lwr

LWR ON BALLASTED DECK

BRIDGES- UIC APPROACH

S. C. Mishra Dy. CE( C ),KOTA,W.C.Rly.

D. W. Patre

Sr. DEN( N ),NGP,C.Rly.

INDEX

Sl. No.

Description Page No.

1 Introductory 1 2 Back ground for the report 1 3 Provisions in LWR manual 1 4 Provisions in UIC Code 2 5 Phenomenon of bridge with LWR 2 6 Parameters affecting Phenomenon-Bridge 3 7 Parameters affecting Phenomenon-Track 4 8 Track Behaviour 5 9 Behaviour of bridge 6 10 Action to be taken into account 8 11 Consequences for bridge and for track 9 12 Calculations with the use of graphs 11 13 Calculations with use of computer program 12 14 Conclusion 12 15 Specimen calculations 12

LWR on Ballasted deck bridges – UIC Approach 1.0 Introductory LWR track is being laid in a dedicated way due to its advantage over conventional jointed track. Ballasted deck bridges are also being extensively provided to have homogeneous running quality on bridges. Under the circumstances, laying of LWR on ballasted deck bridges is inescapable. But, as per LWR Manual very limited provisions are made for laying of LWR on ballasted deck bridges. 2.0 Back ground for preparation of this report While one of the author was associated with the commissioning of 54 km double line diversion between Talvadiya & Khirkiya stations in Iterasi- Khandwa section, LWRs were laid with expansion devices at the start and the end of each block section on the following major/ important bridges. Bridge No. Name of

Bridge Span

603/1 Chhota Tawa 9x18.30mcomposite girders with ballasted deck.

617/1 Ghoda Pachhad 6x18.30 m do 621/3 Ruparail 3x18.30 m do 630/1 Patal 7x18.30 m do 634 A/1 Kalamachak 9x18.30 m do Design calculations, based on UIC Code, for all the above bridges were submitted to RDSO and CRS for approval to lay LWRs on ballasted deck bridges. CRS approved laying of LWRs on the above ballasted deck bridges. Subsequently, RDSO also issued general instructions to lay LWR as per UIC provisions. These LWRs and also bridge structures are behaving satisfactorily. A specimen calculation for laying LWR on 6x18.30 m ballasted deck composite girder bridge is annexed with this report. 3.0 LWR on Ballasted deck bridge as per LWR manual Para 4.5.6, 4.5.7 Bridges with ballasted deck (without bearings and with bearings)

LWR/CWR can be continued over bridges without bearings like slab, box culverts and arches. LWR/CWR should not be continued over bridges with bearings.

4.0 CWR on ballasted deck as per UIC Code Contrary to the above, world over all railways are laying CWR on ballasted deck bridges with long spans. As per UIC Code -720 R (Laying & maintenance of CWR track)

i) CWR should ideally be installed on bridges when the bridge itself is in stress – free condition in order to minimize the effect of expansion of the bridge on the longitudinal forces with rails.

ii) Switches should not be located over bridge bearing. iii) It should be ensured that the presence of check rail or guard rails does not

generate additional Longitudinal forces in CWR track UIC code – 774-3R (Track/bridge interaction Recommendation for

calculations) It stipulates the effect of force generated in the bridge/abutment transition zones on the track alignment and stability of CWR track. This also stipulates the use of CWR track without expansion joints on bridges.

4.1.0 Provision of UIC code for CWR on ballasted deck.

1) It is preferable to avoid expansion device in the track but it should always be

inserted at the free end of the deck if the total additional rail stress or displacements exceed. The permissible values using the possibility of locating the fixed support at the middle of the deck, it is possible to increase the length of single deck carrying CWR.

- 60 m for steel structures carrying ballasted deck track (Max. length of deck with fixed bearing in the middle – 120 m)

- 90 m for structures in concrete or steel with concrete slab carrying ballasted deck track ( Max. length of deck with fixed bearing in the middle – 180 m)

2)The following deck configuration condition also permit laying of CWR on ballasted deck bridge.

a) The track on the bridge and at least on 100 m of the embankment of both sides of the bridge consists of CWR without a rail expansion of device.

(All the decks have the same static arrangement fixed support in the same position.) The number of decks is more than 4, even though the simplified rule can still be

applied for bridge with 4 decks or less, as they can give an over conservative estimate of support reaction.

In case of 35 degree C max temp. variation of decks, their length is less than 30

m.In case of 20 degree C max temp. variation of decks and no possibility of frozen ballast, their length is less than 60 m.

In case of temperature variation of deck between 35 degree C and 20 degree C the

value of maximum permissible length of the decks can be interpolated between 30 m & 60 m.

For reasons of life cycle costs and comfort, a railway bridge should be designed in

such a way that CWR is possible without rail expansion devices.

- One way of avoiding rail expansion devices on long bridges is to divide these bridges into separate deck.

- In case of a succession of simple deck bridges the effects of action can be reduced by shortening the length of the first and last decks. 4.2.0 Phenomenon of a bridge carrying CWR. The use of an expandable deck, capable of moving relative to the CWR track, introduces a discontinuity into the characteristics of the track bed. This discontinuity is responsible for relative movements between the track bed and the track as the deck expands and contracts, causing forces to be applied to the rails and the structure, as well as changes in the additional stresses due to forces induced by traffic loads. 4.2.1 Review of the principles governing CWR. In general, the rail is fixed to the sleeper by elastic fastenings, which apply a predefined clamping force to secure the rail to the sleeper. This clamping force is normally such that all the longitudinal movement of the rail is transmitted to the sleepers, the resistance to rail/sleeper sliding being greater than the resistance to longitudinal movement offered by the ballast, the rails are subject to longitudinal force. CWR includes a central zone where expansion and contraction are completely prevented and two breathing length at each end. 4.2.2 Effect of the presence of a bridge in the track. Introducing a bridge under a CWR track means that the CWR track is resting on a surface subject to the deformation and movements, hence causing displacement of track. Given that both track and bridges are able to move, any face or displacement that acts on one of them will induce forces on other. Interaction therefore takes places between track and the bridge as under. - Forces applied to a CWR track induces additional forces into the track and / or into bearing supporting the deck and movements of the track and of the deck. - Any movement of the deck induces a movement of the track and an additional force in the track and, indirectly, in the bridge bearings. 4.3.0 Parameter affecting the phenomenon -Bridge parameters 4.3.1 Expansion Lengths In case of a simple deck bridge with a simply supported deck or a continuous deck with the fixed elastic support at one end, the expansion length is the span length or the total length of the deck, If the fixed elastic support is located at some intermediate point, the deck is considered to have the expansion lengths, on either side of the fixed elastic support. More generally, the expansion length is the distance between the thermal centre point and the opposite end of the deck. The position of the thermal centre point depends on the position and type of support.

Four types are possible, fixed elastic, moving, moving friction and elastic. (fixed elastic supports consist of a fixed bearing on a flexible structure on pier or abutment) which elastic support consist of a flexible bearing on a flexible substructure. In case of a succession of decks, the total expansion length at a certain joint is the sum of the expansion lengths of the nearest decks. 4.3.2 Span length Because of the fact that the vertical loading on the deck causes a longitudinal displacement of the deck end, the span length influences the track / bridge interaction. 4.3.3 Support stiffness The resistance of the deck horizontal displacement is a fundamental parameter as it affects all the interaction phenomena. This factor is determined primarily by the total stiffness of the supports. The total support stiffness is composed of the stiffness of each support. The stiffness of each support is composed of the stiffness of the bearing and of the various components of the support, the pier, the base the foundations and the soil in which they are embedded. 4.3.4 Bending stiffness of the deck The bending stiffness of the deck is the parameter, is as much as the vertical deformation of the deck displaces the upper edge of the deck in the horizontal direction. This deformation also generates interaction forces. 4.3.5 Height of the deck The distance of the upper surface of the deck slab from the neutral axis of the deck and the distance of the neutral axis from the centre of rotation of the bearing affecting the interaction phenomena due to the bending of the deck. 4.4.0 Track Parameters 4.4.1 Cross sectional area of the rail The cross sectional area of the rail is an important parameter. 4.4.2 Track Resistance The resistance of track per unit length to longitudinal displacement is an important parameter. This parameter depends on large number of factors like, whether track is loaded or unloaded, ballasted or not, the manner in which track is laid, standard of track maintenance etc.

