Develop Factored Load Combinations for Bridge Pier Foundation

Critical load combinations for design of the bridge pier foundation will generally be as follows:

(A) Bearing Resistance and Settlement

The critical load cases will be those resulting in the maximum factored axial load and moment, and the maximum average bearing pressure over the effective bearing area, determined as:

q = Q/Ar

where the net effective bearing area, Ar, is computed as:

Ar = [(B - 2 eB)(L - 2 eL)] = [(1.5 m - 2 eB)(3.5 m - 2 eL)]

Values of the factored axial load and factored average bearing pressure at the base of the pier stem (for B=1.5 m and L=3.5 m) are summarized in Table 4-26. The eccentricities are computed as:

eB = Longitudinal Moment/Axial Load

eL = Transverse Moment/Axial Load

Table 4-26

Summary of Factored Axial Loads and Average Bearing Pressures at Base of Pier Stem

MAXIMUM LOAD MINIMUM LOAD

LOAD CASE Axial

Load (kN) eB (m) (m)eL (mAr 2_{) (kPa)}q Axial Load (kN) eB (m) (m)eL (mAr 2_{) (kPa)}q STR. I 11 348 0.421 0.496 1.650 6876 7866 0.531 0.648 0.965 8148 STR. III 8321 0.126 0447 3.252 2559 5128 0.168 0.657 2.545 2015 STR. V 10 755 0.370 0.494 1.909 5633 7330 0.474 0.656 1.208 6068 A SER. I 7991 0.364 0.476 1.967 4062 7991 0.364 0.476 1.967 4062 STR. I 11 348 0.421 0.496 1.650 6876 7866 0.531 0.648 0.965 8148 STR. III 8753 0.290 0.155 2.935 2982 5519 0.397 0.223 2.156 2560 STR. V 10 755 0.420 0.449 1.717 6263 7330 0.539 0.596 0.974 6808 B SER. I 7991 0.409 0.432 1.798 4445 7991 0.409 0.432 1.798 4445 STR. I 10 671 0.509 0.415 1.287 8292 7254 0.656 0.553 0.450 16 117 STR. III 8321 0.126 0.447 3.252 2559 5128 0.168 0.657 2.544 2015 STR. V 10 233 0.439 0.429 1.643 6227 6858 0.573 0.579 0.829 8271 C SER. I 7623 0.427 0.413 1.727 4413 7623 0.427 0.413 1.727 4413 STR. I 10 671 0.509 0.415 1.287 8292 7254 0.656 0.553 0.450 16 117 STR. III 8753 0.290 0.155 2.935 2982 5519 0.397 0.223 2.156 2560 STR. V 10 233 0.490 0.381 1.424 7187 6858 0.641 0.514 0.539 12 725 D SER. I 7623 0.474 0.367 1.527 4993 7623 0.474 0.367 1.527 4993 STR. I 10 311 0.299 0.602 2.071 4979 6928 0.386 0.810 1.369 5062 STR. III 8321 0.126 0.447 3.252 2559 5128 0.168 0.657 2.545 2015 STR. V 9955 0.270 0.578 2.250 4424 6606 0.351 0.788 1.535 4302 E SER. I 7427 0.277 0.554 2.263 3282 7427 0.277 0.554 2.263 3282 STR. I 10 311 0.299 0.602 2.071 4979 6928 0.386 0.810 1.369 5062 STR. III 8753 0.290 0.155 2.935 2982 5519 0.397 0.223 2.156 2560 STR. V 9955 0.323 0.529 2.085 4774 6606 0.422 0.721 1.350 4893 F SER. I 7427 0.325 0.507 2.113 3515 7427 0.325 0.507 2.113 3515 G STR. I 9905 0.351 0.480 2.027 4887 6561 0.461 0.656 1.265 5188

STR. III 8321 0.126 0.447 3.252 2559 5128 0.168 0.657 2.545 2015 STR. V 9642 0.310 0.481 2.233 4317 6323 0.410 0.663 1.478 4277 SER. I 7206 0.315 0.461 2.243 3213 7206 0.315 0.461 2.243 3213 STR. I 9905 0.351 0.480 2.027 4887 6561 0.461 0.656 1.265 5188 STR. III 8753 0.290 0.155 2.935 2982 5519 0.397 0.223 2.156 2560 STR. V 9642 0.365 0.430 2.033 4743 6323 0.484 0.594 1.230 5140 H SER. I 7206 0.364 0.413 2.064 3491 7206 0.364 0.413 2.064 3491

(I) Deep Foundations:

The critical loading conditions for evaluation of the bearing resistance and settlement of a group of piles or drilled shafts are combinations of axial load and moment which produce the maximum axial stresses in the piles or shafts.

