design of the pile and the pile cap.

1.2 OBJECTIVE OF THE THESIS

Development of an interactive user-friendly software for the analysis and design of substructures of RCC bridges with simply supported spans for river as well as non-river bridge crossings.

1.3 SCOPE OF THE WORK

The analysis of the simply supported super-structure has been carried out for only two loading classes: Class AA and Class A. Two type of piers are included in the software: wall-type and hammer-head wall-type with a circular shaft. Besides gravity loads, lateral loads due to wind, earthquake and hydro-dynamic effect are considered in the analysis. The well

foundation analysis is performed at both elastic and ultimate state. The analysis and design of pile foundation is restricted to under-reamed and bored cast-in-situ piles in both cohesionless and cohesive soils for vertical as well as lateral loads. Structural design of piles and pile-cap is included in the software. The software does not have the option of generating detailing and working drawings of the bridge sub-structure.

1.4 ORGANIZATION OF THE THESIS

The introduction to the thesis & the scope of present work together with the organization of thesis is contained in Chapter 1.

Chapter 2 discusses about the piers in substructure. It contains the details & summarizes the available literature on pier. The steps for analysis for pier are explained in this chapter.

The knowledge base of well foundation is provided in Chapter 3, following the procedure for analysis of well foundation & design of various components of the well. Chapter 4 includes the literature review on pile foundations & discusses the analysis

& design steps of pile foundations.

The features & limitations of the software developed as the part of thesis work are being explained in Chapter 5. The functioning of various modules of the software are explained in the form of flow chart, in the same chapter.

The application of the proposed software to the analysis & design of typical well foundation and pile foundation is presented in Chapter 6.

The conclusions from the present study are discussed in Chapter 7. References form the last part of this thesis.

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CHAPTER 2 PIERS & PIER CAPS

Piers are substructures located at the ends of bridge spans at intermediate points between the abutments. The function of the piers is two-fold: to transfer the superstructure vertical loads to the foundation and to resist all horizontal and transverse forces acting on the bridge. Piers are generally constructed of masonry or reinforced concrete. Being one of the most visible components of a bridge, the piers contribute to the aesthetic appearance of the structure. They are found in different shapes, depending on the type, size and dimensions of the superstructure and also on the environment in which the pier is located.

The pier cap (also known as the bridge seat) is the block resting over the top of the pier or the abutment. It provides the immediate bearing surface for the support of the superstructure at the pier location, and disperses the strip loads from the bearings to the substructure more evenly. The pier cap is given an offset of 75 mm beyond the edge of the pier. This offset prevents rain water from dripping down the sides and ends of the pier and also improves the appearance of the pier. Minimum thickness provided to the pier cap is 225 mm for spans of up to 25 m, otherwise 300 mm.

2.2 TYPES OF PIERS

Typical shapes of piers commonly used in practice are as shown in Fig. 2.1. They can be solid, cellular, trestle or hammer-head types. Solid and cellular piers for river bridges are provided with semicircular cut-waters to facilitate and streamlined flow and to reduce the scour. Solid piers can be of mass concrete or of masonry for heights of up to 6 m and spans up to about 20 m. Hammer-head type piers are increasingly used in urban elevated highway applications, as it provides slender substructure with open and free-flowing perception to the motorists using the road below. It is also used for river crossings with skew alignment, which will result in least obstruction to passage of flood below the bridge. Cellular, trestle, hammer-head types are suitable for heights above 6 m and spans over 20 m. In trestle type piers, concrete hinges have been recently introduced between the top of column and the bent cap in order to avoid moment being transferred from deck to the columns. Reinforced concrete framed types of piers as shown in Fig. 2.1 (e) have also been used in recent years. Such piers lead to economy in cost of superstructure as it reduces the span length of girders on either side of pier, but at the same time it will accumulate debris and floating trees from the stream flow. Two expansion joints formed on each pier will result in riding discomfort.

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(a) Solid Pier

(b) Cellular Type Pier

(c) Trestle R.C. Pier (d) Hammer-head Type Pier

(e) Framed Type Piers

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Minimum top width of pier is kept 600 mm more than the out-to-out dimension of the bearing plates, measured along the longitudinal axis of the superstructure. Length of pier should not be less than 1200 mm in excess of the out-to-out dimension of the bearing plates measured perpendicular to the axis of the superstructure. The bottom width of pier is usually larger than the top width so as to restrict the net stresses within the permissible values. It is normally sufficient to provide a batter of 1 in 25 on all sides for the portion of pier between the bottom of the pier cap and the top of the well or pile cap, as the case may be.

2.3 PROCEDURE FOR ANALYSIS OF PIER

Analysis of pier is carried out considering various forces and loads transmitted from the superstructure and forces acting directly on the pier. Following are the loads and forces to be resisted by a pier:

1. Dead load:

Dead load of superstructure and substructure above the base level of pier.

2. Live load:

This consists of Live load of traffic passing over the bridge. Effect of eccentric loading due to live load should also be considered.

3. Buoyancy:

Buoyancy has the influence of reducing weight. In masonry or concrete structure, the buoyancy effect through pore pressure may be limited to 15 percent of full buoyancy on the submerged portion.

4. Wind load:

Wind load is considered on the live load, superstructure and the part of the substructure above the base of pier or water level, whichever is higher. It acts on the area of the bridge in elevation and is thus always taken to be acting laterally to the bridge only. This force could be considered as per recommendations of IS:8752.