4.5.0 Track behaviour Behaviour of the track on its supporting structure, taking into account the type of track, is arrived at. The relationship between track displacement and force applied depends on the track structure adopted, the standard of maintenance, any defects that may be present, the vertical load applied to the rail and the frequency of the forces applied. 4.5.1 Ballasted deck. The resistance to longitudinal displacement depends on the following.

- The resistance of the rail to displacement relative to sleeper. This resistance is provided by rail fastening and its magnitude depends on the efficiency of the clamping action.

- The resistance of the sleeper / rail assembly to displacement relative to the deck. This resistance is provided by the tendency of the ballast to resist any movement of the sleeper and by the friction between ballast and deck.

4.5.1.1 General principle governing track behaviour The resistance of the track to longitudinal displacement is a function of the displacement of the rails relative to its supporting structure . This resistance increases rapidly while displacement remains low, but remains virtually constant once the displacement has reached a certain magnitude. The resistance to longitudinal displacement is higher on loaded track than on unloaded. 4.5.1.2 Bilinear behaviour of the track The above can be replaced by bilinear functions as shown below : The relationship between resistance and displacement varies according to the type of track structure and maintenance procedure adopted. The conventional values assumed for ballasted deck, are as under :- Displacement Uo between elastic and plastic zones – Uo = 0.5 m for the resist of rail to sliding to the sleeper. Uo = 2 mm for the resist of sleeper in the ballast. 20 kN/m for unloaded, and 60kN/m for loaded track is taken normally. 4.6.0 Behaviour of bridge In order to study the track/bridge interaction on the bridge side the following aspects have to be taken into consideration –

1) The static arrangement of the bridge 2) The behaviour of the bearings. 3) The behaviour of the supports. 4) The total support stiffness. 5) The bending behaviour of the deck.

4.6.1 Static arrangement The static arrangement of a bridge is defined by the number of decks. The number of supports for deck the position of fixed and movable supports, the span length, the expansion length, and the positions of the rail expansion devices, if any, a)

Simply supported deck/no rail expansion device Simply supported deck/with rail expansion device. b)

Continuous deck/no rail expansion device fixed support at one end.

Continuous deck/with rail expansion device fixed support at on c) Continuous deck/no rail expansion device fixed intermediate support.

Continuous deck/with rail expansion device fixed intermediate support. d) Service of simply supported or continuous decks/no rail expansion device.

Service of simply supported or continuous decks/with rail expansion device. 4.6.2 Behaviour of the supports 4.6.2.1 Behaviour of the bearings The types of bearings used and their characteristics have a major effect on the resistance of the deck to displacement. In general the stiffness of a moving bearing is usually ignored. For more accurate calculations and the case of a moving bearing with a certain degree of elastic stiffness like elastomer bearing, the stiffness of the bearing should be taken into account. The value of coefficient of friction may very from 0% to 5 % 4.6.2.2 Resistance of the supports to horizontal displacement The stiffness of the support including its foundation, to displacement along with longitudinal axis of the bridge is given by H (kN) K= -------- �i (cm) �p = displacement the head of the support due with �i=�p+�o+�h+�a to elastic deformation. �o = displacement the head of the support due to rotation of the foundation. �h = displacement at the support due

to horizontal movement of the foundation. �a = The relative displacement between the upper and lower part of the bearing. The value of the displacement component is determined at the level of the bearing or at the level at which other structural assemblies are connected to the supports. 4.6.2.3 Foundation stiffness When calculating the stiffness of the foundations, it is necessary to select the modulus of elasticity appropriate to the various load case. (temperature variations, braking/ acceleration), taking into account the characteristics and geo-technical parameters of the site. The static modulus of elasticity is used when calculating temperature variation and dynamic modulus when calculating the effect of braking and acceleration. 4.6.2.4 Total support stiffness Usually, for braking actions, calculations of total support stiffness should take account of the contributions of all support that resist the longitudinal displacement. In most cases one single fixed support is considered, when there are more than supports contributing to the total stiffness, the sum of their contributions should be considered. In the case of bearings, the total elastic support stiffness is the sum of all the supports, and the locations of the effective resulting fixed point should be determined. The total stiffness k tot is thus given by the �kj + 2�ftj kN/cm where kj is the stiffness of the support with fixed bearings and ftj is the friction resistance of the movable bearings. 4.6.2.5 Bending behavior of the deck Vertical traffic load on the bridge generate large track/bridge interaction forces as a result of deck bending, which causes longitudinal displacement of the upper edge of the deck end. The interaction effects depend primarily on the flexibility of the deck and on the position of its neutral axis, but are also influenced by the stiffness of the fixed elastic support and by the height of the deck. Horizontal displacement of the deck due to traffic load remains constant when considered along the neutral axis but varies when measured at the upper point of slab supporting the track. The flexibility of the fixed support reduces the displacement measured above by a constant amount equal to the backward displacement of the support. The displacements, which result in interaction between the deck and track generate large forces in the track and supports.

4.6 Actions to be taken into account 4.6.1 Introduction The cases that could lead to interaction effect are those that causes relative displacement between the track and the deck. The concern cases are as under-

1. The thermal expansion of the deck only in the case of CWR or the thermal expansion of the deck and of the rail, whenever a rail expansion device is present.

2. Horizontal braking and accelerating forces. 3. Rotation of the deck on its support is a result of the deck bending under

vertical traffic on the load. 4. Deformation of the concrete structure due to creep and shrinkage. 5. Longitudinal displacement of the support under the influence of the thermal

gradient. 6. Deformation of the structure due to the vertical temperature gradient. In most cases the first three effects are of major importance for bridge design.

4.6.2 Action due to changes in temperature The following aspects of temperature variations should be considered. - Change in the uniform component of the temperature which causes a change in length in a free moving structure. - Differences in temperature between the deck and the rails in the case of track with an expansion device. The reference temperature for a bridge is the temperature of the deck when the rail is fixed. The temperature of the bridge does not deviate by more than + 35 degree Celsius from the reference temperature and temperature of the rails does not deviate by more than + 50 degree C. The difference in temperature between deck and rail does not exceed + 20 degree C (In case of track with expansion device). In case of CWR a variation of the temperature of the track does not cause a displacement of the track and thus a there is no interaction effect due to variation in the temperature of the track. 4.6.3 Action due to braking and acceleration The braking and acceleration forces applied at the top of the rail are assumed to be distributed evenly over the length under consideration with the following standard values. Accelerating = 33kN per meter /per track Braking = 20kN per meter/per track. These values are used for all types of track CWR or jointed, with or without expansion device.

The braking acceleration forces are to be combined with the corresponding vertical loads. In case of a bridge carrying two or more tracks, the acceleration forces on one track are to be added and the braking forces on the other. Only two tracks need to be considered. The values for acceleration and braking as per Bridge Rules should be adopted . 4.6.4 Action due to bending of deck Vertical traffic loads cause the deck to bend, which in tern causes rotation of the end sections and displacement of the upper edge of the deck end. These phenomena need to be considered for both deck ends. 4.7 Consequences for the bridge and for the track All the above criteria to be satisfied are given below. 4.7.1 Combining the load case effect For the calculation of the total support reaction and in order to compare the global stress in the rail with permissible value set by the railway, the global effect �R is calculated as under : �R = �R(�T)+�R(breaking)+�R(bending) The values of the coefficients for the support reactions, � , �, � are combination factors. For the calculation of the global values of rail stresses and displacement, � , � and � all have the value 1 for continuous or simply supported decks. 4.8.2 Permissible additional stresses in continuous welded rail on the bridge Total possible value for the increase of rail stresses due to the track/bridge interaction. The maximum permissible additional compressive rail stress in 72 N /mm2. The maximum permissible additional tensile rail stress is 92 N/mm2. 4.7.2 Absolute and relative displacements Limits have to be placed on the displacement of the deck and track in order to prevent excessive deconsolidation of the ballast because if these were to occur, the conditions mentioned in the previous section might no longer be met. The displacement limits also play a roll in limiting indirectly the additional Longitudinal stress in the rail. These limits are as under :- The max. permissible displacement between rail and deck or embankment under breaking and / or acceleration forces is 4 mm.

