Geotechnical Engineering Circular (GEC) No. 8
Design And Construction Of Continuous Flight Auger Piles
Final
April 2007

Appendix B: Example Problems: Spreadsheet Solutions For Axial Capacity Of Single CFA Piles With Depth

B.1 Conventional CFA Pile In Cohesive Soil

Problem Statement

Conventional CFA piles, 18 inches in nominal diameter, are being considered for use to provide support for a highway interchange in a coastal plains area. A subsurface investigation performed, as described in the Chapter 6 example problem (Section 6.7.4, Part A), provided information necessary to develop the generalized soil profile at the pier location as was shown in Figure 5.32. The bottom of the proposed pile cap is at a depth of 4 ft. An allowable stress design (ASD) is to be used with a safety factor of 2.0, as detailed in Chapter 6 (Section 6.7.4 Part D). Note that a safety factor of 2.0 is used, as full-scale load testing will be implemented to verify (or modify if necessary) the pile capacity estimates. Details of the safety factor selection criteria (ASD) will be presented subsequently in Chapter 6. Loading of the bridge and the proposed foundation layout has determined the axial loads to the individual CFA pile (as detailed in Section 6.7.4 Part E). For an allowable pile capacity of 130 kips, what pile embedment depth should be specified in accordance with ASD?

Spreadsheet Solution

The following section presents a spreadsheet solution for the ultimate static axial resistance and the allowable static axial resistance with depth of a single CFA pile in accordance with ASD. Note that a hand calculation of resistance at a pile depth of 60 ft is presented in Section 5.8.1. The recommended method, as detailed in Section 5.3.1.1, for estimating the ultimate resistance of a single CFA pile in cohesive soil was used.

The calculations for an ASD approach are presented in Table B.1. The calculations will be detailed column by column in the section to follow. A graphical presentation of the estimated resistances in accordance with ASD is provided as Figure B.1. It can be seen in this figure that a CFA pile minimum embedment depth of 69 ft is required to provide the specified minimum total allowable resistance of 130 kips, with a safety factor of 2.0 applied to the ultimate resistance.

The following list details the calculations in Table B.1 (column-by-column)

1. Pile Embedment Depth (L) - increments of 1 ft (ΔL) have been chosen for the spreadsheet solution with depth, as it is convenient and customary to provide a required embedment depth, in whole feet (ft). Note that the first whole ft increment with an allowable capacity greater than the required 130 kips should be specified.
2. Undrained Shear Strength (S_u) - provided from the subsurface investigation (from Section 6.7.4, Part A), as was shown in Figure 5.32 at the pier location. The top soil layer (soft clay) was idealized as having constant S_u with depth, while the bottom soil layer (medium to stiff clay) was idealized as having values of S_u that increased linearly with depth. Note that the values of S_u for the bottom soil layer are linearly interpolated from the depth at the mid-point of each of the pile segments.

   Table B.1. ASD Example Calculations for 18-inch Diameter - CFA pile in Cohesive Soils

