Line Load Surcharges

Line loads are defined with two components: a) a vertical Py, and b) a horizontal Px. It is important to note that the many of the equations listed below are, only by themselves, applicable for a load in an infinite soil mass. For this reason, the software multiplies the obtained surcharge by a factor m that accounts for wall rigidity. The software assumes a default value m=2 that accounts for full surcharge “reflection” from a rigid behavior. However, a value m=1.5 might be a reasonably less conservative assumption that can account for limited wall displacement.

For line loads that are located on the surface (or the vertical component strip loads, since strip loads are found by integrating with line load calculations), equations that include full wall rigidity can be included. This behavior can be selected from the Loads/Supports tab as Figure 4.2 illustrates. In this case, the calculated loads are not multiplied by the m factor.

For vertical line loads on the surface:  When the Use Equations with Wall Rigidity option is not selected, the software uses the Boussinesq equation listed in Poulos and Davis, 1974, Equation 2.7a

For a vertical surface line load, when the Use Equations with Wall Rigidity option is selected, the software uses the Boussinesq equation as modified by experiment for ridig walls (Terzaghi, 1954).

For vertical line loads within the soil mass: The software uses the Melan’s  equation listed in Poulos and Davis, 1974, Equation 2.10b pg. 27

For the horizontal component of a surface line load: The software uses the integrated Cerruti problem from Poulos and Davis Equation 2.9b

For the horizontal component of a line load within the soil mass: The software uses Melan’s problem Equation 2.11b pg. 27, from Poulos & Davis

Strip Surcharges

Strip loads in DeepEX can be defined with linearly varying magnitudes in both vertical and horizontal directions. Hence, complicated surcharge patterns can be simulated. Surcharge pressures are calculated by dividing the strip load into increments where an equivalent line load is considered. Then the line load solutions are employed and numerically integrated to give the total surcharge at the desired elevation. The software subdivides each strip load into 50 increments where it performs the integration of both horizontal and vertical loads. On surface loads, the vertical load is calculated from integration along x and not along the surface line.

3D surcharge loads

The software offers the possibility to include other 3-dimensional surcharges. In essence, all these loads are extensions/integrations of the 3D point vertical load solution.

For 3D footings, the surcharge on the wall can be calculated in two ways:

1. By integrating the footing bearing pressure over smaller segments on the footing footprint. In this case the footing is subdivided into a number of segments and the surcharge calculations are slightly more time consuming.
2. By assuming that the footing load acts as a 3D point load at the footing center coordinates.

For loads that are located on the surface: The software program uses the Boussinesq equation. Results from the following equations are multiplied by the elastic load adjustment factor m as previously described.

The radial stress increment is then calculated as:

The hoop stress is defined as:

With the angles defined as:

Then, the horizontal component surcharge is:

For vertical point loads within the soil mass: The software uses the Mindlin solution as outlined by Poulos and Davis, 1974 equations 2.4.a, and 2.4.g