5. Horizontal forces due to water current:

Horizontal force due to water current is considered on that part of substructure that lies between the water level and the base of pier. The water current pressure is given

by Equation 2.1 , (2.1)

where, = intensity of pressure in kN/m2 due to water current,

K = a constant having different values for different shapes of piers.

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Table 2.1

V = velocity of current in m/sec at the point where pressure intensity is being calculated.

It is assumed that the velocity distribution in stream is such that V2 is maximum at the free surface of water, zero at the deepest scour level and varies linearly in between them. Also the maximum velocity of flow is assumed to be equal to times the velocity of the current.

Table 2.1: Value of constant K for Pressure Intensity due to Water Current

SHAPE K – Values

Square ended piers 1.50

Circular piers 0.66

Piers with semi-circular cut-waters 0.66 Piers with triangular cut-waters 0.5 to 0.9 Trestle type piers 1.25

For calculating the pressure on the pier, the angle which the current makes with the axis of the pier should be taken into account. Generally, the maximum variation in the angle of water current to the transverse axis of the bridge is taken as 20°. Thus, the pressure along the axis of the pier and transverse to it is respectively given by,

(2.2) (2.3)

6. Centrifugal forces:

Centrifugal forces are taken into account, when the bridge is located on a curve.

7. Longitudinal forces:

Longitudinal forces are caused due to tractive effort caused through acceleration of the driving wheels, braking effect due to application of brakes to the wheels & frictional resistance offered to the movement of free bearings due to change of temperature. Braking effect is invariably greater than the tractive effort, and as a result the tractive effort of vehicles is neglected.

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8. Seismic forces:

Seismic force acts on all loads, which posses mass at their centre of gravity. Seismic forces acting in horizontal direction, along longitudinal and transverse axis of the bridge are considered. Forces acting in the vertical directions are comparatively small, and are hence neglected. During earthquake, water in river will apply hydrodynamic force on the submerged portion of pier. Seismic forces are considered to act only in one direction at a time.

All the above loads are classified into different loading cases as discussed below.

1. Normal (N) Case loading: It includes dead load, live load, buoyant force, wind load,

forces due to water current, centrifugal forces, braking force/tractive force & horizontal shear force at hinge bearings due to the effect of braking force, wind load.

2. Temperature (T) Case loading: It includes loads due to frictional restraint to

temperature movement at bearings.

3. Seismic (S) Case loading: It includes seismic forces acting in horizontal forces

acting in horizontal direction.

Considering the probability of earthquake with other forces, it is generally assumed that earthquake and wind forces will not occur simultaneously and so only one can be considered at a time. Taking all the case loading into accounts, pier is analyzed for three different load combinations: Normal (N) Case, Normal and Temperature (N + T) Case & Normal, Temperature and Seismic (N + T + S) Case.

Longitudinal forces acting on the bridge like braking effort/tractive effort, frictional resistance at the bearings and seismic forces acting on live load and bridge superstructure will produce horizontal shear force at the bearings. The horizontal shear force will be calculated for different load combinations as discussed above, and later is incorporated into their respective case of load combinations.

Stresses developed into the pier due to different loads and forces are calculated individually, and the resultant maximum stress acting on the pier is worked out for different load combinations. The resultant maximum stress for each load combination should be within the permissible stress limits. For brick masonry in cement mortar, permissible compressive stress is 1 MPa and permissible tensile stress is 0.10 MPa. In stone masonry, compressive stress is limited to 1.5 MPa and tensile stress is limited to 0.10 MPa. Permissible stresses for concrete are given in Table 21 of IS: 456-20001, for different grades of concrete. Table 2.1 shows the permissible stresses for plain concrete used in bridge analysis and design.

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Table 2.2: Permissible Stresses in Concrete

Grade of Concrete

Permissible Stresses in Concrete (in MPa)

For Compression For Tension

M 10 2.5 - M 15 4.0 0.6 M 20 5.0 0.8 M 25 6.0 0.9 M 30 8.0 1.0 M 35 9.0 1.1 M 40 10.0 1.2 M 45 11.0 1.3 M 50 12.0 1.4

IRC: 6-20006 allows the increase in permissible stresses of concrete for different load combinations. For Normal and Temperature (N + T) case i.e. when the effect of temperature is considered, permissible stress can be increased by 15 percent. Finally, for Normal, Temperature and Seismic (N + T + S) case permissible stress can be exceeded by 50%. If the maximum stresses in piers for the worst loading combination are more than the permissible stress, it is required to redesign the piers in order to bring maximum stresses within the permissible limit.

2.4 CONCLUSIONS

The types and the features of piers and pier caps usually employed for bridge crossings have been briefly discussed together with analysis methodology and permissible stresses for design.

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CHAPTER 3 WELL FOUNDATIONS

Well foundations have their origin in India & have been used for hundreds of years for providing deep foundation to important buildings and bridges. Well foundations were freely used during the Moghal Period for bridges across the major rivers. Moghal monuments including Taj Mahal are built on well foundations. Well foundations provide a solid & massive structure. This foundation has maximum sectional modulus for a given cross-sectional area. Wells can resist large horizontal forces & vertical loads even when the unsupported length is large in scourable river beds. A well foundation is monolithic and relatively rigid in its structural behaviour.