For the same breaking / or acceleration forces the max. absolute horizontal displacement of the deck �abs is +/ - 5 mm if the rails run across one or both ends of the bridge, embankment transition. The max. permissible absolute horizontal displacement of the of the deck end without the expansion device due to vertical bending is 10 mm. In case of CWR on ballasted track with expansion devices, the maximum permissible absolute horizontal displacement on the deck under the same loads is 30mm. 4.7.3 End Rotations of the deck The end rotation of a bridge deck due to traffic loads is an important factor determining satisfactory track / bridge interaction behaviour. In order to determined an appropriate limit to the end rotation of the bridge deck it is necessary to consider also other criteria such as dynamic effect (ballast maintenance ) and passenger comfort. Under vertical load, the displacement of the upper edge of the deck end must also be limited, in order to maintain ballast stability. Obviously, the effects of this displacement must be added to the effect of temperature variation and of braking/ acceleration. This limit results in a maximum permissible value for deck end rotation. In case of CWR ballasted track, the permissible displacement between the top of the deck end and the embankment or between the top of the consecutive deck ends due to vertical bending is 8 mm. 4.8.6 Support reactions The interaction results in horizontal support reaction at the fixed elastic supports, and these must be taken into account along with conventional support reaction when calculating the structure support. 4.8.5 Rail expansion devices It is preferable to avoid expansion devices in track, but one should always be inserted at the free end of the track if the total additional rail stress or the same mentioned displacement exceed the permissible values. Using the possibility of locating the fixed support at the middle of the deck, it is possible to increase the length of a single deck carrying CWR. The proof will lead the following conclusion, the maximum expansion length of a single deck carrying CWR without expansion device will be 60 m for steel structure carrying ballasted track (with fixed bearing in the middle 120 m). 90 m for structure in concrete or steel with concrete slab carrying ballasted deck (with fixed bearing in the middle 180 m) It may be necessary to fit an expansion device in the track even when the calculated stresses and displacements do not exceed the permissible values. This is the case when daily variation of the length of the deck exceeds the permissible values taking into account the track maintenance conditions. ( � L is generally between10 and 15 )

4.9.0 Calculations with the use of design graphs Calculations can be done using the design graphs to get interaction effect. 4.9.1 Calculations without interaction In case of continuous welded rail, the max. Permissible additional compressive rail stress due to temperature variation of the deck, breaking/acceleration and deck end rotations is <= 72 N/mm2. The max. permissible additional tensile rail stress due to temperature variation of deck ,braking/acceleration and deck end rotation is 92 N/mm2. The maximum Permissible absolute horizontal displacement of the deck due to breaking / acceleration is 5 mm. The maximum permissible absolute horizontal displacement of the top of the deck ends due to vertical bending ( including dynamic factor ) and calculated without considering any interaction is 10 mm. In case of a deck carrying CWR with an expansion devices at one end. The maximum permissible absolute horizontal displacement of the deck due to breaking / acceleration is 5 mm. The maximum permissible absolute horizontal displacement of the top of the deck end without the expansion device due to vertical bending is 10 mm. In case of a deck carrying an expansion device at both ends or with jointed track the maximum permissible absolute horizontal displacement of the deck due to breaking/acceleration is 30 mm. 4.9.2 Calculations with interaction The permissible displacement of 5mm due to breaking/acceleration is also to be considered as a permissible relative displacement between two consecutive decks. 4.10.0 Calculations with a computer program Computer program has been developed for track/bridge interaction analysis which has been validated by field tests. With the help of this program simplified or complete analysis of separate or simultaneous effects of thermal variations, braking/acceleration forces, vertical deflections can be obtained.

4.11 Conclusion As per provisions stipulated in UIC code, based on theoretical analysis of the bridge and track , the LWR can conveniently be laid on ballasted deck bridges. Detailed calculations are required to be made on case by case basis to know the additional forces acting in bridge and also to know the LWR/bridge interaction and vice – versa. The calculations can be done taking into account LWR forces as per UIC code and other forces as per Bridge Rules. UIC report 774-3R can be utilized for interactive design graph , this can also be done by computer program developed for track- bridge analysis as field tests have validated the results of theoretical analysis. For utilization of the above UIC report, a large number of bridge and track parameters along with structural arrangements with load disposition and permitted displacement is required. It is because of the difficulty in obtaining the above data for each and every bridge and rigorous analysis to be done, that LWR Manual has restricted laying of LWR on ballasted deck bridge with bearings. 4.12 Specimen calculation Calculation sheets of ballasted deck bridge at bridge No.617/1 (chainage-33.25 Km) of Itarsi –Khandawa section, 6x18.30 m span on composite girders with ballasted deck is annexed for better appreciation.

TALVADIYA - KHIRKIYA MAIN LINE DIVERSION.

BRIDGE NO : 42 At km 33.26

RECAPITULATION TABLE AFTER ANALYSIS

Sr. No DESCRIPTION. Abutment Pier Wing wall Remarks

Prop. Rail level 269.295 S.B.C OF SOIL Prop. Formation Level 268.625 AT FRL = 50.00 Prop. Soffit of super str. 266.793 266.79 T/sq.mt Top of foundation 255.750 252.24 Bottom of foundation FRL 255.150 251.64

[1] Dimensional details.(a) (b) Batter from top to G.L : 1 in 7.500 10.00(c) Batter G.L to top of founda.: 1 in 1.250 10.000(d) Wodth up to face of abut. From back 8.419(e) Prop. Total width 8.419 4.800(f)

[2] (a) Pressure at found. level Max. pressure 46.479 55.368

Min pressure 6.216 2.213

(b) At top of foundationMax. pressure 41.959 101.846 Permissible stress Min pressure 5.727 -25.077 for M-15

Comp : 500 T/sq.m (c ) At ground level Tension : -50 T/sq.

Max. pressure 71.748 For M-20 it will Min pressure -19.310 be more.

Prepared by Checked by

TALVADIYA - KHIRKIYA MAIN LINE DIVERSION.NEW BRIDGE NO : 42 , 6x18.3 MT.

BR-42 , CH : 33255.

Bridge no : At km Proposed Type42 33.255 18.30 GB 1797 Total depth T-beam

1.1 DESIGN DATA AND ASSUMPTIONS

[A] SUPER STRUCTUREClear span 18300.00 mmDist. Up to inner face of dirt wall 765.00 mmDist. Up to center of pier 750.00 mmSpan from inner face of dirt walls 19.815 mtOverall length of slab[deduct exp.joint 25mm] 19777.50 mtDetails of Girder 1797.00 1797.00 mm at ends

[a] Top flange width mm PLATE GIRDER [b] Top flange thickness mm AS PER RDSO DRG. [c] Sloped th. Of top fl. mm WT 12 T PER GIRDER [d] Web th. mm

[e] Web ht mm[f] Bottom bulb width mm[g] Bottom bulb ht mm[h] Bot. Bulb incl ht mm[i] ht of end st. section mm

Thickness of pedestal with bearing pad 0.087 mmEffective span [ proposed ] 18.985 mtDist of centre of bearing from face of dirt wall 0.415 mtProposed clear span will be 18300.00 mmWidth of pier 1500.00 mmSpan from centre of pier to inner face of dirt wall 19815.00 mm

Inner span in case of more than one span 19.815 mtEnd span [ or single span ] 19.815 mtEffective span 18.985 mt

Rail level [ proposed ] 269.295 Formation level [ proposed ] = Rail level -0.67 268.625 Existing Natural Ground level at abutment 258.150 mtTop of deck level [ top of slab ] = formation lvl 268.625 mtOverall width of deck [ out to out of balast retainer ] 12.10 mtOver all width of slab without ballast retainers 11.70 mtOverall depth of super structure 1797.00 mm

[B] SUB-STRUCTUREAbutment RL in mt

Top of . bed block 266.741 Th. of pedestal with bearing 0.00Depth of. Bed block 0.525RL of start of rear batter 268.382 ABUTMENT PIERTop of prop. bed block 266.741 Th. of prop. bed block 0.525 1.00Bottom of prop. bed block 266.216 mt

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BR-42 , CH : 33255.

