Loading and Design of Box Culverts To Eurocodes [PDF]

Zitiervorschau

Loading and Design of Box Culverts to Eurocodes by Ubani Obinna Ranks on June 24, 2019 in Bridges, Culverts, Eurocodes, Reinforced Concrete Design, Staad Pro, Statically Indeterminate Structures

Introduction A culvert is a drainage structure designed to convey storm water or stream of limited flow across a roadway. Culverts can consist of single or multi-span construction, with a minimum interior width of 6 m when the measurement is made horizontally along the centreline of the roadway from face to face of side walls. Technically, any such structure with such span over 6 m is not a culvert but can be treated as a bridge. Box culverts consist of two horizontal slabs, and two or more vertical side walls which are built monolithically.

For proper performance of culverts in their design life, there must be hydraulic design, which will give the geometric dimensions or openings that will convey the design flood. It is typical for culverts to be designed for the peak flow rate of a design storm of acceptable return period. The peak flow rate may be obtained from a unit hydrograph at the culvert site, or developed from a stream flow and rainfall records for a number of storm events. In the absence of hydraulic data, it is wise to make conservative assumptions

based on visual inspection of the site, performance of existing culverts and other drainage infrastructures, or by asking locals questions.

Structural Design of box culverts Structural design begins when the structural design units receives the culvert survey, and hydraulic design report from the hydraulics unit. The report in conjunction with the road way plans shall be used to compute the culvert length, design fill, and other items that lead to the completed culvert plans.

Box culverts are usually analysed as rigid frames, with all corner connections considered as rigid and no consideration for sidesway. The centreline of slabs, walls and floor are used for computing section properties and for dimensional analysis. Standard fillets which are not required for moment or shear or both shall not be considered in computing section properties.

Design loads The structural design of a reinforced concrete box culvert comprises the detailed analysis of rigid frame for bending moments, shear forces, and axial forces due to various types of loading conditions outlined below:

(i) Permanent Loads Dead Loads Superimposed Dead Loads Horizontal Earth Pressure Hydrostatic Pressure and Buoyancy Differential Settlement Effects

(ii) Vertical Live Loads HA or HB loads on the carriageway (Load Model 1 of Eurocode) Footway and Cycle Track Loading Accidental Wheel Loading Construction Traffic

(iii) Horizontal Live Loads

Live Load Surcharge Traction Temperature Effects Parapet Collision Accidental Skidding Centrifugal Load

I believe that these loads are very familiar to designers, otherwise the reader should consult standard text books. However, I am going to point out some important considerations worthy attention while assessing design loads on culverts.

Loading of Box Culverts to Eurocode 1 Part 2 (EN 1991-2) The traffic loads to be applied on box culverts is very similar to those to be applied on bridges. The box culvert will have to be divided into notional lanes as given in Table 1;

Table 1: Division of Carriageway into Notional Lanes

The loading of the notional lanes according to Load Model 1 (LM1) is as given in Figure 1;

Fig 1: Application of Traffic Load on Notional Lanes

Concentrated loads According to BD 31/01, no dispersal of load is necessary if the fill is less than 600 mm thick for HA loading. However, once the fill is thicker than 600 mm, 30 units of HB loads should be used with adequate dispersal of the load through the fill. This same concept can be adopted for LM1 of EN 1991-2.

Earth Pressure Depending on the site conditions, at rest pressure coefficient ko = 1 - sin (∅) is usually used for analysing earth pressure.

Loading Example 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.

Geometry of the culvert 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

Materials property 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

Load Analysis 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 2: Division of the Culvert Carriageway into Notional Lanes

Fig 3: Loading of the Notional Lanes

Fig. 4: Section of the Culvert across Notional Lane 1

(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

Fig 5: Permanent Action on Top of the Box Culvert

(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

Fig 6: Horizontal Earth Pressure on the Culvert Walls

(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

Fig 7: Live Load Surcharge on the Walls of the Culvert

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.

Fig 8: LM1 Tandem System

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;

Fig 11: Equivalent Traffic Load Distribution on Top of the Box Culvert

(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

Fig 12: Earth Load on Buried Culvert

(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

Fig 13: Horizontal Earth Pressure on Buried Box Culvert

(d) Surcharge load The horizontal surcharge load distribution on the buried box culvert will be the same as that of case A.