   		Side Shear Resistance							End Bearing Resistance						Total Resistance
   	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P
   	L (ft)	Su (ksf)	α	fs (ksf)	ΔRs (kips)	Rs (kips)	SF	RS(Allow) (kips)	Su(ave,2-D) (ksf)	Nc′	qp (ksf)	RB (kips)	SF	RB(Allow) (kips)	RT (kips)	RT(Allow) (kips)
   	1	0.60	0.55	0.33	1.56	0.0	2.0	0.0	0.60	5.07	3.04	6.4	2.0	2.7	5.4	2.7
   	2	0.60	0.55	0.33	1.56	0.0	2.0	0.0	0.60	5.57	3.34	5.9	2.0	3.0	5.9	3.0
   	3	0.60	0.55	0.33	1.56	0.0	2.0	0.0	0.60	6.08	3.65	6.4	2.0	3.2	6.4	3.2
   	4	0.60	0.55	0.33	1.56	0.0	2.0	0.0	0.60	6.59	3.95	7.0	2.0	3.5	7.0	3.5
   	5	0.60	0.55	0.33	1.56	0.0	2.0	0.0	0.60	6.84	4.10	7.3	2.0	3.6	7.3	3.6
   	6	0.60	0.55	0.33	1.56	0.0	2.0	0.0	0.60	6.84	4.10	7.3	2.0	3.6	7.3	3.6
   	7	0.60	0.55	0.33	1.56	0.8	2.0	0.4	0.60	6.84	4.10	7.3	2.0	3.6	8.0	4.0
   	8	0.60	0.55	0.33	1.56	2.3	2.0	1.2	0.60	6.84	4.10	7.3	2.0	3.6	9.6	4.8
   	9	0.60	0.55	0.33	1.56	3.9	2.0	1.9	0.60	6.84	4.10	7.3	2.0	3.6	11.1	5.6
   	10	0.60	0.55	0.33	1.56	5.4	2.0	2.7	0.60	6.84	4.10	7.3	2.0	3.6	12.7	6.3
   	11	0.60	0.55	0.33	1.56	7.0	2.0	3.5	0.60	6.84	4.10	7.3	2.0	3.6	14.3	7.1
   	12	0.60	0.55	0.33	1.56	8.6	2.0	4.3	0.60	6.84	4.10	7.3	2.0	3.6	15.8	7.9
   	13	0.60	0.55	0.33	1.56	10.1	2.0	5.1	0.60	6.84	4.10	7.3	2.0	3.6	17.4	8.7
   	14	0.60	0.55	0.33	1.56	11.7	2.0	5.8	0.60	6.84	4.10	7.3	2.0	3.6	18.9	9.5
   	15	0.60	0.55	0.33	1.56	13.2	2.0	6.6	0.60	6.84	4.10	7.3	2.0	3.6	20.5	10.2
   	16	0.60	0.55	0.33	1.56	14.8	2.0	7.4	0.60	6.84	4.10	7.3	2.0	3.6	22.0	11.0
   	17	0.60	0.55	0.33	1.56	16.3	2.0	8.2	0.60	6.84	4.10	7.3	2.0	3.6	23.6	11.8
   	18	0.60	0.55	0.33	1.56	17.9	2.0	8.9	0.60	6.84	4.10	7.3	2.0	3.6	25.1	12.6
   	19	0.60	0.55	0.33	1.56	19.4	2.0	9.7	0.60	6.84	4.10	7.3	2.0	3.6	26.7	13.3
   	20	0.60	0.55	0.33	1.56	21.0	2.0	10.5	0.60	6.84	4.10	7.3	2.0	3.6	28.2	14.1
   	21	0.60	0.55	0.33	1.56	22.5	2.0	11.3	0.60	6.84	4.10	7.3	2.0	3.6	29.8	14.9
   	22	0.60	0.55	0.33	1.56	24.1	2.0	12.1	0.60	6.84	4.10	7.3	2.0	3.6	31.4	15.7
   	23	0.60	0.55	0.33	1.56	25.7	2.0	12.8	0.60	6.84	4.10	7.3	2.0	3.6	32.9	16.5
   	24	0.60	0.55	0.33	1.56	27.2	2.0	13.6	0.60	6.84	4.10	7.3	2.0	3.6	34.5	17.2
   	25	0.60	0.55	0.33	1.56	28.8	2.0	14.4	0.60	6.84	4.10	7.3	2.0	3.6	36.0	18.0
   	26	0.60	0.55	0.33	1.56	30.3	2.0	15.2	0.60	6.84	4.10	7.3	2.0	3.6	37.6	18.8