Formation Lvl 268.625 mt Bed level 258.150 mt Projections in foundations at , RL of end of front batter 258.150 mt Horizontal Vertical thk. Actual depthTop of foundation 255.750 mt projection from FRL of projectionDepth of bottom of found. 0.600 mt Rear 0.30 0.60 0.600Bottom of foundation 255.150 mt 1.200Barrel length reqd. 12.10 mt 0.900Height of rear batter 12.632 mt 0.600Width of rear batter 3.609 mt 0.300Thk. of central portion 1.215 mt Front batter width mt Thk. of prop. dirt wall 0.450 mt Rear batter 1 in 3.5

Soil Bearing Capacity as per the Soil Investigation Report = 50.0 T/m2

SOIL STRATA IS BASALIK HARD ROCK.1.2 CALCULATION FOR HORIZONTAL FORCES BASED ON UIC - 774 - 3R

SIMPLY SUPPORTED DECK WITH ONE ELASTIC FIXED SUPPORT AND NO EXPANSION DEVICE. DECK LENGTH = 19.82 DEFLECTION MAX. = 9.50 mm, assumed as L/2000

-1 Φ = Tan [ 9.50 x π ]

[ 9907.50 x 180.00 ]

= 0.00095887 RADIANS

ΦH = 0.00095887 x 1797.00 = 1.72 mm

1.2.1 RESISTANCE OF THE UNLOADED TRACK : A displacement of 2 mm and resistance of 20 kn/mt

RESISTANCE OF THE LOADED TRACK : A displacement of 2 mm and resistance of 60 kn/mt

Eventhough, both the supports are with sliding bearing , for analysis purpose , one support is treated as elastic fixed support.

The stiffnes of the fixed support K :

Tractive and the breaking forces over the bridge will be from Bridge rules will be,75.00 + 50.60 T for 20 mt span

This force will be distributed over two piers, hence force per pier will be , half of above.= 62.80 T

Hence force per metre = 62.80 / 19.82 = 3.17 T/mt= 31.69 kn/mt

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BR-42 , CH : 33255.

β = Reduction factor = 0.50 from Table - 1

hence K = 31.69 x 0.50 x 19.825.00

= 62.80 and 62.80 / 19.8 = 3.17

= 3.17 LSUPPORT REACTION [1] F SUPPORT : Temperature From App-A , fig : 6 , for span = 20 mt , K2 - k40 , support reaction = 200.0 Kn ∆T Deck 35 degree F support ∆T Deck = 200.00 Kn Hence for 17 degree = 200.00 x 17.00 / 35.00 = 97.1 Kn

[2] F SUPPORT breaking From Appendix : A , figure 3 , for span = 20 mt , K2 - k60 , support reaction = 50.0 Kn

∆T Deck, breaking = 50.00 Kn628.00

Hence for double track = ----------------------- x 50.00 20.00 x 19.82

= 79.23

[3] F SUPPORT : Vertical bending of deck. [ For calculation of Gamma, detailed, drawings etc are needed, however, following has been taken, From figure B-5 , for span = 20 mt , Gamma 0.5 / K-2 , support reaction = 100.0 Kn

∆T Deck, breaking = 100.00 Kn

Hence total reaction = 97.14 + 79.23 + 100.00 = 276.4 Kn= 27.6 T

FOR ABUTMENT THE ABOVE WILL BE HALF i.e = 13.8 T The above reactions will be considered due to continuation of LWR, along with forces due to tractive & Breaking.

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BR-42 , CH : 33255.

0.45

[10] DI 0.415R

T [15] BED

W BLOCK 0.525

1.215(S1)

[14][2] 8.066

[9] 8.066 [11]

[13]

'G.L.5.269 1.0750

[3] 2.400 (S2) [12]

[1](S3)

0.300 3.609 1.2150.241 1.0750 1.20

[5] [4] 0.60 1.92 0.300.600 0.60

SURCHARGE ACTIVE 8.419

EARTH PRESSURE C/S OF ABUTMENT

ALL THE MOMENTS ARE CALCULATED FROM THIS POINT.[C] DETAILS of wall Thickness of prop. dirt wall = 0.45 = 450.0 mm Proposed dist. From face of dirt wall to center of bearing = 415.00 mmMin. Distance from center of bearing to edge of abutment = 350.00 mm

-------------- hence min width required at abutment top for prop. Bridge = 1215.00 mmWidth of abutment at bed blocl level = 1.215 = 1215.0 mm

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BR-42 , CH : 33255.

DETAILS OF BATTER PROPOSED IN FRONT PORTION.Height from bot. of proposed bed block to end of 1st batter = 8.066 Height from bot of bed block to GL = 8.066

Th. at G. L. with Batter of 1 in 7.5 = 8.066 / 7.500 += 1.0750 +

Width of batter up to end of 1st batter will be = 1.0750 mtHeight between end of 1st batter to top of exist. Foundation = 2.400So, thickness With batter of 1 in 1.25 will be = 2.400 / 1.25

= 1.920Additional width in front from face of abutment will be = 1.075 + 1.920

= 2.995 mtProposed projections in foundations at front portion Horizontal Vertical projection depth of itFront 1st 0.30 0.60Front 2ndFront 3rdFront 4th PCC

0.30Widrh of foundation up to face of abut. = 8.419 + + +

= 8.419 mt Total width at FRL 0.300 + 3.609 + 1.215

[Rear proj.] [Rear batter ] [Central portion]

+ + 1.0750 + 1.920 +['Front batter] [Batter GL to top of found.]

Projections at bottom. + 0.30 + + + [ all projections in the front ]

Total prop. Width at FRL = 5.124 + 2.9950 + 0.30 = 8.419HENCE, THK. In front after face of abut. AT FRL = 2.9950 + 0.3000 -

= 3.295 mt[D] LOADING : MBG loading [E] EARTH PRESSURE : as per codal provisions at abutment.

Field density of soil 1.70 T/mt2

Saturated weight of soil 1.80 T/mt2

1.2 REFERENCES( 1 ) Tender conditions( 2 ) IRS Bridge rules( 3 ) IRS code of practice for design of foundation & Sub structure

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BR-42 , CH : 33255.

2.0 NORMAL LOADS2.1 Super imposed dead load in T/mt

(a) Ballast retainer 2.0 x 0.105 x 0.05 x 0.75 x 2.50 = 0.020(b) Wearing coat 11.700 x 0.075 x 2.500 = 2.194(c) Ballast 400 Max 11.700 x 0.400 x 2.200 x 1.00 = 10.296(d) PSC sleepers 2.00 x 0.810 = 1.620

rails etc i.e P. way----------------

Total load in T/mt of deck width 14.13However, 14.13 / 1.00 = 14.13As for load of p.way, in normal practice of railway, load taken is = 6.75 T/mt Hence total load 2.0 x 6.75 x 19.82 = 267.50 T From Central Span 6.75 x 19.82 = 267.50 T From End Span

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BR-42 , CH : 33255.

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BR-42 , CH : 33255.

2.3 TOTAL DEAD LOAD OF SUPER STRUCTURE Central span End span

S.I.D.L. 267.50 267.50GIRDERS 48.00 48.00End wideningINT. DIAPHRAGMS SLAB 131.87 131.87END DIAPHRAGMS

--------------- ------------------ Total load in T will = 447.37 447.37

2.4 SUB STRUCTURE2.4.1 SUB STRUCTURE for abutment :

The abutment sub structure has been provided with M-15 mass concretethe section of the same is as shown in the figure.