3.2 TYPES OF WELL FOUNDATIONS

Different types of wells in common use are shown in Fig. 3.1 The controlling factors in selecting the shape of the well foundation are: the base dimensions of pier or abutment, the ease with which the well can be sunk, cost, considerations of tilt and shift, ease of sinking and the magnitude of the forces to be resisted by the foundation. Circular wells are used most commonly and the mains points in their favour are their strength, simplicity in construction and ease of sinking. However, in terms of the lateral stability for a given cross-sectional area, circular wells offer the least resistance against tilting when compared with other sections. Circular wells also suffer from the disadvantage that in the case of large oblong piers, the diameter of a circular well becomes excessive which renders them uneconomical besides creating obstruction to the flow of water.

Two or three independent circular, square or rectangular wells in section suitably connected can be used for supporting long piers. Such wells are called tied wells. Tied wells of different shapes are preferred to avoid relative tilts between wells. Double-D shaped and dumb-bell shaped wells are the most commonly used shapes of tied wells. Double octagonal well is also a monolithic well consisting of two circular dredge holes. On account of its shape, the flexural stresses developed in the steining are relatively less compared to a double-D shape. However, sharp corners of double octagonal wells produce grater scour. Rectangular wells are generally adopted for bridge foundations having shallow depths. They can be adopted very conveniently where the bridge is designed for open foundations and change to well foundation becomes necessary during the course of construction on account of adverse conditions such as excessive inflow of water and silt into the excavation. For piers of

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very large sizes, wells with multiple dredge holes are used. Wells of this type have been used for the towers of the Howrah Bridge.

(a) Circular well (b) Double-D well

(c) Double octagonal well (d) Double rectangular well

(e) Dumb-bell (f) Rectangular well

(g) Multiple dredge-hole well Fig. 3.1 Different Shapes of Well

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3.3 ELEMENTS OF A WELL FOUNDATION

A well foundation is a type of foundation which is generally built in parts at the surface and sunk to its final position, where it forms the permanent foundation. Fig. 3.2 shows a typical section of a circular well foundation.

Fig. 3.2 Typical Section of Well Foundation

(a) Well-cap:

It is a RCC slab laid at the top of the well steining to transmit the loads and moments from the pier to the well or wells below. Shape of well cap is same as that of well with a possible overhand of 150 mm all-around to accommodate lengthy piers. It is designed as a two-way slab with partial fixedity at supports. The top of the well cap is usually kept at the bed level in case of rivers with seasonal flow or at about the low water level in case of perennial rivers. Thickness of well cap is usually between 1500 mm to 2000 mm.

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(b) Steining:

It is the main body of the well which transfers load to the base of the foundation. Steining is normally of reinforced concrete. Minimum grade of concrete used in steining is M20 with cement content not less than 310 kg/m3. To facilitate well sinking an off-set of 75 mm to 100 mm is provided in well steining at its junction with the well curb.

The thickness of well steining should not be less tan 500 mm nor less than that given by Eq. 3.1.

(3.1)

where, t = minimum thickness of concrete steining, m, D = external diameter of circular well or dumb bell shaped well or smaller

plan dimension of twin D well, m, L = depth of well in m below L.W.L. or top of well cap whichever is greater,

K = a constant depending on the nature of subsoil and steining material (taken as 0.30 for circular well and 0.039 for twin – D well for concrete steining

in sandy strata and 10% more than the corresponding value in the case of clayey soil).

(c) Well curb:

It is the wedge shaped RCC ring beam located at the lower portion of the well steining provided to facilitate sinking. Well curb carries cutting edge for the well and is made up of reinforced concrete using controlled concrete of grade M25. The cutting edge usually consists of a mild steel equal angle of side 150 mm. In case blasting in anticipated, the outer face of the well curb should be protected with 6 mm thick steel plate and the inner face should have 10 mm thick plate up to the top of the curb and 6 mm plate further up to a height of 3 m above the top of the curb.

(d) Bottom plug:

After the well is sunk to the required depth, the base of the well is plugged with concrete. This is called the bottom plug. It acts like an inverted dome supported by the steining on all the sides and transmits the load to the subsoil and acts as a raft against soil pressure from below. Minimum grade of concrete used in bottom plug is M15. Thickness of bottom plug should not be less than the half of dredge-hole diameter nor less than the value calculated in Eq. 3.2.

, (3.2) where, W = total bearing pressure at the base of well,

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fc = flexural strength of concrete in bottom plug,

, and,

= Poisson‟s ratio for concrete, 0.18 to 0.20.

(e) Top plug:

The top plug is an unreinforced concrete plug, generally provided with a thickness of about 600 mm beneath the well cap to transmit the loads from the pier to the steining. Minimum grade of concrete used in top plug is M15.

The space inside the well between the bottom of the top plug and the top of bottom plug is usually filled with clean sand, so that the stability of the well against overturning is increased. While this practice is good in case of wells resting on sand or rock, the desirability of sand filling for wells resting on clayey strata is doubtful, as this increases the load on the foundation and may lead to greater settlement. In the latter case, the sand filling is done only for the part of well up to scour level, and remaining portion is left free.

(f) Intermediate plug:

As discussed above, for wells resting on clayey strata, it is not preferable to fill the space inside the well completely with sand. In such cases, sand filling is not done or sand is filled up to the scour level. A concrete plug covering the filling is usually provided, known as intermediate plug. Usually, thickness of intermediate plug is taken as 500 mm.

