A vehicle’s wheel loads are distributed through the soil above the culvert creating a stress prism. The prism increases in width based on the distribution ratio and as such the pressure decreases linearly as a function of depth.

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At a given depth z the contact area is equal to:

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The vertical earth pressure is converted into a lateral earth pressure by multiplying it by the lateral earth pressure coefficient.

The individual wheel load prisms are used to determine which wheels are to be considered for each member. For example, in the figure below the left wall will use wheel A only, the top slab uses wheel’s B and C, and the right wall will use only wheel C.

The walls are split into several segments, based on the user input. At each segment, the total lateral pressure is computed for each wheel and stored for later use. If wheel loads are being combined a single pressure will be computed for each group of wheels that are overlapping.

Combining Wheel Loads

Wheel loads are, potentially, combined at each depth that is checked. These depths include the top and bottom of the culvert, and each location on the wall being checked. For a given depth, if two wheels prisms overlap, they are combined into a single contact area. The new pressure for the wheels is equal to the total load divided by the area of the new contact area. This check is preformed between all wheels at a given depth, because of this it is possible (and common) to combine the rear axles into one group and the front axle into another group for a single vehicle. It will not assume a single group is made.

Vehicle Position

Once the pressure from each wheel has been determined, the vehicle is then positioned to maximize the load on the culvert. This position is the longitudinal position of the center of the vehicle on the culvert. The program checks are the center of each wheel and the center of each axle for the controlling case. The controlling case is the location at which the pressure applied to the culvert is maximized.

Converting Pressures to Line Loads

Once the location is determined the creates the maximum amount of load, these pressures are the computed into line loads. This is handled by multiplying the pressure of the wheel load by the tributary width at the given depth. The tributary width is the lesser of the distribution width, defined above, and the unit length of the culvert. For example, near the top of the culvert the distribution width may be less than the design width of the culvert in which case the line load would use the distribution width as it’s tributary width. As the depth increases, the wheel’s load prism will be wider than the culvert is long, for this case the tributary width will use the design length of the culvert.