Volume Weight(i) Prop. Bed block 1.000 x 0.765 x 0.525 x 12.20 = 4.90 11.76(ii) Proposed Dirt wall 1.000 x 0.450 x 1.884 x 12.20 = 10.34 24.82 ----------------

Total volume = 15.24Hence total wt. = 15.24 x 2.40 = 36.58 T

2.5 LIVE LOAD :1 Max. live load reaction for foundation will be from span = 19.82 mt

From bridge rules for span = 19.82 Max live load on the above span = 200.00 T [ ref : IRS Bridge rules ] Hence for two tracks loaded = 400.00 T [ ref : IRS Bridge rules ]

For two span loaded condition span = 39.63Max live load on the above span = 356.70 T [ ref : IRS Bridge rules ] IN CASE OF 2 TRACK BRIDGE = 713.40 Hence wt on pier = 356.70CDA will not be considered for foundation design.

Tractive effort = 75.00 T Braking force will be = 50.60 T For two tracks force to be considered is 125.60As per cl : 2.8.2.3 , above horizontal force will be dispersed to Min. 16 T for BGHence horizontal force to be considered for single track will be 59.00 THence horizontal force to be considered for double track will be 93.60 T

hence reactiom on abutment will be half of the above = 46.80Additional force of continuation of LWR will be = 13.82Horizontal force at abutment will be = 60.62 T

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BR-42 , CH : 33255.

FOR PIER : 2 span loaded condition will govern the design.Hence , Tractive effort = 100.00 T Braking force will be = 83.20 T For two tracks force to be considered is 183.20As per cl : 2.8.2.3 , above horizontal force will be dispersed to Min. 16 T for BGHence horizontal force to be considered for single track will be 84.00 THence horizontal force to be considered for double track will be 151.20 T

Hence horizontal force at pier will be 75.60 TAdditional force of continuation of LWR will be = 27.64 Hence horizontal force at pier will be = 103.24 T

2.6 EARTH PRESSURE, EARTH LOAD, SURCHARGEAngle of internal friction of earth filling = 30 0

= friction between wall and earth fill = 20 0 i = Surcharge = 0

α = Angle of earth face with vertical = degreeusing coulomb's theory

φ = 30.00

α =

δ = 20.00

Ι =

Cos2 ( φ−α ) = 0.750

Cos ( α +δ ) = 0.940

Sin ( φ+δ ) = 0.766

Sin ( φ+Ι ) = 0.500

Cos ( α −δ ) = 0.940

Cos ( α−Ι ) = 1.000

Cos ( δ ) = 0.940

SIN ( δ ) = 0.3420.75

= ½ 2

0.77 x 0.50 0.94 1.0 + 0.94 x 1.00

0.75 = 2

0.94 1.00 + 0.64

( )( ) ( ) ( )

( ) ( )[ ]2coscossinsin2

2

1cos cos

cos

ii

ka−⋅−−⋅+++

−=

αδαθδθδαα

αθ

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BR-42 , CH : 33255.

= 0.2974

Hence Ka = 0.297 This force will act at normal to earth face abut. by angle delta Hence horizontal component = 0.297 x cos (20) = 0.2795 And vertical component of earth pressure =

0.297 x Sin (20) = 0.10

Earth pr. coeff. Kh = 0.27952.6.1 Earth pressure on abutment system for foundation pressure check & design

Top of dirt wall = 268.625Formation LVL. = 268.625GL / Bed level = 258.150 D. from form TO GL = 10.475 mtBottom of abut. Foundation FRL = 255.150 D from form TO FRL = 13.475 mt RL of top of foundation = 255.750 D from form TO TOF = 12.875Ht. Between GL & FRL = 3.000 As the bridge is with two tracks Surcharge pressure at top = 4.567 X 0.2795 = 1.276 T/mt2

[ 13.7 / 3 ] Ka

Surcharge pressure at found. 0.832 X 0.2795 = 0.232 T/mt2

13.7/(3+depth up to bottom of found.)

Surcharge pressure at GL 1.017 X 0.2795 = 0.284 T/mt2

13.7/(3+depth up to ground level )

Sur. Pr. at top of foundation 0.863 X 0.2795 = 0.241 T/mt2

13.7/(3+depth up to top of foundationl )

Hence ordinate of triangular force 1.276 - 0.284 = 0.992

Pa at top of dirt wall = 0.00 = Pa at G.L = 10.475 X 0.279 X 1.800 = 5.269 hence Pa at foundation = same below G.L due to passive = 5.269 Dist between G.L to foundation = 258.150 - 255.15 = 3.000 mt

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BR-42 , CH : 33255.

Formation level 268.63

10.475

G.L 5.269 258.152.400

Top of found. 255.75 5.269 0.600 Bot. of found. 255.15

Active earth pr. Diagram.

Hence total pressure at foundation lvl[1] From Surcharge (a) Ractangle 0.232 X 13.48 = 3.13

Acting at height/2 = 13.475 / 2.00 = 6.74 i.e RL = 261.89 mt

(b) Triangle 1.044 x 13.48 x 0.50 = 7.03 Acting at 2 h/ 3 = 2 x 13.475 / 3.00 = 8.98

i.e. R.L. = 264.13 mt[2] From Active earth pressure (a) Triangle up to G.L = 0.50 X 5.269 X 10.475 = 27.60

Acting at h/3 from GL = 10.475 X 0.33 = 3.492i.e. R.L. = 261.642 mt

(b) Ractangle below GL 1.00 x 5.269 x 3.000 = 15.81 Acting at h/2 = 3.000 / 2.00 = 1.500 i.e. R.L. = 256.650 mt

[3] Vertical component of earth pressure Total earth pressure on back face of the wall is = 27.597 + 15.807 = 43.404 Total EP on back face of the wall at TOF is = 27.597 + 12.646 = 40.242 Total EP on back face of the wall at GL is = 27.597 = 27.597

HENCE, Vertical component of earth pressure will be = 43.404 / 0.279 x 0.102

= 15.794 TVertical component of EP AT Top of found. = 40.242 / 0.279 x 0.102

= 14.644 TVertical component of EP AT GL = 27.597 / 0.279 x 0.102

= 10.042 TActing at back surface of earth face i.e at centre of back inclined portion

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BR-42 , CH : 33255.

3.0 ANALYSIS AND DESIGN FOR ABUTMENT

3.1 Summary of loads and moments at bottom of abutment structure[1] Moment at toe of wall i.e end point on soil side

Data: Abutment RL in mtTop of bed block = 266.741 Thk. of abut bed block 0.53Bottom of bed block = 266.216 mt so, height of dirt wall = 1.88Formation Lvl = 268.625 mtBed level = 258.150 mtTop of foundation = 255.750 Projections in foundations at ,Depth of bot. Of found. = 0.600 mt Horizontal VerticalBottom of foundation = 255.150 mt projection depth of itBarrel length reqd. = 12.100 mt Rear 0.30 0.60Top of dirt wall = 268.625 Front 1st

front 2ndTop of exist. Bed block = 266.741 Top of exist. Found. = 255.750Hence ht of exist. Back inclined portion = Central Exist. Th of abut. = 1.215 mtHt of inclined portion = 266.74 - 255.750 = 10.99 mt

Width of rear inclined 3.609 width of foundation Central portion 1.215 [a] Top of foundation = 4.82Front inclination 1 in [b] Bottom of foundation = 5.12Width of back projection 0.300 [c] at first projection = 5.12Width of front 1st proj. [ Top of found. + rear projection + front 1st proj]

Width of 2nd projection [d] at 2nd projection = 5.12 Width of 3rd projection [e] at 3rd projection = 5.12

Centre of bearing from toe = 0.300 + 3.609 + 0.450 + 0.415

[Rear projec.] [Rear batter] [Dirt wall ] Dist. From face of dirt wall]

= 4.774 i.e load point of super structure

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BR-42 , CH : 33255.

