2.5 Structural Analysis Approaches
2.5.1 Design Loads
In general, design loads used for BCMS can be classified into permanent loads and imposed loads. Permanent loads comprise of the loads due to self weight of soil and other permanent materials directly above the structure. Imposed loads may include construction, highway, railway, aircraft, stockpile, mine vehicle and abnormal loads.
Earthquake loadings may also need to be considered if applicable.
Permanent loads
The load due to the self weight of the soil is calculated using the density of the soil. For normal fill material a unit weight of fill of 22 kN/m3 is used; however, the unit weight of soil may vary
significantly depending on the soil origin, i.e. volcanic or oxide origins. The load factors for permanent loads on buried structures are specified in AS 5100.2 (2004).
The load effects resulting from permanent loads are taken as the calculated pressure at the crown of the BCMS as follows in Equation 1.
h
pG =γ 1
where
pG = pressure at the crown resulting from dead load, in kPa γ = backfill density, in kN/m3
h = height of fill from surface to neutral axis of corrugated section, in m, (refer to Figure 2.10).
Figure 2.10: Height of fill for calculation of dead load pressure
The soil weight experienced by a culvert can increase or decrease based on the characteristics and compaction of the soil above the culvert. This is known as soil arching. Pritchard (2008) described arching as follows. Positive arching occurs when the weight of the soil acting on the culvert is less than the soil immediately above the culvert. Negative arching occurs when the weight of the soil acting on the culvert is in excess of the soil above the culvert.
Typically, positive arching should not be considered when calculating soil loads because conditions can change over time resulting in possible non-conservative assumptions. AS/NZS 2041 (1998) and the current draft AS/NZS 2041.1 (2010) does not make provisions for positive soil arching.
A soil arching factor is used in the draft AS/NZS 2041.1 (2010) standard for the limit states approach to structural analysis (Section 2.5.3). This factor depends on the effective vertical and horizontal dimensions as well as the height of cover of the structure. The soil envelope surrounding the structure is assumed to always exhibit negative arching i.e. soil settlement increases the load on the structure, using the limit states method.
Construction loads
Construction loads are often the largest load effect the BCMS may be subjected to. Such loads occur when the cover depth is not fully constructed or the roads or other structures above are not completed. Besides normal road vehicles that may pass over, loads may include large construction equipment such as scrapers, dumpers or similar equipment. Loading parameters associated with this equipment such as axle load, footprint, axle spacing, load factor and dynamic load allowance are largely dependent on the specific construction site. These parameters should therefore be determined on a site-specific basis.
Where the actual construction equipment to be used is not known at the time of design, a typical construction vehicle load as shown in Figure 2.11 can be used.
Source: Draft AS/NZS 2041.1 (2010).
Figure 2.11: Typical heavy construction vehicle load
Construction loads are calculated as a uniform pressure at the level of the structure crown, in which the wheel load is distributed through fill over the structure, from the imprint of the rectangular wheel contact area at the road surface to a rectangular distribution area at the level of the structure crown. The length of the sides of this distribution rectangle is determined as follows (AS 5100.2):
For a cover depth of up to 200 mm – sides of distribution rectangle = sides of wheel contact rectangle + 0.5h, where h is the depth of fill cover in mm.
For cover depth greater than 200 mm – sides of distribution rectangle = sides of wheel contact rectangle + 100 mm + 1.2 x (h – 200).
Where distribution areas from several wheels overlap, the total load may be considered to be evenly distributed on the surface over the total area of distribution. The un-factored imposed load pressure (
pQ) is calculated using Equation 2.
)
pQ = unfactored imposed pressure, in kPa
P = unfactored wheel, axle or track load applied over the footprint, in kN. For multiple axle vehicles, P is the total load of all axles being considered lt and ll = sizes of the distribution rectangle at structure crown level, in m
DLA = dynamic load allowance.
Highway loads
At the time of publication the following load cases are required by AS 5100.2 to determine the most adverse effects on a culvert:
single wheel load W80
axle load A160
S1600 load
M1600 tri-axle group
M1600 load.
Heavy load platform loads HLP320 or HLP400 may be included as required by the relevant road authority.
