The loading of the notional lanes according to Load Model 1 (LM1) is as given in Figure 1;
A culvert on a roadway corridor has the parameters given below. The culvert was founded at a location with no ground water problem. Using any suitable means, obtain the design internal forces induced in the members of the culvert due to the anticipated loading conditions when the culvert is empty under the following site conditions:
(1) The top slab of the culvert is in direct contact with traffic carriageway and overlaid with 75 mm thick asphalt
(2) There is a 1.2 m thick fill on the top of the culvert before the carriageway formation level.
Total length of culvert = 8 m
Width of culvert c/c of side walls = 2.5 m
Height of culvert c/c of top and bottom slabs = 2.0 m
Length of wing walls = 2.12 m
Thickness of all elements = 300 mm
Thickness of asphalt layer = 75 mm
Angle of internal friction of fill soil = 30°
Unit weight of water = 9.81 kN/m3
Unit weight of back fill soil = 19 kN/m3
Unit weight of concrete = 25 kN/m3
Unit weight of asphalt concrete = 22.5 kN/m3
fck = 30 Mpa
fyk = 500 Mpa
Concrete cover = 50 mm
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Width of carriage way = 8 m
Number of notional lanes = 8/3 = 2 notional lanes
Width of the remaining area = 8 – (2 × 3) = 2 m
(1) Case 1: Box culvert with no earth fill
(a) Applying the recommended traffic actions on the notional lanes
|Fig 3: Loading of the Notional Lanes|
(b) Permanent actions
The self weight of the structure should be normally be calculated by Staad Pro software, but let us show how we can easily compute and apply it on the structure;
(i) Self weight of top slab
Thickness of top slab = 300 mm = 0.3 m
Self weight of the slab per unit length = 0.3 m × 25 kN/m3 = 7.5 kN/m2
(ii) Permanent action from asphalt layer
Thickness of asphalt = 75 mm = 0.075 m
Self weight of the asphalt per unit length = 0.075 m × 22.5 kN/m3 = 1.69 kN/m2
For the purpose of simplicity, let us combine these two actions such that the permanent action is given by gk = 7.5 + 1.69 = 9.19 kN/m2
(iii) Earth Pressure
At rest earth pressure coefficient ko = 1 – sin (∅) = 1 – sin (30) = 0.5
Maximum earth pressure on the side walls p = koρH = 0.5 × 19 kN/m3 × 2.3m = 21.85 kN/m2
(iv) Live load Surcharge
Consider a live load surcharge of q = 10 kN/m2
Therefore horizontal surcharge pressure = koq = 0.5 × 10 kN/m2 = 5.0 kN/m2
When the culvert is full, the hydrostatic pressure profile inside the culvert can also be easily obtained. However this was not considered in this analysis.
(2) Case 2: Box culvert with 1.2 m thick earth fill
(a) Traffic Load on the Box Culvert
In this case, since the thickness of the fill is greater than 0.6 m, we are going to consider the wheel load of the traffic actions dispersed to the top slab of the culvert as uniformly distributed load. The UDL of traffic action will not be considered.
For this case, let us use Load Model 1 of EN 1991-2 which is recommended by clause 4.9.1 of EN 1991-2. The tandem load can be considered to be dispersed through the earth fill and uniformly distributed on the top of the box culvert. The contact surface of the tyres of LM1 is 0.4m x 0.4m, which gives a contact pressure of about 0.9375 N/mm2 per wheel.
We are going to disperse the load through the earth fill to the box culvert by using the popular 2(vertical):1(horizontal) load increment method. This is the method recommended by BD 31/01, otherwise, Boussinesq’s method can also be used. However, clause 4.9.1 (Note 1) of EN 1991-2:2003 recommends a dispersal angle of 30° to the vertical for a well compacted earth fill. A little consideration will show that this is not so far away from the 2:1 load increment method.
|Fig 9: Single Wheel Load Distribution Through Compacted Earth Fill|
For the arrangement in Fig 9 above;
P1 = 150 kN
L1 = 0.4 m
L2 = 0.4 + D = 0.4 + 1.2 = 1.6 m
Therefore, the equivalent uniformly distributed load from each wheel to the culvert is;
qec = 150/(1.6 × 1.6) = 58.593 kN/m2
It is acknowledged that the pressure from each wheel in the axles can overlap when considering the tandem system as shown in the figure below. This is considered in the lateral and longitudinal directions.
|Fig 10: Overlapping Tandem Axle Load Dispersion Through Earth Fill|
When considering the tandem system as shown in Figure 10;
∑Pi = 150 + 150 + 150 + 150 = 600 kN
L2 = 1.2 + 0.4m + 1.2m = 2.8 m (Spacing of wheels + contact length + depth of fill)
B2 = 2.0 m + 0.4m + 1.2m = 3.6 m (Spacing of wheels + contact length + depth of fill)
qec = 600/(2.8 × 3.6) = 59.523 kN/m2
As can be seen, the difference between considering the entire tandem system and one wheel alone is not much. But to proceed in this design, we will adopt the pressure from the tandem system.
Therefore the traffic variable load on the box culvert is given in Fig 11 below;
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(b) Earth load on top of the box culvert
At a depth of 1.2 m, the earth pressure on the box culvert is given by;
p = 1.2 × 19 kN/m3 = 22.8 kN/m2
(c) Horizontal Earth Pressure on the Box Culvert
Since the box culvert is buried under the ground, the pressure distribution is as given in Figure 13.
The maximum pressure at the base of the culvert (at 2.3 m) is given by;
pmax = koρH = 0.5 × 19 kN/m3 × 3.5 m = 33.25 kN/m2
The minimum pressure at the top of the culvert (at 1.2 m below the ground) is given by;
pmin = koρH = 0.5 × 19 kN/m3 × 1.2 m = 11.40 kN/m2
(d) Surcharge load
The horizontal surcharge load distribution on the buried box culvert will be the same as that of case A.
Thank you for visiting Structville today. We are going to present actual analysis and design of box culverts using Staad Pro in our next post which will come shortly. Please stay tuned and God bless you.