Abutment Top RL = 266.216 Bot RL = 255.150 Height of abut. 11.07 Dist of

Length Width Height Density Weight C.G from toeFront triangle [1] 12.10 10.99 2.40Central portion [2] 12.10 1.22 10.99 2.40 387.80 # 4.517Rear Incl.portion [3] 12.10 1.80 10.99 2.40 575.96 # 2.706Bottom block : [4] 12.10 4.82 0.60 2.40 84.05 # 2.712Rear projection [5] 12.10 0.30 0.60 2.40 5.23 # 0.150Wt. of soil on projectionOn rear projection [13] 12.10 0.30 10.99 1.70 67.83 # 0.150On rear inclined [14] 12.10 1.80 10.99 1.70 407.97 # 1.503Ractangle [15] 12.10 3.91 1.88 1.70 151.49 # 1.955

EARTH PRESSURE Pressure Acting at Total pr. L.A from toeDue to surcharge [ 9] 12.10 3.131 261.89 37.89 6.737Surch. Triangle [10] 12.10 7.032 264.13 85.09 8.983Earth pre. Upto GL [11] 12.10 27.597 261.64 333.92 6.492Earth pr GL to FRL [12] 12.10 15.807 256.65 191.27 1.500

WT. AND MOMENT FROM FRONT PORTION OF M-25 CONC. Provided after face of abutment wall

Total pr. L.A from toe Triangle up to GL [ S1 T] 12.10 0.5375 8.066 2.40 125.90 5.482Rectangle G.L to top of f.[ S2] 12.10 1.075 2.400 2.40 74.92 5.662Triangular [S3] 12.10 0.960 2.400 2.40 66.91 6.839[ Projection - 1 [ S 4 ] 12.10 3.295 1.200 2.40 114.82 6.772[ Projection - 2 [ S 4 "] 12.10 3.295 0.900 2.40 86.12 6.772[ Projection - 3 [ S 5 ] 12.10 3.295 0.600 2.40 57.41 6.772 PCC projection has been avoided in taking weight. width of foundation at foundation RL up to face = = 5.1240width at front due to proposed batter & steps = = 3.2950

Total width at foundation 8.4190

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BR-42 , CH : 33255.

[2] ANALYSIS FOR ABUTMENT FORCES TAKING MOMENT AT TOE OF WALL AT FRL

Sr. Load Vertical Lever arm BendingNo. Forces Parallel Perpendicular from toe moment

to Traffic to Traffic of wall at RL 255.150

1 Dead load of super

structure 223.69 4.774 1067.882 Live load 200.00 4.774 954.80

Footpath load 3 Sub structure

(a) Dirtwall 25.86 4.059 104.96(b) Return wall(c) Pedestal / Bed block 12.25 4.774 58.48(d) Abut.cap 4.217(e) Abutment

Front triangle [1]Central portion [2] 387.80 4.517 1751.51

Inclined portion [3] 575.96 2.706 1558.54Bottom block : [4] 84.05 2.712 227.95Rear projection [5] 5.23 0.150 0.78

4 Earth pressure [9] 37.89 6.74 255.28[10] 85.09 8.98 764.42[11] 333.92 6.49 2167.70[12] 191.27 1.50 286.90

5 Wt of soil on [13] 67.83 0.15 10.17

back projections [14] 407.97 1.50 613.18[15] 151.49 1.95 296.09

Vertical comp of EP 15.79 2.10 33.24

6 Front portion of batter & steps

Sec. up to G.L [ S-1 ] 5.1240[ S1 T] 125.90 5.4823 690.24

G.L to top of fond.[ S2] 74.92 5.6615 424.18Triangular [S3] 66.91 6.8390 457.58

[ Projection - 1 [ S 4 ] 114.82 6.7715 777.53[ Projection - 2 [ S 4 ] 86.12 6.7715 583.15[ Projection - 3 [ S 5 ] 57.41 6.7715 388.77

[ Projection - 4 7 Longitudinal forces

(a) breaking 60.62 11.59 702.63

Horizontal force

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BR-42 , CH : 33255.

1 Normal:1+2+3++ 7 2684.00 708.79 14175.95With live load

2 Normal : 1+3+4+5+6 2484.00 648.17 12518.52Without Live load BREAKING AND LL ARE DEDUCTED

Case : 1 X bar = 5.28

Eccen. = B/2 -Xbar = 4.21 - 5.28 = -1.07Hence absolute e = = 1.07Total width B = 8.419 So, B / 6 = 1.40

Comparing B/6 & Eccentricity ,provided Total B = 8.42 mt. is in order

Hence Eccen = 4.21 - 5.28 = -1.07

Hence Pmax = 2684.00 [ 6.00 X 1.072 ] ------------- -------------- X 1.00 + ------------------------------------]

12.10 x 8.419 [ 8.419 ]

Pmax = 26.35 X 1.76 = 46.48 T/mt2 Which is less than 50.0(SBC)

Pmin = 26.35 X 0.236 = 6.216 T/mt2 Which is greater than 0.00Hence Safe

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BR-42 , CH : 33255.

3.2 Summary of loads and moments at GL for abutment structure [1] Moment at toe of wall i.e end point on soil side

Data: Abutment RL in mtTop of bed block = 266.741 Th. of abut bed blockBottom of bed block = 266.216 mt so, height of dirt wall = 1.88Formation Lvl = 268.625 mtBed level = 258.150 mtTop of foundation = 255.750 Barrel length reqd. = 12.100 mt Top of dirt wall = : 268.625 Bottom of prop. bed block 266.216 Check given at Level = 258.150Central str. Th of abut. = 1.215 mt

Ht. of back inclined portion = 266.22 - 258.150 = 8.066 mtWidth of rear inclined 1 in 4 = 2.305 Total width of foundationCentral portion = 1.215 at Ground level = 4.59 = Inclined str. At GL 1.075Front portion after face of abut. = 1.075 Centre of bearing from toe = + 2.305 + 0.450 + 0.42

[Rear batter] [Dirt wall ] Dist. From face of dirt wall]

= 3.170 i.e load point of super structureCentre of bearing from toe 3.170 i.e load point of super structure

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BR-42 , CH : 33255.

0.45

[10] DIR

[15] T BED

W BLOCK

1.215[1]

[14][2] 8.066

[9] [11] [3]

[1A]

[13] 'G.L.

SURCHARGE ACTIVE 2.305 1.22 1.0750 LINE OF EARTH PRESSURE STRENGTHENING

C/S OF ABUTMENTALL THE MOMENTS ARE CALCULATED FROM THIS POINT.

Abutment Top RL = 266.741 Bot RL = 258.15 So RL of toe = 258.15Height of abut. Up to GL 8.59 Dist of C.G.

Length Width Height Density Weight from toeFront ractangle [1] 12.10 8.066 2.40 3.520

Front triangle [1A] 12.10 0.538 8.066 2.40 125.90 3.878Central portion [2] 12.10 1.215 8.066 2.40 284.60 # 2.912Inclined portion [3] 12.10 1.152 8.066 2.40 269.91 # 1.536Wt. of soil on projection

[14] 12.10 1.152 8.066 1.70 191.18 # 0.768[15] 12.10 2.305 2.409 1.70 114.20 # 1.152

EARTH PRESSURE Pressure Height Acting at Total pr. L.A. from toeDue to surcharge [ 9] 12.10 0.28 10.475 263.39 36.01 5.238Surcharge Triangle [10] 12.10 0.99 10.475 265.13 62.87 6.983

Active earth pressure[11] 12.10 5.27 10.475 261.64 333.92 3.492

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BR-42 , CH : 33255.

[2] ANALYSIS FOR ABUTMENT FORCES TAKING MOMENT AT TOE OF WALL AT GLSr. Load Vertical Lever arm BendingNo. Forces Parallel Perpendicular from toe moment





(a) Dirtwall 25.86 2.455 63.47(b) Return wall(c) Pedestal / Bed block 12.25 3.170 38.83 (e) Abutment

Front triangle [1] 3.520Front triangle [1A] 125.90 3.878Central portion [2] 284.60 2.912 828.77

Inclined portion [3] 269.91 1.536 414.68

4 Earth pressure [9] 36.01 5.24 188.61[10] 62.87 6.98 439.04[11] 333.92 3.49 1165.94

5 Weight of soil on back

inclined portion [14] 191.18 0.77 146.87[15] 114.20 1.15 131.59

Vertical comp of EP 10.04 0.5375 5.40

6 Longitudinal forces (a) breaking 60.62 8.59 520.78

1 Normal:1+2+3+4+5+6 1457.63 493.42 5286.86With live load

2 Normal : 1+3+4+5 1257.63 432.80 4132.17Without Live load BREAKING AND LL ARE DEDUCTED

Horizontal force

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BR-42 , CH : 33255.