For design at the Strength Limit State, the critical combinations from Table 4-25 are:

• Case A, Strength I Limit State, Max Loads - produces maximum combination of axial load (11 348 kN) and moment (5632 kN-m) in the transverse direction.

• Case D, Strength I Limit State, Max Loads - produces maximum combination of axial load (10 671 kN) and moment (5427 kN-m) in the longitudinal direction.

For design at the Service Limit State, the critical combinations from Table 4-25 are:

• Case A, Service I Limit State & Case E, Service I Limit State produce maximum combinations of axial load and moment in the transverse direction, respectively:

Case A, Service I: Q = 7991 kN; MT = 3803 kN-m

Case E, Service I: Q = 7427 kN; MT = 4114 kN-m

• Case B, Service I Limit State & Case D, Service I Limit State produce maximum combinations of axial load and moment in the longitudinal direction, respectively:

Case B, Service I: Q = 7991 kN; ML = 3269 kN-m

Case E, Service I: Q = 7623 kN; ML = 3614 kN-m (II) Spread Footing Foundations:

The critical loading conditions for evaluation of bearing resistance and settlement of spread footing foundations are those which produce the maximum factored and unfactored bearing pressures.

For design at the Strength Limit State, the critical load combination from Table 4-26 is:

• Case C/D, Strength I, Minimum Loads q = 16 117 kPa

For design at the Service Limit State, the critical load combination from Table 4-26 is:

• Case D, Service I Limit State q = 4993 kPa

(B) Overturning: (I) Deep Foundations:

Overturning failure is not typically evaluated for deep foundation systems for bridge piers.

Overturning would be considered only for structures subjected to extreme uplift and/or horizontal loads which could result in net tension loading of deep foundation elements.

(II) Spread Footing Foundations

The critical loading condition for spread footing foundations are those which produce the maximum base pressure resultant eccentricity. This failure mode is checked only for the

Strength Limit State.

The critical loading conditions, from Table 4-26, are:

• Case C/D, Strength I, Minimum Loads - produces maximum eccentricity in the longitudinal direction:

eB = 0.656 m

• Case E/F, Strength I, Minimum Loads - produces maximum eccentricity in the transverse direction:

eL = 0.810 m

(C) Lateral Loading/Sliding and Lateral Deflection

(I) Deep Foundations

The critical loading conditions for lateral loading of deep foundation groups are generally combinations of maximum horizontal load, moment and axial load which produce the greatest foundation element stresses and lateral deflections.

For Strength Limit State Design, the critical load combinations from Table 4-25 are:

• Cases A/C, Strength III, Maximum Loads - produce most severe loading in the transverse direction:

Horizontal load = 270 kN

• Cases C/D, Strength I, Maximum Loads - produce most severe loading in the longitudinal direction:

Horizontal load = 317 kN

• Cases A/E, Service I - produce most severe loading in the transverse direction:

Case A, Service I: Horizontal load = 115 kN; MT = 3803 kN-m

Case E, Service I: Horizontal load = 100 kN; MT = 4114 kN-m

• Case D, Service I - produces most severe loading in the longitudinal direction:

Case D, Service I: Horizontal load = 261 kN; ML = 3614 kN-m (II) Spread Footing Foundations

The critical loading conditions for sliding of spread footing foundations are those which produce the greatest horizontal loads and horizontal to vertical load ratios. This failure mode is checked only for the Strength Limit State. The critical load combinations for sliding of spread footing foundations, from Table 4-25, are:

• Case A/C, Strength III, Minimum Loads - produces maximum horizontal load (245 kN) and horizontal to vertical load ratio (0.05) in the transverse direction

• Case D, Strength V, Minimum Loads - produces maximum horizontal load (294 kN) and horizontal to vertical load ratio (0.04) in the longitudinal direction

(E) Summary of Critical Loading Combinations: Table 4-27

Critical Load Combinations for Deep Foundations

Critical Load Combination Evaluation Criteria Cases A/D, Strength I, Max Loads Bearing Resistance Cases A/C, Strength III, Max Loads