Analysis and Design of Box Culvert Using Staad Pro by Ubani Obinna Ranks on June 26, 2019 in Bridges, Culverts, Eurocodes, Reinforced Concrete Design, Staad Pro, Statically Indeterminate Structures, Structural Analysis

In our last post, we were able to establish how we can load box culverts properly. If you missed the post, kindly follow the link below to read it; Loading and Analysis of Box Culverts to Eurocode 2

In this post, we are going to describe how we can model, load, and analyse box culverts using Staad Pro software. Here is a quick a recap of the properties of the box culvert under consideration;

Geometry of the culvert 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 = 70 mm

Materials property 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

Fig 1: Section of the Box Culvert

The steps in modelling the structure on Staad Pro are as follows;

(1) Meshing Here, the box culvert is idealised with dimensions based on centre to centre of the slabs and walls. This means that the width of the box culvert that will be input into Staad Pro is 2.5 m, while the depth will be 2.0 m. This can be started by forming the nodes in the global XY plane, and then copying and pasting for the length of 8 m in the Z global direction. The output of this operation is as given below;

Fig 2: Initial Nodes for Commencement of Modelling

After forming this, the wing walls can also be formed, which is followed by meshing (rectangular or polygonal) to form the shell of the box culvert. The final output of the meshing operation is as shown below;

Fig 3: Fully Meshed Box Culvert

The meshing process can be completed by adding plate thickness of 300 mm to all the elements.

(2) Assigning of support conditions/foundations This is an important aspect of modelling structures. A purely rigid approach will involve using fixed supports, but note that employing 3D model for this purpose will not be very appropriate, but a simple 2D frame model will be better. There are many proposals on how culverts can be modelled as 2D frames, and the reader is advised to consult as many publications as possible. However, to incorporate the effects of soil-structure interaction (to a limited degree though) on our model, we can employ the use of 'elastic plate' foundation option on our model.

If we assume that the supporting soil and the backfill are of the same material, then we can maintain the same angle of internal friction of 30°. Angle of internal friction of 30° can suggest a loose - medium dense sand in its undisturbed state, therefore we can take a modulus of subgrade reaction of 50,000 kN/m2/m for a well compacted sand. For a slightly compacted sand, you can take a value of 30,000 kN/m2/m.

So we can input this option into Staad Pro using 'compression only' option (see the dialog box below in Fig 4);

Fig 4: Elastic Mat Foundation Dialog Box

When this is applied on the structure, we have the final model as shown in Fig 5;

Fig 5: Application of Elastic Mat Foundation on the Model

What this model (Fig. 5) means is that every node of the base slab is in contact with the soil, and the soil is represented by a spring of stiffness 50,000 kN/m2/m which is the subgrade modulus of the soil.

[Get this publication on Design of Swimming Pools and Underground Water Tanks into your mailbox by clicking HERE or by clicking on the book cover]

Do you wish to get trained in theory of structures, structural design, and use of Staad Pro for analysing and designing of complex structures? Then quickly contact us; Email: [email protected] or [email protected] WhatsApp: +2347053638996 (3) Loading This is another important aspect of modelling structures because analysis results would go very wrong if the loads are not applied properly. If you review our previous post, we considered two construction cases;

(A) where the culvert is buried under the soil, and (B) where is there no earth fill on top of the culvert.

When there is no earth fill on the culvert, the traffic load is directly on the top slab of the culvert as tandem loads and as UDL, but when there is earth fill, traffic load is dispersed in the ratio of 2:1 as UDL on the culvert. We are going to consider 5 load cases in our analysis in this model;

(1) Self weight and other superimposed actions (2) Vertical earth load (3) Traffic load (4) Surcharge load (5) Horizontal earth pressure load

These load cases are considered independently at first, and then combined with appropriate partial factors of safety to determine the design actions. Please note that effects of ground water and the pressure in the shell of the culvert when it is filled with water is an important load case too but was not considered in this post. We have determined the magnitude of these loads in our previous post, and we

are going to apply them on the box culvert for Case A and Case B.

In our previous post, we were able to analyse the loads on the culvert for Case A as follows;

(1) Self weight: To be calculated automatically by Staad + 1.69 kN/m2 (self weight of asphalt wearing course) NB: In some cases, the partial factor of safety for self weight of concrete elements and other superimposed dead loads like asphalt wearing course might be different, so in that case, it is very advisable to treat each of them as a separate load case on Staad. (2) Vertical earth load on the culvert = 22.80 kN/m2 (3) Traffic load dispersed as UDL = 59.523 kN/m2 (4) Horizontal surcharge load = 5.0 kN/m2 (5) Horizontal earth pressure load = trapezoidal distribution with minimum earth pressure of 11.40 kN/m2 at the top of the culvert and 33.25 kN/m2 at the bottom of the culvert

Load cases 1-4 are very easy to apply on Staad by utilising uniform pressure action on plates, however while load cases 1-3 are applied in the global Y direction (gravity loads), load cases 4-5 are applied in the global X direction (horizontally). I will only demonstrate how load case 5 can be applied, since it will involve using the hydrostatic load command on Staad. This is shown on Fig. 6.