   	27	0.60	0.55	0.33	1.56	31.9	2.0	15.9	0.60	6.84	4.10	7.3	2.0	3.6	39.1	19.6
   	28	0.60	0.55	0.33	1.56	33.4	2.0	16.7	0.60	6.84	4.10	10.9	2.0	5.5	44.4	22.2
   	29	0.60	0.55	0.33	1.56	35.0	2.0	17.5	0.60	6.84	4.10	14.7	2.0	7.3	49.7	24.8
   	30	1.51	0.55	0.83	3.91	36.5	2.0	18.3	1.53	8.36	12.79	22.6	2.0	11.3	59.1	29.6
   	31	1.53	0.55	0.84	3.96	39.3	2.0	19.6	1.55	8.37	12.97	22.9	2.0	11.5	62.2	31.1
   	32	1.55	0.55	0.85	4.01	43.2	2.0	21.6	1.57	8.39	13.16	23.3	2.0	11.6	66.5	33.2
   	33	1.57	0.55	0.86	4.07	47.2	2.0	23.6	1.59	8.40	13.34	23.6	2.0	11.8	70.8	35.4
   	34	1.59	0.55	0.87	4.12	51.2	2.0	25.6	1.61	8.41	13.53	23.9	2.0	12.0	75.2	37.6
   	35	1.61	0.55	0.88	4.17	55.3	2.0	27.7	1.63	8.43	13.72	24.2	2.0	12.1	79.6	39.8
   	36	1.63	0.55	0.90	4.22	59.5	2.0	29.7	1.65	8.44	13.90	24.6	2.0	12.3	84.0	42.0
   	37	1.65	0.55	0.91	4.27	63.7	2.0	31.8	1.67	8.45	14.09	24.9	2.0	12.5	88.6	44.3
   	38	1.67	0.55	0.92	4.32	67.9	2.0	34.0	1.69	8.47	14.28	25.2	2.0	12.6	93.2	46.6
   	39	1.69	0.55	0.93	4.37	72.2	2.0	36.1	1.71	8.48	14.47	25.6	2.0	12.8	97.8	48.9
   	40	1.71	0.55	0.94	4.42	76.6	2.0	38.3	1.73	8.49	14.66	25.9	2.0	13.0	102.5	51.2
   	41	1.73	0.55	0.95	4.47	81.0	2.0	40.5	1.75	8.51	14.85	26.2	2.0	13.1	107.2	53.6
   	42	1.75	0.55	0.96	4.52	85.4	2.0	42.7	1.76	8.52	15.04	26.6	2.0	13.3	112.0	56.0
   	43	1.76	0.55	0.97	4.57	89.9	2.0	44.9	1.78	8.54	15.23	26.9	2.0	13.5	116.8	58.4
   	44	1.78	0.55	0.98	4.62	94.4	2.0	47.2	1.80	8.55	15.42	27.3	2.0	13.6	121.7	60.8
   	45	1.80	0.55	0.99	4.68	99.0	2.0	49.5	1.82	8.56	15.61	27.6	2.0	13.8	126.6	63.3
   	46	1.82	0.55	1.00	4.73	103.7	2.0	51.8	1.84	8.58	15.81	27.9	2.0	14.0	131.6	65.8
   	47	1.84	0.55	1.01	4.78	108.4	2.0	54.2	1.86	8.59	16.00	28.3	2.0	14.1	136.7	68.3
   	48	1.86	0.55	1.02	4.83	113.1	2.0	56.6	1.88	8.60	16.19	28.6	2.0	14.3	141.8	70.9
   	49	1.88	0.55	1.04	4.88	117.9	2.0	59.0	1.90	8.68	16.51	29.2	2.0	14.6	147.1	73.6
   	50	1.90	0.55	1.05	4.93	122.8	2.0	61.4	1.92	8.68	16.69	29.5	2.0	14.7	152.3	76.1
   	51	1.92	0.55	1.06	4.98	127.7	2.0	63.9	1.94	8.69	16.86	29.8	2.0	14.9	157.5	78.8
   	52	1.94	0.55	1.07	5.03	132.7	2.0	66.3	1.96	8.69	17.04	30.1	2.0	15.1	162.8	81.4
   	53	1.96	0.55	1.08	5.08	137.7	2.0	68.8	1.98	8.69	17.21	30.4	2.0	15.2	168.1	84.0