Cases C/D, Strength I, Max Loads Lateral Load Resistance Cases A/B/D/E, Service I Settlement and Lateral _Deflection

Table 4-28

Critical Load Combinations for Spread Footing Foundations

Critical Load Combinations Evaluation Criteria Cases C/D, Strength I, Min Loads Bearing Resistance

Cases C/D/E/F, Strength I, Min Loads Overturning (Eccentricity) Cases A/C, Strength III, Min Loads

Case D, Strength V, Min Loads Sliding

Case D, Service I Settlement

Factored Foundation Design Loads

The factored loads and moments in Table 4-25 represent values at the base of the pier stem (i.e., at the top of the footing or pile cap) resulting from the dead load of and external loads on the bridge superstructure and pier. For geotechnical and structural design of the pier foundation, the loads must be adjusted to include the effects of the footing weight, the weight of soil above the foundation, and any lateral loads associated with the overlying soil.

For this example, the ground surface at the pier location is essentially horizontal, such that adjustments are required only for the weight of the footing (or pile cap) and overlying soil. Assume a footing or pile cap having plan dimensions (BF X LF) of 5.2 m by 5.2 m and a

thickness of 1.2 m overlain by 0.5 m of soil having a density,  = 18.835 kN/m3.

(I) Footing/Pile Cap Weight

The unfactored dead load of the footing is: DCF = 765 kN

The factored dead load of the footing is: QF = 0 ((DC DCF)

For an importance factor (0i) of 1.05 and a maximum dead load factor ((DC) of 1.25

QF = 1.05 (1.25) 765 kN = 1004 kN

For an importance factor (0i) of 0.95 and a minimum dead load factor ((DC) of 0.90:

QF = 0.95 (0.90) 765 kN = 654 kN

For design at the Service Limit State, 0 =1.0 and (DC = 1.0, such that:

QF = 765 kN

(II) Soil Pressure on Footing

EV = 206 kN

• The factored earth pressure on the footing is: QS = 0 ((EV EV)

For an importance factor 0I = 1.05 and a maximum earth load factor, (EV = 1.35:

QS = 1.05(1.35)206 kN = 292 kN

For an importance factor (0) of 0.95 and a minimum load factor of 0.90: QS = 0.95(0.90)206 kN = 176 kN

For design at the Service Limit State: QS = 206 kN

(III) Summary of Factored Loads for Possible Critical Loading Combinations

For this example, it is assumed that the pier stem is centered on the footing. Therefore, the footing and overlying soil weight impart no unbalanced loading such that they only increase the vertical load at the base of the footing. The factored loads from Table 4-25 for the possible critical loading combinations in Tables 4-27 and 4-28, adjusted for footing weight and embedment, are summarized in Table 4-29.

Table 4-29

Summary of Factored Loads for Critical Foundation Design Load Combinations

MAXIMUM LOADS MINIMUM LOADS

Moments Horiz. Load Moment Horiz. Load

LOAD CASE

Long.

(kN-m) (kN-m)Trans.

Axial Load

(kN) Long. _(kN) Trans. _{(kN) (kN-m)}Long. _(kN-m)Trans.

Axial Load (kN) Long. _(kN) Trans. _(kN) STR I 4772 5632 12 644 317 77 --- --- --- --- --- STR III 1046 3723 9617 74 270 862 3369 5958 67 245 A SER I 2912 3803 8962 220 115 --- --- --- --- --- STR I 4772 5632 12 644 317 77 --- --- --- --- -- B SER I 3269 3454 8960 261 85 --- --- --- --- --- STR I 5427 4432 11 967 317 77 4761 4010 8084 287 70 C _{STR III 1046 3723 9617 74 270 862 3369 5958 67 245} STR I 5427 4432 11 967 317 77 4761 4010 8084 287 70 STR V --- --- --- --- --- 4398 3528 7688 294 102 D SER I 3614 2801 8594 261 85 --- --- --- --- --- STR I --- --- --- --- --- 2671 5613 7758 182 45 E _{SER I 2060 4114 8398 157 100 --- --- --- --- ---} F STR I --- --- --- --- --- 2671 5613 7758 182 45

The design of a pile foundation to support the pier in this example is described in Chapter 9, Design Example 1, Section 9.6.

CHAPTER 5