Fig 6: Application of Horizontal Earth Pressure as Hydrostatic Load on Staad

The steps involved in applying hydrostatic load can be described as follows:

(i) Launch the hydrostatic plate pressure load on Staad (ii) Select/highlight all the plates that will receive the load (iii) Input the minimum and maximum pressure loads based on the notation given on Staad (in this case you can see that our maximum pressure load served as W1), and also input the sign conventions properly in order to identify the direction of pressure. (iii) Put the interpolation direction (in this case we interpolated the load in the Y-direction) (iv) Add the load case

After all said are done, the output should be as given below;

Fig 7: Earth Pressure on the Culvert

At this point, we are going to define the load combination for ultimate limit state as succinctly as possible. The reader is advised to consult the relevant code of practice and standard textbooks on how to group and combine loads involving traffic actions, earth load, etc. In this case, EN 1990, EN 1991-1, EN 1991-2, and EN 1997-1 can be consulted. Note that culverts are also analysed for other loads such as temperature effects, collision on head walls, centrifugal actions, braking actions, etc.

The load combination principle adopted here is based on expressions (6.10a and 6.10b) of EN 1990.

From Table A2.4(B) of EN 1990:2002 + A1:2005, we are going to adopt the following partial factors:

   

All permanent actions including superimposed dead load and vertical earth pressure γG = 1.35 Leading/main traffic action γQ,1 = 1.35 Traffic surcharge γQ,2 = 1.5 Horizontal earth pressure and ground water γQ,2 = 1.5

We will now apply this load combination on Staad Pro as shown in Fig. 8.

Fig 8: ULS Load Combination Dialog Box

(4) On

Analysis analysing

the

structure,

we

obtain

the

following

results

at

ultimate

limit

state;

Fig 9: Transverse Bending Moment

Fig 9: Longitudinal Bending Moment

Fig 10: Base Pressure

Fig 11: Transverse Shear Stress

A little consideration will show that the top slab is subjected to an ultimate design moment MEd of 56.5 kNm/m and an axial pull of NEd of 91.5 kN/m (check for membrane stresses in your own Staad Model).

NB: Shear and membrane forces in plates are expressed in Mpa in Staad, so will you have to multiply them with the thickness of the element to get the values in kN/m.

For the top slab of the culvert, the M-N interaction chart is given in Fig. 11 below for obtaining the design reinforcement.

Fig 12: M-N Interaction Chart on the Box Culvert

When designed, the area of steel for the axial compression and bending is 1223 mm2/m. Therefore, provision of H16@200 c/c (Asprov = 2010 mm2) on each face will be adequate.

Design Case B: No Earth Fill on Box Culvert (1) Traffic Loads When there is no earth fill on the box culvert, all we have to do is to remove the vertical earth fill load, apply direct traffic load on the top slab, and edit the horizontal earth load from trapezoidal to rectangular. As a reminder, the nature of Load Model 1 (which can be used for global and local verification) on the culvert is given in Fig 14 below;

Fig 14: Load Model 1 on the Culvert

The ideal thing is to apply a moving load on Staad after vehicle definition, such that the worst effect can be obtained. Note that you cannot apply a moving load directly on plate elements on Staad Pro, but you will need to create dummy beam members of negligible stiffness so that the axles can sit on them. In this post, we are not going to bother ourselves with the process, but we are going to treat the wheel load as static.

Influence line has shown that the most onerous bending moment is obtained when the front axle is 0.26 m beyond the mid-span of the culvert. Therefore, we are going to apply static wheel load at that location. Remember that it is always recommended to apply the full tandem system of LM1 whenever applicable. The critical location of wheel load on the box culvert for maximum moment is given in Fig 15 below;

Fig 15: Most Critical Location of Wheel Load on the Culvert

When the static traffic load is applied on Staad and viewed longitudinally on the box culvert, we can see it as given in Fig 16 (note that the unloaded areas represent the wing walls).

Fig 16: Application of LM1 on Staad Pro

(2) Non-traffic Loads For Design Case A, it is observed that the self weight of the structure and asphalt layer remains the same, the surcharge load also remains the same, but the horizontal earth pressure changes to triangular distribution with a maximum pressure of 21.85 kN/m2 at the bottom of the culvert.

(3) Analysis When the structure is analysed, the results at ultimate limit state are as shown below;

Fig 17: Transverse Bending Moment

Fig 18: Longitudinal Bending Moment

Fig 19: Base Pressure

Our analysis results have shown that when there is earth fill, the bending moment at ultimate limit state on top of the culvert is about 56.5 kNm/m, but when traffic is directly on top of the culvert, the bending moment is about 62 kNm/m. This is about 8.8% difference.