In all the above load cases, the corresponding load factors, accompanying lane factors and dynamic load allowances are taken as per AS 5100.2 provisions.
The highway load is calculated as a uniform pressure at the level of the structure crown. Dynamic load allowances are considered at the crown level. It is also important to note that the dynamic load allowance diminishes with depth. AS 5100.2 (2004) dictates that the dynamic load allowance
diminishes linearly to 0.1 at 2 m depth. The distribution of highway load through fill is calculated as per AS 5100.2 (2004) and is illustrated in Figure 2.12.
Source: Draft AS/NZS 2041.1 (2010).
Figure 2.12: Distribution of vehicle loads through fill
Figure 2.13 shows that for shallow applications (cover depth ≤ 1.45 m) the wheel load W80
controls, while at cover depths of greater than 1.45 m, the M1600 load is the controlling load case.
When HLP load is considered, it controls when the cover depth is greater than 1.45 m.
1 10 100 1000
0.1 1 10
Depth of Fill above Crown of Culvert, H (m) Live Load Pressure, pQ(1+α) (kPa)
HLP400
M1600 x two lanes M1600
A160 W80
1.45
Source: TMR nd b.
Figure 2.13: Live load pressure vs. depth of fill for MS1600 and HLP loadings
Railway loads
The current railway design load is 300LA as specified in AS 5100.2. The multiple track factor, dynamic load allowance and distribution of railway loads are calculated as also specified in
AS 5100.2. The railway load is calculated as a uniform pressure at the level of the structure crown.
Aircraft loads
The required imposed loads, load distributions and dynamic load allowance for the calculation of pressure due to aircraft should be obtained from the relevant regulatory authority. The method of design should be in accordance with the relevant regulatory authority’s specification.
Stockpile loads
Vertical loads at the base of stockpiles are considered permanent loads and are calculated using the specified average density of the stockpiled material. A stockpile influence factor (ks), which accounts for stockpile geometry and internal stockpile arching should be included in calculating the vertical loads. A value of 1.0 is taken for ks unless a value has been determined for the situation being considered.
The pressure at the crown level due to stockpile load is ksps = ksγs hs, where γs is the unit weight of stockpile material, in kN/m3 per cubic metre, and hs is the stockpile height above the crown at the section being considered in metres.
Mine vehicles and abnormal loads
If vehicles other than those included in construction load or highway load categories are used such as mine haul vehicles or heavy earthmoving plant, the loads are calculated using the expected vehicle loads with appropriate load factor and dynamic load allowance.
Earthquake
A design of BCMS should also consider earthquake loadings. The draft AS/NZS 2041.1 (2010) suggests that earthquake design be considered where any of the following occurs:
The structure falls into Importance Level 4 (AS/NZS 1170.4-2007).
The structure is in Importance Level 3 with a design working life of 50 years or more and the earthquake hazard factor (Z) is greater than 0.09.
The structure is in Importance Level 2 with design working life of 50 years or more and the earthquake hazard factor (Z) is greater than 0.12.
For any case other than the above cases where a special requirement is more stringent.
Structures falling into Importance Level 1 and structures with a diameter dh of less than or equal to 3000 mm need not be designed for earthquake loadings.
Earthquakes generate actions in vertical and horizontal directions. The vertical component is usually calculated as 50% of the maximum horizontal component. Only permanent or long-term loadings are considered for design action because of the low occurrence of earthquakes and the low probability of a vehicle being on a structure when an earthquake strikes.
For design of BCMS, only vertical earthquake forces are considered because the horizontal earthquake forces are restrained by the stiffness of the surrounding backfill.
Equation 3 is used to calculate earthquake design action (draft AS/NZS 2041.1-2010).
)
Eu = vertical ultimate earthquake action
G = permanent action as specified for ring compression or limit state design method
kp = probability factor as given in AS 1170.4 (2007) appropriate to the annual probability of exceedance given in AS/NZS 1170.0 (2002) or AS 5100.2 (2004)
Z = earthquake hazard factor as given in AS/NZS 1170.4 (2007)
Ch(0.5) = spectral shape factor for the site sub-soil class appropriate to the site, using T (natural period of structure) = 0.5 s as given in AS 1170.4 (2007).