Dr. P. NANJUNDASWAMY Department of Civil Engineering S J College of Engineering Mysore

Transcription

1 Dr. P. NANJUNDASWAMY Department of Civil Engineering S J College of Engineering Mysore pnswamy@yahoo.com

2 In this presentation Rigid pavement design considerstions Wheel load and temperature stresses Design considerations as per IRC Design of Slab Design of Joints Dowel bar design Tie bar design

3 Structural Response Models Different analysis methods for AC and PCC AC Base Subgrade Layered system behavior. All layers carry part of load. Subgrade Slab action predominates. Slab carries most load.

4 General Design Considerations Modulus of Subgrade Reaction Relative Stiffness of Slab to Subgrade Equivalent Radius of Resting Section Critical Load Position Wheel Load Stresses Temperature Stresses Critical Combination of Stresses

5 Modulus of Subgrade Reaction Pressure sustained per unit deflection Plate bearing test (IS : ) Limiting design deflection = 1.25mm

6 Modulus of Subgrade Reaction K P P = pressure sustained in kg/cm 2 by a rigid plate of diameter 75 cm = design deflection = cm

7 Plate Bearing Test

8 Plate Bearing Test

9 Plate Bearing Test

10 Plate Bearing Test

11 Plate Bearing Test

12 Plate Bearing Test Results

13 Plate Bearing Test Corrections Allowance for Worst Subgrade Moisture K K S US P P S US Correction for Small Plate Size r K K 1 1 r

14 Radius of relative stiffness Pressure deformation characteristics of rigid pavement is a function of relative stiffness of slab to that of subgrade l 4 Eh ( 1 ) K

15 Equivalent Radius of Resisting Section When a < h 2 b 1. 6a h h 2 When a h b a a = radius of wheel load distribution, cm h = slab thickness, cm

16 Critical Load Position PCC SLAB Corner Edge Interior

17 Wheel Load Stresses & Deflections Westergaard s Stress Equation Assumptions The reaction of the subgrade is vertical only and is proportional to the deflection of the slab. (The support provided by the subgrade is similar to that given by a dense fluid and the subgrade has no shear strength) Load Deflected Slab Reaction

18 Wheel Load Stresses & Deflections Westergaard s Stress Equation Assumptions The load in the interior and corner is circular in shape and the edge loading is semi-circular Load - edge Load - interior SLAB

19 Wheel Load Stresses & Deflections Westergaard s Stress Equation Assumptions The concrete slab is homogeneous and isotropic The slab is uniform in thickness The reaction of the subgrade at a point is equal to K x Deflection at that point

20 Wheel Load Stresses & Deflections Corner Loading Westergaard (1929) Stress Load - corner SLAB Deflection

21 Wheel Load Stresses & Deflections Corner Loading - Ioannides et al (1985) Stress Load - corner SLAB Deflection

22 Wheel Load Stresses & Deflections Interior Loading Westergaard (1929) Stress Load Interior SLAB When μ = 0.15

23 Wheel Load Stresses & Deflections Interior Loading Westergaard (1929) Deflection Load - interior SLAB

24 Wheel Load Stresses & Deflections Edge Loading Westergaard (1926, 1933, 1948) Load - edge Stress SLAB

25 Wheel Load Stresses & Deflections Edge Loading - Circle Ioannides et al. (1985) Stress Load - edge SLAB Deflection

26 Wheel Load Stresses & Deflections Edge Loading - Semicircle Ioannides et al. (1985) Stress Load - edge SLAB Deflection

27 Wheel Load Stresses & Deflections Ioannides et al. (1985)

28 Dual Tyres S d 0.3 L 0.4 L L 0.3 L 0.6 L S d 0.6 L 0.6 L

29 Wheel Load Stresses for Design IRC : Westergaard s edge load stress equation, modified by Teller and Sutherland Load - edge SLAB

30 Wheel Load Stresses for Design IRC : Westergaard s corner load stress equation, modified by Kelley Load - corner SLAB

31 Temperature Stresses Westergaard s concept of Temperature Stresses Warping Stresses Frictional Stresses

32 Warping Stresses

33 Bradbury s Warping Stress Coefficients

34 Bradbury s Warping Stress Coefficients Guide line as per IRC L/l C L/l C

35 Temperature Differential Guide line as per Table 1 of IRC

36 Frictional Stresses B = Slab width L = Slab length H = Slab thickness γ c f = Unit weight of concrete = Coefficient of subgrade restraint (max 1.5)