3.4 ANALYSIS AND DESIGN OF WELL FOUNDATION

In order to design the well foundation, maximum depth of scour should be determined first since the maximum scour depth decides the depth of the well foundation.

3.4.1 DETERMINATION OF MAXIMUM SCOUR DEPTH

The codes IRC: 78-20008 and IS:3955-19675 recommend that the maximum scour depth in a stream should be ascertained, whenever possible, by actual soundings at or near the site proposed for the bridge, during or immediately after a flood before the scour holes have had time to silt up appreciably. In case actual soundings are not possible, depth of scour in stream can be ascertained using theoretical methods taking into account the velocity of stream, characteristics of the river bed materials, and many other factors.

The IRC: 78-20008 recommended formula for calculating the mean depth of scour below High Flood Level (HFL) for natural channels flowing over scourable bed is as follows:

, (3.3)

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= , Q is the design discharge in the stream in m3/sand is the linear waterway, m,

Ksf = Silt factor for a representative sample of the bed material obtained up

to the level of the anticipated deepest scour, and,

= 1.76 , dm is the median size of the bed sediments in mm.

Table 3.1 presents the IRC: 78-20008 recommended values of silt factor for various types of sandy beds for ready reference and adoption.

Table 3.1: Silt factors for Sandy beds, IRC: 78-20008

The normal scour depth for natural streams in alluvial beds can also be calculated using Lacey‟s formula given below:

, (3.4) where, d = Normal depth of scour below highest flood level for regime conditions in

a stable channel, m.

Q = Designed discharge, m3/s and,

f = Lacey‟s silt factor for a representative sample of the bed material. This can be determined from Table 3.1.

The scour depth with maximum value, obtained from any of the formulae as discussed above will be considered as , the mean scour depth for design of foundation.

As per the recommendations of IRC: 78 – 20008, at the noses of piers, the maximum depth of scour, dmax, is taken as twice of mean scour depth, .

(3.5)

Type of bed material

Coarse silt Silt/fine sand Medium sand Coarse sand

Fine bajri and sand Heavy sand 0.04 0.081 to 0.158 0.233 to 0.505 0.725 0.988 1.29 to 2.00 0.35 0.5 to 0.6 0.8 to 1.25 1.5 1.75 2.0 to 2.42

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The well foundation shall be taken to such a depth that it is safe against scour. Apart from this, the depth of the well foundation should also be sufficient from considerations of bearing capacity, settlement stability and suitability of strata at the founding level. Invariably, the well foundation in all cases shall be taken down to a depth which will provide sufficient grip. The grip length below the anticipated maximum scour level shall not be less than 1/3rd the maximum anticipated depth of scour below H.F.L.

3.4.2 LOADS FOR WELL FOUNDATION DESIGN

After determining the depth of the well foundation, the dimensions of well and its different components are empirically assumed.

The following loads are considered for the analysis and design of well foundation: 1. Dead load

2. Live load 3. Buoyancy 4. Wind load

5. Horizontal force due to water current 6. Centrifugal forces

7. Longitudinal forces 8. Seismic forces

9. Horizontal shear forces at bearings due to longitudinal forces and seismic forces 10. Forces due to tilt and shift.

The loads mentioned above are discussed in Section 2.2 of Chapter 2. These loads are calculated with respect to the bridge superstructure and substructure and correspondingly, the total vertical load, the total horizontal forces acting along the longitudinal direction and the transverse direction of bridge and the moments about the transverse and longitudinal axis of the bridge are obtained for the design of the well foundation. Moments due to shift and tilt of wells are also be included in the analysis of the well.

3.4.3 STABILITY ANALYSIS OF WELL FOUNDATIONS

The stability of well foundation under the action of lateral loads, particularly large magnitudes of seismic forces, depends on the passive resistance of the soil on the sides and the base of the well. As the lateral load increases for a given magnitude of the vertical load, the soil deformation increases disproportionately when compared with the deformation at initial loading. Under the combined action of vertical and lateral loads the mechanism of sharing the applied loads between the sides and the base of the well also gets significantly modified. Hence, the behaviour of the soil at ultimate loads is different form that at the elastic

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stage which is assumed to prevail under vertical loading. The IRC: 45-19727 therefore specifies two checks, one for soil pressures under working loads and the other for the factor of safety available with respect to ultimate strength of the surrounding the well.

As per IRC: 45-19727, the resistance of the soil surrounding the well is checked using: a. Elastic theory

b. Plastic theory (also called as Ultimate Resistance Method)

The following assumptions are made in computing soil pressure using elastic theory:

i. The soil surrounding the well and below the base is perfectly elastic, homogeneous and obeys Hooke‟s law

ii. Under design loads, the lateral deflections are so small that the unit soil reaction „p‟ increases linearly with increasing lateral deflections „z‟. Hence p = KHz

where, KH is the coefficient of horizontal subgrade reaction at the base.

iii. The coefficient of horizontal subgrade reaction increases linearly with depths in the case of cohesionless soils.

iv. The well is assumed to be a rigid body, subjected to an external unidirectional horizontal force „H‟ and moment „M‟ at scour level.

As a consequence of the above assumptions, the pressure distribution is parabolic on the sides of the well and linear at the base.