   	54	1.98	0.55	1.09	5.13	142.7	2.0	71.4	2.00	8.69	17.39	30.7	2.0	15.4	173.4	86.7
   	55	2.00	0.55	1.10	5.18	147.8	2.0	73.9	2.02	8.70	17.56	31.0	2.0	15.5	178.9	89.4
   	56	2.02	0.55	1.11	5.23	153.0	2.0	76.5	2.04	8.70	17.74	31.3	2.0	15.7	184.3	92.2
   	57	2.04	0.55	1.12	5.29	158.2	2.0	79.1	2.06	8.70	17.91	31.7	2.0	15.8	189.9	94.9
   	58	2.06	0.55	1.13	5.34	163.5	2.0	81.7	2.08	8.70	18.09	32.0	2.0	16.0	195.4	97.7
   	59	2.08	0.55	1.14	5.39	168.8	2.0	84.4	2.10	8.70	18.26	32.3	2.0	16.1	201.0	100.5
   	60	2.10	0.55	1.15	5.44	174.1	2.0	87.1	2.12	8.71	18.44	32.6	2.0	16.3	206.7	103.4
   	61	2.12	0.55	1.16	5.49	179.5	2.0	89.8	2.14	8.71	18.61	32.9	2.0	16.4	212.4	106.2
   	62	2.14	0.55	1.18	5.54	185.0	2.0	92.5	2.16	8.71	18.79	33.2	2.0	16.6	218.2	109.1
   	63	2.16	0.55	1.19	5.59	190.5	2.0	95.3	2.18	8.71	18.97	33.5	2.0	16.8	224.0	112.0
   	64	2.18	0.55	1.20	5.64	196.1	2.0	98.0	2.20	8.72	19.14	33.8	2.0	16.9	229.9	115.0
   	65	2.20	0.55	1.21	5.69	201.7	2.0	100.8	2.22	8.72	19.32	34.1	2.0	17.1	235.8	117.9
   	66	2.22	0.55	1.22	5.74	207.4	2.0	103.7	2.24	8.72	19.50	34.5	2.0	17.2	241.8	120.9
   	67	2.24	0.55	1.23	5.79	213.1	2.0	106.5	2.25	8.72	19.67	34.8	2.0	17.4	247.8	123.9
   	68	2.25	0.55	1.24	5.84	218.9	2.0	109.4	2.27	8.73	19.85	35.1	2.0	17.5	253.9	127.0
   	69	2.27	0.55	1.25	5.90	224.7	2.0	112.3	2.29	8.73	20.02	35.4	2.0	17.7	260.1	130.0
   	70	2.29	0.55	1.26	5.95	230.5	2.0	115.3	2.31	8.73	20.20	35.7	2.0	17.8	266.2	133.1
   	71	2.31	0.55	1.27	6.00	236.5	2.0	118.2	2.33	8.73	20.38	36.0	2.0	18.0	272.5	136.2
   	72	2.33	0.55	1.28	6.05	242.4	2.0	121.2	2.35	8.74	20.55	36.3	2.0	18.2	278.8	139.4
   	73	2.35	0.55	1.29	6.10	248.5	2.0	124.2	2.37	8.74	20.73	36.6	2.0	18.3	285.1	142.5
   	74	2.37	0.55	1.30	6.15	254.5	2.0	127.3	2.39	8.74	20.91	36.9	2.0	18.5	291.5	145.7
   	75	2.39	0.55	1.32	6.20	260.7	2.0	130.3	2.41	8.74	21.09	37.3	2.0	18.6	297.9	149.0
   	76	2.41	0.55	1.33	6.25	266.8	2.0	133.4	2.43	8.75	21.26	37.6	2.0	18.8	304.4	152.2
   	77	2.43	0.55	1.34	6.30	273.1	2.0	136.5	2.45	8.75	21.44	37.9	2.0	18.9	310.9	155.5
   	78	2.45	0.55	1.35	6.35	279.3	2.0	139.7	2.47	8.75	21.62	38.2	2.0	19.1	317.5	158.8
   	79	2.47	0.55	1.36	6.40	285.7	2.0	142.8	Su needed 2-Diameters Below Tip
   	80	2.49	0.55	1.37	6.45	292.0	2.0	146.0