37 Stress levels load and temperature Corner Stress Due to Load Due to Temperature Edge Stress Interior Stress Increases Increases

38 Plain Jointed Rigid Pavement Design (IRC : )

39 Wheel Loads Axle loads Single Tandem Tridem : 10.2 tonnes : 19.0 tonnes : 24.0 tonnes Sample survey Min sample size 10% in both directions

40 Wheel Loads Tyre pressure Range 0.7 to 1.0 MPa No significant effect on pavements 20cm thick 0.8 MPa is adopted Load safety factor Expressway/NH/SH/MDR 1.2 Lesser importance with lower truck traffic 1.1 Residential and other streets 1.0

41 Design Period Depends on traffic volume growth rate capacity of road and possibility of augmentation Normal 30 years Accurate prediction not possible 20 years

42 Design Traffic Average annual growth rate 7.5% Design traffic 2-lane 2-way road 25% of total for fatigue design 4-lane or multi-lane divided traffic 25% of total traffic in the direction of predominant traffic. New highway links where no traffic data is available - data from roads similar classification and importance

43 Design Traffic Cumulative Number of Repetitions of Axles A = Initial number of axles per day in the year when the road is operational r = Annual rate of growth of commercial traffic n = Design period in years

44 Temperature Differential Guide line as per Table 1 of IRC

45 Characteristics of Sub-grade Modulus of sub-grade reaction (k) Pressure sustained per unit deflection Plate bearing test (IS : ) Limiting design deflection = 1.25mm K 75 = 0.5 k 30 One test/km/lane

46 Approximate k-value Approximate k-value corresponding to CBR values for homogeneous soil subgrade Soaked CBR (%) k-value (kg/cm 3 )

47 Approximate k-value k-value of subgrade (kg/cm 3 ) k-values over Granular and Cemented Sub-bases Untreated granular subbase of thickness in cm Effective k (kg/cm 3 ) Cement treated sub-base of thickness in cm

48 Approximate k-value k-value over Dry Lean Concrete Sub-base k-value of subgrade (kg/cm 3 ) Effective k over 100 mm DLC (kg/cm 3 ) Effective k over 150 mm DLC (kg/cm3)

49 Characteristics of Concrete Modulus of Elasticity Experimentally determined value 3.0 x 10 5 kg/cm 2 Poisson s ratio µ = 0.15 Coefficient of thermal expansion α = 10 x 10-6 per C

50 Fatigue behaviour of cement concrete Fatigue Life (N) for SR < 0.45 when 0.45 SR 0.55 for SR > 0.55 where SR Stress Ratio

51 Fatigue behaviour of cement concrete

52 Fatigue behaviour of cement concrete

53 Calculation of Stresses Edge Stress Due to Load Picket & Ray s chart Due to Temperature E t C te 2

54 Corner Stress Due to Load Calculation of Stresses c 3P h 2 1 a l Due to temperature negligible and hence ignored

55 Calculation of Stresses Radius of relative stiffness is given by 4 Eh ( 1 ) k

56 Typical Design Charts

57 Typical Design Chart

58 Typical Design Chart

59 Design Procedure Stipulate design values for the various parameters Decide types and spacing between joints Select a trial design thickness of pavement Compute the repetitions of axle loads of different magnitudes during design period Calculate cumulative fatigue damage (CFD) If CFD is more than 1.0 revise the thickness Check for temp+load stress at edge with modulus of rupture Check for corner stress

60 Example Total two-way traffic = 3000 CVPD at the end of construction period Flexural strength of concrete = 45kg/cm 2 Modulus of subgrade reaction = 8 kg/cm 3 Slab dimension 4.5 m x 3.5 m

61 Example - Axle Load Spectrum Single Axle Loads Axle Load % of axle loads Tandem Axle Loads Axle Load % of axle loads < < Total 93.0 Total 7.0

62 Example Design traffic Cumulative repetition in 20 years is C 365* A{(1 r) 1} r n = 47,418,626 commercial vehicles Design traffic = 25 % of above = 11,854,657