The elastic theory gives the soil pressure in the sides and the base of the well under design loads. However, to determine the actual factor of safety against failure it is necessary to calculate the ultimate soil resistance which is done by assuming plastic behaviour of the soil at ultimate loads. For checking the ultimate load capacity of the well foundation, the applied loads are multiplied by suitable load factors for various load combinations and the ultimate resistance is reduced by appropriate under-strength factors and the two are then compared.

A step-wise description of these two methods of analysis of well foundations is given below:

Both the above methods are applicable if the well foundation is resting on

non-cohesive soil like sand and is surrounded by the same soil below the maximum scour level.

The above methods should not be used for analysis if the depth of embedment of the well is less than 0.5 times the width of foundation in the direction of the principal lateral forces.

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1. ELASTIC THEORY

STEP 1: Determine the values of W, H and M under combination of normal loads

without wind and seismic loads

where, W = total downward load acting at the base of well, including self weight of well

H = external horizontal force acting on the well at scour level

M = total applied external moment about the base of well, including those due to tilts and shifts,

STEP 2: Compute and and ;

where, (3.6) = moment of inertia of base about an axis normal to the direction of

horizontal forces and passing though the C.G. of the well.

= moment of inertia of the projected area in elevation of the soil mass offering lateral resistance = ;

L = projected width of the soil mass offering lateral resistance multiplied by the appropriate value of shape the factor. The value of shape factor for circular wells shall be taken as 0.9. For square or rectangular wells where the resultant horizontal force acts parallel to the principal axis, the shape factor shall be unity and where the forces are inclined to the principal axis, a suitable shape factor based on experimental results is used.

D = depth of well below scour level,

m = KH/K; Ratio of horizontal to vertical coefficient of sub grade reaction at

base of well. In the absence of values for KH and K determined by field

tests m shall generally be assumed to be unity,

= coefficient of friction between the sides of the well and the soil = , where δ is the angle of wall friction between well and the soil,

α = for a rectangular well, = for a circular well.

STEP 3: Ensure the following:

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(3.8)

where, ,

= coefficient of friction between the base of the and the soil. It shall be taken as

= angle of internal friction of soil.

STEP 4: Check the elastic state

(3.9) where, = density of the soil (submerged density to be taken when under water or

below water table)

= passive and active pressure coefficients to be calculated using Coulomb‟s theory, assuming „δ‟, the angle of wall friction between well and soil to be equal to , but limited to a value of .

(3.10)

(3.11)

STEP 5: Calculate (3.12)

where, & = maximum and minimum base pressures, respectively,

A = area of the base of well,

B = width of the base of well in the direction of forces and moments, P = M/r,

STEP 6: Check i.e. no tension, and,

& allowable bearing capacity of soil.

STEP 7: If any of the conditions in Step 3 or Step 4 is not satisfied, then the grip length of

the well may be increased and all the calculations are revised. If the conditions in Step 5 are not satisfied then, either the grip length of the well or the diameter of the well is increased.

STEP 8: The above steps are repeated for load combinations containing seismic and wind

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2. ULTIMATE RESISTANCE METHOD

STEP 1: Check that , (3.13)

where, W = total downward load acting at the base of well, taking appropriate load factors as per the combinations given below:

1.1D

1.1D + B + 1.4(WC + EP + W or S)

1.1D + 1.6L

1.1D + B + 1.4(L + WC + EP)

1.1D + B + 1.25(L + WC + EP + W or S)

where, D = dead load

L = live load including barking load and other forces related to live load B = Buoyancy

WC = water current force

EP = earth pressure

W = wind force S = seismic force

A = area of the base of well

= ultimate bearing capacity of soil below the base of well (taking a factor of safety of 2.5).

STEP 2: Calculate the base resisting moment, Mb, at the base of well using the following

equation:

Mb = QWB , (3.14)

where, B = width, in the case of square and rectangular wells measured parallel to the direction of forces and diameter for circular wells

Q = a constant whose values are given in Table 3.2 below for wells with a square or a rectangular base. A value of 0.60 is taken for circular wells = angle of internal friction of soil.

Table 3.2 Values of the constant Q for square or rectangular wells

D/B 0.5 1.0 1.5 2.0 2.5

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The ultimate moment of resistance of the well sides due to the passive resistance of the soil, , is calculated next.

(3.15) where, = density of soil (submerged density to be taken for soils under water or

below the water table),

L = projected width of the soil mass offering resistance. In case of circular wells, it shall be 0.9 times the well diameter

= passive and active pressure coefficients to be calculated using Coulomb‟s

theory, assuming „δ‟, the angle of wall friction between the well and the surrounding soil to be equal to but limited to a value of .

STEP 3: The ultimate moment of resistance of the well sides due to friction, , is calculated

(i) For rectangular wells,

(3.16) (ii) For circular wells,

(3.17) STEP 4: The total ultimate moment of resistance of the well is taken as Mt

Mt = 0.7(Mb + Ms + Mf) (3.18)

Where 0.7 is the strength reduction factor STEP 5: Check Mt M

where, M = Total applied external moment about the plane of rotation of the well taking appropriate load factors as per combinations given vide step 1. STEP 6: If the conditions in Steps 1 and 5 are not satisfied, the well shall be redesigned.

3.4.4 DESIGN OF WELL CURB

When the well is dredged during the process of sinking, the curb cuts through the soil under the action of the dead weight of the steining including kentledge, if any and hence hoop tension is developed in the well curb. The well curb has to be designed for the hoop tension.