   Figure B.1. ASD Example for CFA Pile in Cohesive Soils

   

3. Alpha Factor (α) - because the ratio of the undrained shear strength to standard atmospheric pressure is less than 1.5 (S_u/P_a ≤ 1.5), the alpha factor (α) is constant at 0.55. Note that for S_u/P_a >1.5, α would need to be reduced as detailed in Section 5.3.1.1.
4. Ultimate Unit Side Shear (f_S) - the product of columns "C" and "B" (f_S = α S_u).
5. Ultimate Side Shear for Pile Segment (ΔR_S) - the product of column "D" and the peripheral area of the pile segment (ΔR_S = f_S A_(peripheral) = f_S π D_(diameter) ΔL).
6. Ultimate Side Shear (R_S) - the sum of the pile segment ultimate side shear values (Σ Δ R_S) to the pile embedment depth with the following contributions discounted: The top 5 ft (shaded section in Column "F"), and the bottom section of pile equal in length to one pile diameter (1.5 ft for this example). Discounting of sections at the top and bottom of pile is detailed in Section 5.3.1.1. Note that if an evaluation of the depth of seasonal moisture change were to reveal a depth in excess of 5 ft, then this larger depth would be discounted from contributing to the side shear resistance.
7. The Safety Factor (SF) - given in problem statement as 2.0.
8. The Allowable Side Shear Resistance (R_S(Allow)) - column "F"divided by column "G".
9. Average Undrained Shear Strength Below the Pile Tip (S_u(ave,2-D)) - the average of column "B" from the pile tip to a depth of 2 pile diameters below the pile tip (in this example 3 ft). This is as recommended in Section 5.3.1.1; solutions for the depth of influence of end-bearing typically range from as shallow as 2 diameters above the tip and as deep as 3 to 4 diameters below the tip.
10. Bearing Capacity Factor (N_c^*) - linearly interpolated from the undrained shear strength (S_u) of each soil layer from the values listed in Table B.1, because modulus data (E_S) was not obtained in the site investigation. Note that the bearing capacity factor has been further reduced for embedment depths less than 3 pile diameters (L < 3 D_(diameter)) as detailed in Section 5.3.1.1 (shown as shaded section of column "J" in Table 5.3).
11. Ultimate Unit End-Bearing (q_p) - the product of columns "J" and "I" (q_p = N_c^* S_u(ave,2-D)).
12. Ultimate End-Bearing (R_B) - the product of column "K" and the cross-sectional area of the pile (R_B = q_p A_{(cross-section)} = q_p (π/4) D_(diameter)²).
13. The Safety Factor (SF) - given in problem statement as 2.0. Note that a safety factor of 2.0 is used, as full-scale load testing will be implemented to verify (or modify if necessary) the pile capacity estimates.
14. The Allowable End-Bearing Resistance (R_B(Allow)) - Column "L"divided by column "M".
15. Ultimate Total Resistance (R_T) - sum of columns "F" and "L" (R_T = R_S + R_B).
16. The Allowable Total Resistance (R_T(Allow)) - sum of columns "H" and "N". Note this could be calculated as the product of column "O" and the Safety Factor, as only an overall safety factor was specified.

