Soil Structure Interaction for box culverts in Codes and Standards

Several versions of the American Association of State and Highway Transportation Officials (AASHTO 1994, 1996, 2002, 2005, 2007) proposed calculating the vertical and horizontal soil pressure around box culverts using the principles of soil mechanics, and based on Article 6.2. In this article the density of soil for vertical and horizontal pressures are assigned as shown in Table 2.2.

For any type of box culvert construction method either the case-in-place or precast concrete units, the soil structure interaction factors can be multiplied by the calculated soil pressure obtained using the Article 6.2 in AASHTO. Then, the total earth load WE on the box

culvert section can be obtained by:

H gB F

W_E  _e_{s c} (2.34)

where: WE is the total un-factored earth load, Fe is the soil structure interaction factor, Bc is the outside width of culvert, H is depth of backfill, g is the acceleration of gravity, and s is the density of backfill, as shown in Figure 2.31.

Up until the 12th edition of the AASHTO specification (AASHTO, 1977), the vertical loading was essentially 70% of the weight of the earth prism above the top slab. Starting from the 13th edition of AASHTO, the soil structure interaction factors have different notations depending on the version of ASSHTO used. The older versions use the notation Fe for embankments installation and Ft for trench installation method. While new versions use Fe1 for embankment installation and Fe2 for trench installation technique. The values of soil structure interaction factors depend on the type and installations of box culverts. ASSHTO (2002) requirements are based on the Marston-Spangler Theory to determine the soil structure interaction factors Fe.

For embankments installation the soil structure interaction factor is:

c e

B H

Fe1 need not be greater than 1.15 for installations with compacted fill at the sides of the box section, and need not be greater than 1.4 for installations with un-compacted fill at the sides of the box section.

For trench installation the soil structure interaction factor is:

1 2 2 e c d d e F HB B C F   (2.36)

where: Bd is the horizontal width of the trench, Cd is a coefficient specified in Figure 2.32 for normally encountered soils. The maximum value of Fe2 need not exceed Fe1. It should be noted that the factor Fe only considers the overall vertical load attracted to the culvert, and not the actual distribution of pressure against the different structural elements.

Table 2.2: Density of Soil according to AASHTO Article 6.2

Culvert in trench, or culvert un-trenched on yielding foundation

(A)Rigid culverts except reinforced concrete boxes

(1) For vertical earth pressure 120 pcf (1922.2 Kg/m3 = 18.86 KN/m3) For lateral earth pressure 30 pcf (480.6 Kg/m3 = 4.71 KN/m3) (2) For vertical earth pressure 120 pcf (1922.2 Kg/m3 = 18.86 KN/m3)

For lateral earth pressure 120 pcf (1922.2 Kg/m3 = 18.86 KN/m3) (B)Reinforced concrete boxes

(1) For vertical earth pressure 120 pcf (1922.2 Kg/m3 = 18.86 KN/m3) For lateral earth pressure 30 pcf (480.6 Kg/m3 = 4.71 KN/m3) (2) For vertical earth pressure 120 pcf (1922.2 Kg/m3 = 18.86 KN/m3)

For lateral earth pressure 60 pcf (961.1 Kg/m3 = 9.42 KN/m3) (C)Flexible Culverts

For vertical earth pressure 120 pcf (1922.2 Kg/m3 = 18.86 KN/m3) For lateral earth pressure 120 pcf (1922.2 Kg/m3 = 18.86 KN/m3)

Culvert un-trenched on unyielding foundation

(a) (b) Figure 2.31: Box culvert installation:

(a) Embankment installation and (b) Trench installation

2.2.3.2 CHBDC

The Canadian Highway Bridge Design Code (CHBDC, 2000, 2006) specifies the vertical and horizontal arching factors as shown in Table 2.3. To calculate the vertical and horizontal earth loads, the weight of the earth over the top of the box culvert should be multiplied by the vertical and horizontal arching factor v and h respectively. Earth pressures on the box culvert are assumed to be uniformly distributed vertical pressures v and varying linearly horizontal pressures has follows: c v v W   (2.37) c h h W   (2.38)

where Wc is the weight of a column of unit area of fill above the reference point. The maximum and minimum values of λhshould be used to obtain the maximum positive and negative moments in the culvert walls. The reaction pressure on the bottom of the box assumed to be uniformly distributed.

The commentary of the Canadian Highway Bridge Design Code (CHBDC, 2006) shows that these soil structure interaction factors for box culverts are based on previous practice and limited soil-structure interaction analyses by the finite element method.

The soil structure interaction factors depends on the two standard installation methods B1 and B2 for box culverts are defined as shown in Table 2.4, and the soil groups are classified in Table 2.5.

Table 2.3: Arching factors for box sections in standard installations (from CHBDC, 2006)

Installation Type Vertical Arching Factor, v

Horizontal Arching Factor, h Minimum Maximum

B1 1.20 0.30 0.50

Table 2.4: Soils and compaction requirements for standard installations for concrete boxes (from CHBDC, 2006)

Installation type Soil group Equivalent minimum Standard Proctor

compaction in sidefill and outer bedding zones

B1

I 90 %

II 95 %

III Not permitted

B2

I 80 %

II 85 %

III 95 %

Table 2.5: Classification of placed soils (from CHBDC, 2006)

Soil group Description Unified Soil Classification Symbols I Sand and Gravel SW, SP, GW, GP

II Sandy Silt GM; SM; ML; GC and SC with less than 20% passing #200 sieve

2.2.4 Comparison of Soil Structure Interaction Factors given in the Standards and the