Total hoop tension, (3.19)

where, N = running load of the well steining on the curb, d = mean diameter of well steining,

= angle of beveled edge of well curb with horizontal, and,

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A minimum reinforcement of 72 kg/m3 is provided in the well curb. The reinforcement is provided in the form of rings distributed along the perimeter of the well curb, the rings being enclosed within stirrups.

3.4.5 DESIGN OF WELL STEINING:

Before designing the section of the steining, the stresses in the steining are calculated at the level of maximum scour.

(3.20) (3.21) where, W = total vertical load acting up to the maximum scour depth,

A = area of cross-section of well steining,

M = Resultant moment due to various loads as considered during analysis of well at maximum scour level

Z = Section modulus of well steining.

The stresses should be within the permissible limits. Permissible limit of stresses for different grades of concrete can be obtained from Table 2.2. If the stresses exceed the permissible limits, the thickness of the well steining has to be increased.

A minimum thickness of the steining, tmin, given by the following equation is required

to avoid the excessive kentledge during sinking of the well.

Thickness, (3.22) where, d = external diameter of well,

= density of concrete, and,

f = skin friction acting on the curved surface area of the well, =

where, = coefficient of friction between soil and concrete, KA = coefficient of active earth pressure

= submerged density of soil on the sides of steining h = height of well.

After performing the checks for stresses and thickness of steining, the reinforcements in the steining are calculated. The vertical reinforcements in the steining should not be less than 0.12 percent of the gross sectional area of the actual thickness provided for the steining. The vertical reinforcement should be equally distributed on both the faces of the steining. The

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vertical reinforcement should be tied up with hoop steel not less than 0.04 percent of the volume per unit length of the steining.

3.4.6 DESIGN OF BOTTOM PLUG

The bottom plug has to be checked for minimum thickness given by the following equations,

(For circular wells), (3.23) (For rectangular wells), (3.24)

where, r = radius of well at the base

q = unit bearing pressure against the base of the well

= flexural strength of concrete used in bottom plug b = short side of well

α = short side/long side ratio of well.

3.4.7 DESIGN OF WELL CAP

A well cap is needed to transfer the loads and moments from the pier to the well. The shape of the wall cap is normally kept the same as of the well with a possible overhang of 150 mm. The top of the well cap is usually kept at about the low water level in case of perennial rivers. The well cap is designed as a two-way reinforced concrete slab resting over the top of well. The support conditions are taken partially restrained.

The design of the well cap is carried out by assuming that the load from the pier acts on an imaginary circle having an area equal to the area of dispersion of the loads transferred from the pier to the well cap.

Since the well-cap is assumed to be partially restrained by the steining, the moments in the well-cap are calculated for circular patch loading and for U.D.L. (self-weight of well cap) for the following two conditions:

(1) Well cap freely supported on steining (2) Well cap fully clamped on steining

Condition 1: Well cap freely supported on the steining

Take, Poisson‟s ratio of concrete, w = weight of well cap per unit area V = vertical load acting on the well-cap h = effective diameter of well-cap,

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In the first instance, the moments in the well cap due to vertical loads transferred from the pier and the self weight of the well cap are determined.

(i) Moments beneath loaded area due to circular patch loading

(3.25)

(3.26)

d = diameter of equivalent circular patch loading (ii) Moments beneath unloaded area due to circular patch loading

(3.27) (3.28)

At support, d = h; = 1

The radial and tangential moments in the well cap due to U.D.L. are given by

(3.29)

(3.30)

At centre, d = 0; = 0 At support, d = h; = 1

Condition 2: Well cap fully clamped at support (i) Moments beneath loaded area due to circular patch loading

(3.31)

(3.32)

d = diameter of equivalent circular patch loading (ii) Moments beneath unloaded area due to circular patch loading

(3.33)

(3.34)

The radial and tangential moments in the well cap due to U.D.L. are given by

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(3.36)

At centre, d = 0; = 0

If is the resultant moment per metre length of the pier, then maximum reactive moment at the support =

Hence, the maximum moment at the centre of the well cap due to moments transferred form pier =

The maximum moment at the edges of the well cap due to moments transferred from pier = .

The resultant moments for the design of the well-cap section at mid-span and at supports can be found out as follows.

Mcentre = (Mean radial moment due to patch loads beneath the loaded area)

+ (Mean radial moment due to U.D.L. at the centre of well-cap)

+ (moment at the centre of well cap due to moments transferred from pier) Medge = (Mean radial moment due to patch loads beneath unloaded area)

+ (Mean radial moment due to U.D.L. at the support of well-cap)

+ (moment at the edges of well cap due to moments transferred from pier) Hence, the reinforcement at the centre of the well-cap is calculated for the moment Mcentre

and the reinforcement at the edges of well-cap is calculated for the moment Medge. Half of the

main tension reinforcement at the centre and at the support sections of the well cap is provided on the compression face. All reinforcement in the well-cap is provided as an orthotropic mesh.

The well-cap is finally checked for punching shear as per IS: 456-20001.

3.5 CONCLUSIONS

The role and the features of well foundations have been discussed in this chapter. This stability analysis of well foundations has been explained and the design of various components has been briefly reviewed.