63 Example Fatigue analysis AL 1.2AL Stress SR ER N ER/N Single axle Tandem axle x10e

64 Example Fatigue analysis Cumulative fatigue life consumed = Hence revise the depth to 33 cm

65 Example Fatigue analysis AL 1.2AL Stress SR ER N ER/N Single axle Tandem axle Cumulative fatigue life consumed = 0.47

66 Example Check for Stresses Edge warping stress = kg/cm 2 Load stress = kg/cm 2 Total = kg/cm 2 Corner Load stress = kg/cm 2 Both are Less than 45 kg/cm 2 The Flexural strength

67 Design of Joints

68 Joints in Concrete Pavement

69 Types of Joints Longitudinal Joint Warping Joint Construction Joint Joints Expansion Joint Transverse Joint Contraction Joint Construction Joint

70 Spacing of Joints Spacing of Expansion Joint If δ' is the maximum expansion in a slab of length L e with a temperature rise from T 1 to T 2, then α is the thermal expansion of concrete Expansion joint gap δ = 2 δ'

71 Spacing of Joints Spacing of Expansion Joint Recommended (by IRC) Maximum expansion joint gap = 25 mm Maximum Spacing between expansion joints for rough interface layer 140 m all slab thicknesses for smooth interface layer when pavement is constructed in summer 90 m upto 200 mm thick slab 120 m upto 250 mm thick slab when pavement is constructed in winter 50 m upto 200 mm thick slab 60 m upto 250 mm thick slab

72 Spacing of Joints Spacing of Contraction Joint σ tc = Allowable tensile stress in concrete h = Slab thickness B = Slab width L c γ c = Slab length or spacing b/w contraction joints = Unit weight of concrete f = Coefficient of subgrade restraint (max 1.5) If Reinforcement is provided, replace LHS by σ ts A s

73 Spacing of Joints Spacing of Contraction Joint Recommended (by IRC) Maximum Spacing between contraction joints for unreinforced slabs 4.5 m all slab thicknesses for reinforced slabs 13 m for 150 mm thick slab 14 m for 200 mm thick slab

74 Load Transfer Dowel Bars

75 Dowel Bars and Tie Bars

76 Dowel Bars

77 Dowel Bars Bradbury s analysis Load transfer capacity of a single dowel bar shear Bending Bearing

78 Bradbury s analysis P' = Load transfer capacity of a single dowel bar, kg d = Diameter of dowel bar, cm L d = Total length of embedment of dowel bar, cm δ = Joint width, cm F s = Permissible shear stress in dowel bar, kg/cm 2 F f = Permissible flexural stress in dowel bar, kg/cm 2 F b = Permissible bearing stress in concrete, kg/cm 2

79 Dowel bar design - Length The load capacity of the dowel bar in bending and bearing depend on the total embedded length L d on both the slabs Balanced design for equal capacity in bending and bearing, the value of Ld is obtained for the assumed joint width and dowel diameter using Minimum dowel length L = L d + δ

80 Dowel design - Spacing Load capacity of dowel system = 40% of wheel load Required load capacity factor = Effective distance upto which there is load transfer = 1.8 (radius of relative stiffness) Variation of capacity factor linear from 1.0 under the load to 0.0 at effective distance LOAD 1.8 L Design spacing = The spacing which conforms to required capacity factor

81 Dowel bars design details

82 Tie bar design Diameter & Spacing Area of steel per unit length of joint is obtained by equating the total friction to the total tension developed in the tie bars σ ts = Allowable tensile stress in steel A s = Area of steel per unit length of joint B = distance b/w the joint and nearest free edge h = Slab thickness γ c = Unit weight of concrete f = Coefficient of subgrade restraint (max 1.5)

83 Tie bar design Length Length of embedment required to develop a bond strength equal to working stress of the steel or σ ts = Allowable tensile stress in steel σ bc = Allowable bond stress in concrete A s = Area of tie bar L t P = Length of tie bar = Perimeter of tie bar d = Diameter of tie bar

84 Tie bars design details σ ts = Allowable tensile stress in steel = 1400 kg/cm 2 σ bc = Allowable bond stress in concrete = 24.6 kg/cm 2 for deformed tie bars = 17.5 kg/cm 2 for plain tie bars

85 Thank you