X bar = 3.63Eccen = B/2 -Xbar = 2.30 - 3.63 = -1.33Hence absolute e = = 1.33Total width B = 4.59 B / 6 = 0.77

Width B = 4.595 mt.

Hence Eccentricity = 2.30 - 3.63 = -1.33

Hence Pmax = 1457.63 [ 6.00 X 1.330 ] ------------- -------------- X 1.00 + ------------------------------------]

12.10 x 4.595 [ 4.595 ]

Pmax = 26.22 X 2.74 = 71.75 T/mt2

Pmin = 26.22 X -0.737 = -19.310 T/mt2

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BR-42 , CH : 33255.

3.3 SUMMARY & ANALYSIS AT TOP OF FOUNDATION FOR ABUTMENT.

0.45

[10] DI 0.415R

T [15] BED

W BLOCK 0.53

1.215(S1)

[14][2] 8.066

[9] 8.066 [11]

(S1T)

[13] 'G.L.

5.269 LINE OF

[3] 2.400 [12]

[1]

0.300 3.609 1.215 1.92000.241 4.824 (S4)

[8]

SURCHARGE ACTIVE

EARTH PRESSURE C/S OF ABUTMENT

ALL THE MOMENTS ARE CALCULATED FROM POINT

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BR-42 , CH : 33255.

3.3.1 Earth pressure on abutment system for foundation pressure check & design

Top of dirt wall = 268.625Formation LVL. = 268.625GL / Bed level = 258.150 Depth from formation lvl = 10.475 mtBottom of abut. Foundation FRL = 255.150 RL of top of foundation = 255.750 Depth from formation lvl = 12.875Ht. Between GL & TOP OF FOUN. = 2.400

Surcharge pressure at top = 4.567 X 0.2795 = 1.276 T/mt2

[ 13.7 / 3 ] Ka

Surcharge pressure at top of found. 0.863 X 0.2795 = 0.241 T/mt2

13.7/(3+depth up to top of found.)

Pa at top of dirt wall = 0.00 = Pa at G.L = 10.475 X 0.279 X 1.800 = 5.269 hence Pa at foundation = same below G.L due to passive = 5.269 Dist between G.L to top of found = 258.150 - 255.75 = 2.400 mt

Formation level 268.63

10.475

G.L 5.269 258.152.400

Top of found. 255.75 5.269 0.600 Bot. of found. 255.15

Active earth pr. Diagram.

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BR-42 , CH : 33255.

Hence total pressure at foundation lvl[1] From Surcharge (a) Ractangle 0.241 X 12.875 = 3.10

Acting at height/2 = 12.875 / 2.00 = 6.44 i.e RL = 262.19 mt

(b) Triangle 1.035 x 12.875 x 0.50 = 6.66 Acting at 2 h/ 3 = 2 x 12.875 / 3.00 = 8.58

i.e. R.L. = 264.33 mt[2] From Active earth pressure (a) Triangle up to G.L = 0.50 X 5.27 X 10.475 = 27.60

Acting at h/3 from GL = 10.475 X 0.33 = 3.492i.e. R.L. = 261.642 mt

(b) Ractangle below GL 1.00 x 5.27 x 2.400 = 12.65 Acting at h/2 = 2.400 / 2.00 = 1.200 i.e. R.L. = 256.950 mt

[3] Vertical component of earth pressure Total earth pressure on back face of the wall is = 27.597 + 12.646 = 40.242 HENCE,

Vertical component of earth pressure will be = 40.242 / 0.279 x 0.102= 14.644 T

Acting at back surface of earth face i.e at centre of back inclined portion

3.4 ANALYSIS AND DESIGN FOR ABUTMENT3.4.1 Summary of loads and moments at top of foundation at

[1] Moment at toe of wall i.e end point on soil sideData: Abutment RL in mt

Top of bed block = 266.741 Thk. of abut bed block 0.53Bottom of bed block = 266.216 mt so, height of dirt wall = 1.88Formation Lvl = 268.625 mtBed level = 258.150 mtTop of foundation = 255.750 Depth of bot. Of found. = 0.600 mt Bottom of foundation = 255.150 mt Barrel length reqd. = 12.100 mt Top of dirt wall = 268.625 255.750

Top of exist. Bed block = 266.741 Top of exist. Found. = 255.750Hence ht of exist. Back inclined portion = Central Exist. Th of abut. = 1.215 mtHt of inclined portion = 266.74 - 255.750 = 10.99 mt

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BR-42 , CH : 33255.

Width of rear inclined 3.609 Total width up to face of abutmentCentral portion 1.215 [a] Top of foundation = 4.82Front inclination 1 in [b] Bottom of foundation = 4.82 Centre of bearing from toe = 3.609 + 1.22 - 0.415

[Rear inclined] [Central portion] [Dist. From face of dirt wall to center of bearing]

= 4.409 i.e load point of super structure

Abutment Top RL = 266.216 Bot RL = 255.750 Height of abut. 10.47 Dist of

Length Width Height Density Weight C.G from toeFront triangle [1] 12.10 10.99 2.40Central portion [2] 12.10 1.22 10.99 2.40 387.80 # 4.217Rear Incl.portion [3] 12.10 1.80 10.99 2.40 575.96 # 2.406Wt. of soil on projectionOn rear inclined [14] 12.10 1.80 10.99 1.70 407.97 # 1.203Ractangle [15] 12.10 3.61 1.88 1.70 139.86 # 1.805

EARTH PRESSURE Pressure Acting at Total pr. L.A from RL 255.750

Due to surcharge [ 9] 12.10 3.105 262.19 37.57 6.438Surch. Triangle [10] 12.10 6.663 264.33 80.62 8.583Earth pre. Upto GL [11] 12.10 27.597 261.64 333.92 5.892Earth pr GL to TOP [12] 12.10 12.646 256.95 153.01 1.200

WT. AND MOMENT FROM FRONT PORTION OF STRENGTHENING IN M-200 CONC. WITH DOWELLING

Total pr. L.A from toeSec. up to G.L [ S-1 ] 12.10 8.066 2.40 4.824 [ S1 T] 12.10 0.5375 8.066 2.40 125.90 5.182G.L to top of fond.[ S2] 12.10 1.075 2.400 2.40 74.92 5.362Triangular [S3] 12.10 0.960 2.400 2.40 66.91 6.539 Total width of existing foundation at top of found = = 4.8240Additional width at front due to strengthening = = 2.9950

Total width at foundation 7.8190

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BR-42 , CH : 33255.

[2] ANALYSIS FOR ABUTMENT FORCES TAKING MOMENT AT TOE OF WALL AT FRL






(a) Dirtwall 25.86 3.759 97.20(b) Return wall(c) Pedestal / Bed block 12.25 4.409 54.01(d) Abut.cap 4.217(e) Abutment

Front triangle [1]Central portion [2] 387.80 4.217 1635.17

Inclined portion [3] 575.96 2.406 1385.75

4 Earth pressure [9] 37.57 6.44 241.86[10] 80.62 8.58 691.99[11] 333.92 5.89 1967.35[12] 153.01 1.20 183.62

5 Wt of soil on [13]

back projections [14] 407.97 1.20 490.79[15] 139.86 1.80 252.38

Vertical Comp of EP 14.64 1.80 26.43

6 Strengthened portion

Sec. up to G.L [ S-1 ] 4.8240[ S1 T] 125.90 5.1823 652.47

G.L to top of fond.[ S2] 74.92 5.3615 401.70Triangular [S3] 66.91 6.5390 437.51


Horizontal force

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BR-42 , CH : 33255.

1 Normal:1+2+3++ 7 2255.76 665.74 11052.51With live load

2 Normal : 1+3+4+5+6 2055.76 605.12 9504.45Without Live load BREAKING AND LL ARE DEDUCTED

Case : 1 X bar = 4.90

Eccen. = B/2 -Xbar = 3.91 - 4.90 = -0.99Hence absolute e = = 0.99Total width B = 7.82 So, B / 6 = 1.30

Comparing B/6 & Eccentricity ,provided Total B = 7.82 mt. is in order

Hence Eccen = 3.91 - 4.90 = -0.99

Hence Pmax = 2255.76 [ 6.00 X 0.990 ] ------------- -------------- X 1.00 + ------------------------------------]

12.10 x 7.819 [ 7.819 ]

Pmax = 23.84 X 1.76 = 41.96 T/mt2

Pmin = 23.84 X 0.240 = 5.727 T/mt2 Which is greater than -5.00Hence Safe

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BR-42 , CH : 33255.