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CHAPTER 4 PILE FOUNDATIONS

Piles are relatively long and slender members used to transfer loads through weak soil or water to deeper soil or rock strata having a high bearing capacity. Piles are usually installed in clusters/group to provide foundations for bridges. A pile foundation may have vertical piles or batter piles or a combination of vertical and batter piles. Well foundations are provided to the bridges, only when soils with high bearing capacity are available at the shallow depths in ground, in order to resist loads and moments transferred by well to the soil. It is not preferable to use well foundations, when low bearing strata like clay is present in the ground up to greater depths.

The uses of piles for bridge foundations are justified in the following cases:

(a) The upper soil strata are too compressible or too weak to support the heavy vertical reaction transmitted by the superstructures and piers. In this instance, piles serve as extensions of piers to carry the loads to deep, rigid stratum such as rock. Such piles are called as point or end bearing Piles. If a rigid stratum does not exist within reasonable depth, the load must be gradually transferred, mainly by the friction, along the pile shafts. Piles transferring loads to soil by skin friction through its lateral surface area are called as Friction Piles.

(a) Point Bearing Piles (b) Friction Piles

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(b) Piles are also frequently required because of relative inability of other foundations to transmit inclined, horizontal, or uplift forces and overturning moments. As the name implies, uplift piles are used for resisting uplift forces on foundations.

Fig. 4.2 Uplift Piles

(c) Pile foundations are often required when scour around the foundations can cause erosion in spite of presence of strong, incompressible strata (such as sand, gravel, etc.) at shallow depths. In such cases, piles can be particularly effective in bypassing scourable strata and transferring loads to in erodible soil.

Fig. 4.3 Use of piles in scourable beds

(d) In areas where expansive or collapsible soil extends to considerable depth below the ground, pile foundations may be needed to ensure safety against undesirable seasonal movements of foundations.

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Fig. 4.4 Piles in expansive soils can control seasonal movements

Piles can be classified according to the materials of which they are made of. The main materials used in makings piles are timber, reinforced concrete and steel. Reinforced concrete piles are generally used in pile foundations for bridges. Concrete piles are either precast or cast-in-situ. Precast piles are installed into the ground by drilling, while cast-in-situ piles are bored pile. Under-reamed pile is a special type of bored pile having one or more bulbs. With the presence of under-ream, substantial bearing or anchorage is available. These piles find application in widely varying situations in different types of soils where foundations are required to be taken down to a certain depth. Diameters of bulbs are usually 2 to 3 times the diameter of the pile shaft. The under-ream increases the load carrying capacity of the pile. Such piles are claimed to be useful and economical in expansive soils like black cotton soils of India, where shrinkage and swelling of clays rules out the use of shallow spread footings.

Piles in foundations are usually installed in a group. The top of the piles are connected together with a stiff reinforced concrete slab called pile cap. All the piles are projected atleast 50 mm in the concrete of the cap.

A pile group having pile cap standing clearly above the ground is know as a free standing pile group. Free standing pile groups are used in river bridge crossings, where the top of the pile cap is usually kept at the level of L.W.L. A pile group in which the pile cap rests on the soil, partially or is fully buried below ground level is known as piled foundation. In a piled foundation, the pile cap may, under certain soil conditions, help in transmitting a part of the load to the soil on which it rests. Piled foundations are generally used for elevated highways and flyovers where pile cap is fully buried inside the ground to provide space for the roadways.

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Fig. 4.5 Free Standing Pile Group Fig. 4.6 Piled Foundation

4.2 DESIGN OF PILE FOUNDATIONS

If pile foundations are to be used for river bridge crossings, then the maximum scour depth for the stream has to be determined. The calculation of maximum scour depth is discussed in Section 3.3.1 of Chapter 3. For river bridge crossings, the top of the pile cap is placed at the level of L.W.L., while for non-river bridge crossings, the pile cap is fully buried into the ground with its top placed at ground level. Later, the forces and moments acting at the top of pile cap i.e. at the base of pier are calculated, during the analysis of pier. After calculating the forces and moments at the base of pier, the axial loads in the piles due to applied forces and moments are determined for an assumed size and configuration of piles in a pile group. The assumed pile properties are subsequently checked for safety.

4.2.1 UNDER-REAMED PILES

The diameter of under-reamed piles in bridge applications is generally not taken less than 300 mm. The length of the pile is selected as per the nature of the soil strata. For example, if a weak layer is underlain by a strong stratum at a reasonable depth, the length of the pile is so chosen such that the penetration of the pile into the strong stratum (bearing stratum) is a minimum of 5 times the pile diameter or width. On the other hand, if the weak layer extends to a considerable depth, the length of pile is so chosen as to obtain adequate pile capacity through skin resistance.

The design of under-reamed piles can be carried out with the aid of Table 1 of IS: 2911(Part III) – 19804. Table 1 of IS: 2911(Part III)– 19804 which is reproduced in toto as Table 4.3 in this thesis is a useful guide for selecting important parameter w.r.t. under-reamed piles viz. Diameter of pile shaft and under-ream, length of pile number of under-reams and the capacity of a selected configuration of under-reamed pile in compression, tension and

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lateral load carrying capacity. Usually a suitable value is selected as the diameter of the pile shaft. The diameter of the under-ream is taken as 2.5 times the diameter of pile shaft. Piles can have one or more than one under-reams, but it is not advisable to have more than two under-reams on one pile without ensuring their feasibility in strata needing stabilization of boreholes by drilling mud. For piles up to 300 mm diameter, the spacing between consecutive under-reams should not exceed 1.5 times the diameter of the under-ream. For piles of diameter greater than 300 mm, spacing can be reduced to 1.25 times the stem diameter. The top-most under-ream should be at a minimum depth of 2 times the under-ream diameter below the ground. In expansive soils, the top-most under-ream should not be less than 1.75 m below ground level. Clearance between the underside of pile cap embedded in the ground and the top under-ream should be minimum 1.5 times the under-ream diameter. Columns (3) & (4) of Table 4.3 provide minimum length for single and double under-reamed piles, respectively.

After fixing the dimensions of the under-reamed pile, the load bearing capacity of a single under-reamed pile is estimated. The pile capacity is compared with the maximum load expected on the pile to ensure an adequate margin of safety.

4.2.2 BORED CAST-IN-SITU PILES

The safe bearing capacity of a pile can be determined from its ultimate bearing capacity, by using a suitable factor of safety. The methods available to estimate the ultimate capacity of a single pile in compression can be grouped into the following categories:

i. Static-in-situ test. ii. Static analysis, iii. Dynamic analysis,

The static-in-situ test, popularly known as pile load test, is the only direct method for determining the allowable load on piles. It is considered to be the most reliable of all the approaches, primarily due to the fact that it is an in-situ test performed on a pile of prototype pile dimension. Pile load test is a costly test and is used to confirm whether the actual pile installed in the filed can take the load predicted by static or dynamic analysis. Dynamic analysis is used for determining ultimate capacity of driven piles. Static analysis, which is based on „soil mechanics‟ approach provides approximate estimates of pile capacity, as values of a number of parameters appearing in the static formulae are assigned empirically. For bored piles, static analysis is performed. A brief description of static analysis of piles is presented next.

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pile and through point bearing at the tip of the pile. Thus, the ultimate capacity of a pile may be obtained as,

, (4.1) where,

= total skin frictional resistance, = total point bearing resistance,

= unit skin frictional resistance, = unit point resistance,

= lateral surface area of the pile, and, = area of the pile tip.

Fig. 4.7 Load resisting mechanism in a pile

The unit frictional resistance, and the unit point bearing resistance, , depend on many factors such as the type of soil, method of installation and the pile material. Of these, the method of pile installation affects the pile capacity significantly, and also makes the estimation of pile capacity more complex. In order to clearly identify the effect of pile installation and account for the same, it is convenient to discuss separately the case of piles in cohesion-less soils and cohesive soils.

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Piles in Cohesion-less soil:

As suggested in Eq. 4.1, the pile capacity can be obtained as the sum of point bearing resistance and skin friction resistance.

Point Bearing Resistance:

The unit point bearing resistance in cohesion-less soil is given by,

, (4.2) where, = effective overburden stress at the level of the pile tip,

B = diameter or width of pile,

= density of the soil,

= shape factor, 0.4 for square or rectangular piles, and,0.3 for circular piles, and,

& = bearing capacity factors.

The second term in Eq. 4.2, is usually neglected, particularly in the case of long piles, as this constitutes an insignificant part of the total capacity. The first term in Eq. 4.2 implies that the base resistance increases linearly with depth. The bearing capacity factor, is a function of the angle of internal friction of soil, , and its value can be obtained from Fig. 1 of IS: 2911 (Part 1) – 19793, reproduced here as Fig. 4.8. The bearing capacity factor,

can also be read off from Table4.1.

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Table 4.1 Bearing Capacity Factor, ,

Angle of internal friction of soil

( , in ( ° ) 0 0.00 5 0.45 10 1.22 15 2.65 20 5.39 25 10.88 30 22.40 35 48.03 40 109.41 45 271.76 50 762.89

Skin Frictional Resistance:

The unit skin frictional resistance at any depth, z, below the ground level may be obtained as follows

, (4.3)

where, = the effective overburden stress at the depth considered, = angle of wall friction of the material of the pile,

= of the angle of friction of soil( ) = coefficient of horizontal stress.

The value of depends on the soil properties and the method of installation of the pile. The appropriate value of can be selected from Table 4.2

Table 4.2 Value of coefficient of horizontal soil stress (

Installation Method

Driven piles, large displacement 1 to 2 Driven piles, small displacement 0.75 to 1.25 Bored and cast-in-situ piles 0.70 to 1 Jetted piles 0.50 to 0.70

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Here, . (4.4)

Piles in cohesive soils:

The point bearing resistance and the skin frictional resistance of a pile in cohesive soil i.e. clay, can be determined as follows:

Point Bearing Resistance:

The unit point bearing resistance is obtained as follows,

, (4.5) where, = undrained cohesion at the pile tip, and,

= bearing capacity factor, generally taken as 9.

Skin Frictional Resistance:

The unit skin resistance is obtained as follows,

, (4.6) where, α = adhesion factor.

The adhesion factor depends on the cohesive strength of the soil. It can be obtained from Fig. 4.9.

Fig. 4.9 Adhesion factor for cohesive soils

The safe bearing capacity of a bored pile can be computed by dividing the ultimate bearing capacity of the pile by an appropriate factor of safety. The minimum factor of safety for static analysis is 2.5.

Bridge Substructure Analysis & Design

ABSTRACT

CONTENTS

LIST OF TABLES

LIST OF FIGURES