3.3 ANALYSIS AND DESIGN FOR PIER Bridge No. 423.3.1 Summary of loads and moments at bottom of pier str.

Moment at FRLData: Pier RL in mt

Top of bed block = 266.741 mt. Thk. of pier bed block = 1.00Bottom of bed block = 265.741 mt.Formation Lvl = 268.625 mt.Bed level = 253.073 mt.Top of foundation = 252.240 mt. Projections in foundations at ,Depth of bot. of found. = 0.600 mt. Horizontal VerticalBottom of foundation = 251.640 mt. projection depth of itStr.Pier length required = 6.925 mt. Pier length for design = 8.425 mt. Width of pier = 1.500 mt. 1st proj. 0.300

2nd proj.Top of exist. Bed block = 266.741 mt. 3rd proj.Top of exist. Found. = 252.240 mt. Width of batter at top of found. = mt

Total 0.300DETAILS AT PIERTop Width of exist. Pier = 1.500 mt. Width at top of foundation = 1.500 mt.Width at bottom of foundation = 1.500 mt.

= 2.000 x 1.350 proposed batter = 2.700 mt. [ Total of both sides ]

Additional thicknesses at1st proj. 0.30 0.3002nd proj.3rd proj.4th proj.5th proj. Hence total width at foundation = 1.500 + + 2.700 + 0.60 = 4.800 mt.

Hence total length of foundation at FRL = 8.425 + 2.700 + 0.60 + += 11.725

Height from bot of proposed bed block to top of foundation = 265.74 - 252.240 = 13.501 mt.

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BR-42 , CH : 33255.

1500RL of Top of Bedblock = 266.741

1500.00

Proposed batter 1 in 10

RL of top of foundation = 252.240

1500

4800 (Total width of foundation WITH BATTERS)

CROSS SECTION OF PIER AFTER STRENGTHENING

Width at top of foundation = 1500.00 + 2700.00 = 4200.00 mm= 4.200

Preoposed batters : Ht. from bot. of bed block to GL = 265.741 - 253.07 = 12.67 Ht. from GL to top of foundation = 253.073 - 252.24 = 0.83 From top to G.L 1 in 10.00 = 12.668 / 10.00 = 1.267 mt From GL to TO fn 1 in 10.00 = 0.833 / 10.00 = 0.083 mt Hence additional width at top of foundation

10.00 1.350 pier : Average width of pier= [ 1.50 + 1.50 ] / 2.0 = 1.50

1.50 X 14.101 X 8.43 X 2.40 = 427.68Projections 0.300 X 8.43 X 2.40 =

8.43 X 2.40 = 8.43 X 2.40 = 8.43 X 2.40 = 8.43 X 2.40 =

1450

1

PAGE NO : 27 - RO


BR-42 , CH : 33255.

M-20Top straight 14.101 X 8.43 X 2.40 =Batter 1.350 X 14.101 X 8.43 X 2.40 = 384.91Projections 0.60 X 0.300 X 8.43 X 2.40 = 3.64

8.43 X 2.40 =8.43 X 2.40 =8.43 X 2.40 =8.43 X 2.40 =

816.24Centre of bearing 0.375 i.e load point of super structure

Pier Top RL = 266.741 Bot RL = 255.15 Height of pier 11.59 Total width of existing foundation at foundation RL = = 1.50 Additional width due to BATTERS = = 3.300

--------------- Total width at foundation 4.800




structure 447.372 Live load [ one span ] 200.00 0.375 75.00

Two span loaded. 356.70

3 Sub structurePier 816.24

7 Longitudinal forces

(a) Tractive ( one span 60.62 11.59 702.63(a) Tractive ( two span 103.24 11.59 1196.63

1 Normal:1+2+3++ 7 1463.61 60.62 777.63live load one span

2 Normal : 1+3+4+5+6 1620.31 103.24 1196.63Live load two span

Horizontal force

PAGE NO : 28 - RO


BR-42 , CH : 33255.

Area of the foundation = 11.725 x 4.800 = 56.28 mt2

Modulus of section = 1 / 6 x B x D2 = 45.02 mt2

P M 1620.31 1196.63Hence Pmax = -------------- + ------------- = ----------------- + ---------------

A Z 56.28 45.02= 55.37 T/mt2 Which is less than 50.0

P M 1620.31 1196.63Hence Pmin = -------------- - ------------- = ----------------- - ---------------

A Z 56.28 45.02

= 2.21 T/mt2 Which is greater than 0.00Hence Safe

AS ROCKEY STRATA IS MET WITH, AND ANCHORS HAVE ALREADY BEEN PROVIDED THE SMALL AMOUNT OF TENSION, IS NEGLIGIBLE, AND WILL BE TAKEN CARE BY ROCK ANCHORES PROVIDED. CHECK AT TOP OF FOUNDATION FOR PIER.EXISTING DETAILS AT PIERTop Width of exist. Pier = 1.500 mt. Width at top of foundation = 1.500 mt. Hence batter in Pier = 1 in Width at bottom of foundation = 1.500 mt.

DETAILS OF PIER : thk. At top of foundation due to batter = 2.000 x 1.350

= 2.700 mt. [ Total of both sides ]

Hence width at top of foundation = 1.500 + + 2.700 = 4.200 mt.

Height from bot of proposed bed block to top of foundation = 265.74 - 252.240 = 13.50 mt.

PAGE NO : 29 - RO


BR-42 , CH : 33255.

1500RL of Top of Bedblock = 266.741

1500.00

Proposed batter 1 in 10

RL of top of foundation = 252.240

1500

4800 (Total width of foundation )

CROSS SECTION OF PIER

Width at top of foundation 1500.00 + 2700.00 = 4200.00 mm= 4.200

Preoposed batters : Ht. from bot. of bed block to GL = 265.741 - 253.07 = 12.67 Ht. from GL to top of foundation = 253.073 - 252.24 = 0.83

From top to G.L 1 in 10.00 = 12.668 / 10.00 = 1.27 mt From GL to TO fn 1 in 10.00 = 0.833 / 10.00 = 0.08 mt Hence additional width at top of foundation

= 1.350 Central portion of pier : Average width of pier= [ 1.50 + 1.50 ] / 2.0 = 1.50Self weight of pier 1.50 X 13.501 X 3.82 X 2.40 = 185.67 M-25Top straight 13.501 X 8.43 X 2.40 =Batter 1.350 X 13.501 X 8.43 X 2.40 = 368.56

1450

1

PAGE NO : 30 - RO


BR-42 , CH : 33255.

554.23

Centre of bearing 0.375 i.e load point of super structure

Pier Top RL = 266.741 Bot RL = 252.24 Height of pier 14.501 Wwidth of existing foundation at top of foound. = = 1.50 Additional width at front due to batter = 2.700

--------------- Total width at foundation 4.200




structure 447.372 Live load [ one span ] 200.00 0.375 75.00

Two span loaded. 356.70 3 Sub structure

Pier 554.23


103.24 14.50 1497.05 1 Normal:1+2+3++ 7 1358.30 103.24 1572.05

live load 2 span 1358.30

BREAKING AND LL ARE DEDUCTED

Horizontal force

PAGE NO : 31 - RO


BR-42 , CH : 33255.

Area of the foundation = 8.43 x 4.20 = 35.39 mt2

Modulus of section = 1 / 6 x B x D2 = 24.77 mt2

P M 1358.30 1572.05Hence Pmax = -------------- + ------------- = ----------------- + ---------------

A Z 35.39 24.77= 101.85 T/mt2 for M-20 conc safe.= 10.18 kg/sq.cm

P M 1358.30 1572.05Hence Pmin = -------------- - ------------- = ----------------- - ---------------

A Z 35.39 24.77= -25.08 T/mt2 = -2.51 kg/sq.cm

PAGE NO : 32 - RO

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