B.2 Conventional CFA And Drilled Displacement Piles In Cohesionless Soils

Problem Statement

Both conventional CFA piles and drilled displacement piles, either of which have a nominal diameter of 18 inches, are being considered for use to provide support for a bridge over a small stream within a flood plain. A subsurface investigation performed provided information to develop the generalized soil profile at the pier location, as was shown in Figure 5.33, in terms of SPT-N values, soil descriptions, and unit weights. While the pier location is usually accessible by track mounted equipment, extreme high tides have been known to bring the water level up to that of the site. The hydraulic engineer for the project has indicated that potential scour exists at the pier to a depth of 6 ft. The bottom of the proposed pile cap is also proposed at a depth of 6 ft. An allowable stress design (ASD) may be used with a safety factor of 2.5. Note that details of the safety factor selection criteria (ASD) were presented in Chapter 6. Loading of the bridge and the proposed foundation layout has determined an allowable total capacity of 170 kips per pile (in accordance with ASD). What minimum pile embedment depth for both pile types should be specified in accordance with ASD.

Spreadsheet Solution

The recommended method for estimating the ultimate resistance of a single CFA pile in cohesionless soil was used as detailed in Section 5.3.2.1, and the recommended method for estimating the ultimate resistance of a single drilled displacement pile in cohesionless soil was used as detailed in Section 5.4.2. The calculations for the conventional CFA pile are presented in Table B.2., while the calculations for the drilled displacement pile are presented in Table B.3. All calculations will be detailed column by column in the section to follow.

For the conventional CFA pile, a graphical presentation of the estimated resistances in accordance with ASD is provided as Figure B.2 for the conventional CFA pile, and as Figure B.3 for the drilled displacement pile. It can be seen in these figures that the specified minimum total allowable resistance of 170 kips, with a safety factor of 2.5, may be provided by a conventional CFA pile minimum embedment depth of 62 ft, while a drilled displacement pile minimum embedment depth of only 37 ft is required. Note from the borings near the pier location (Figure 5.33) that a depth of 37 ft corresponds to the transition from soil layer 2 (Silty Fine Sand) to the more competent soil layer 3 (Shelly Sand). Prudence suggests that the embedment depth should be extended a couple of feet to ensure that the pile is tipped into this more competent soil layer in order to take advantage of the associated greater end-bearing development.

Figure B.4 presents the ultimate resistances of both the conventional CFA pile and the drilled displacement pile with depth to illustrate the capacity advantage that can be realized with a drilled displacement technique in cohesionless soils. For this example, the drilled displacement piles provide a total resistance of approximately 3.5 times (on the average) the total resistance provided by the CFA pile at any given depth.

The following list details the CFA pile calculations in Table B.2 (column-by-column)

1. SPT-N Values - from the subsurface investigation, as was shown in Figure 5.33.
2. Depth of SPT-N Values - from the subsurface investigation, as was shown in Figure 5.33.
3. Pile Embedment Depth (L) - increments (ΔL) have been chosen for the spreadsheet solution such that the division between pile sections lies midway between the reported SPT-N values with depth. The pile was segmented in this way mainly for ease in illustrating the recommended method for estimating the end-bearing resistance with SPT-N values. However, minor differences in SPT-N values obtained within a soil layer type may very well be an artifact of testing inconsistencies as much as soil variation, and even if attributable to soil variation construction of the CFA pile may tend to average out these effects. Alternatively, either simple averages of similar soil types and strengths or a linear fit of the strengths with depth (perhaps from multiple borings) are routinely performed and easily accommodated.
4. Depth to Mid-Point of Pile Segment (L_(mid)) - midpoint between pile tip elevation and pile tip elevation from previous segment.
5. Length of Pile Segment (ΔL) - difference between pile tip elevation and pile tip elevation from previous segment.
6. Vertical Effective Stress at Mid-Point of Pile Segment (σ′_v) - total vertical stress minus hydrostatic pressure. Further, the solution in this example has assumed a worst case "bed" scour where the top 6 ft has been discounted (shown as shaded areas in columns "F" and "G") in calculating both the effective stress distribution and beta factor (β) with depth. Note that if the scour was anticipated to be only "localized", the top 6 ft need not be discounted in calculating the effective stress distribution and beta factor (β).
7. Beta Factor (β) - determined as a function of pile embedment depth (L) in accordance with Section 5.3.2.1. Note that the β factor for the first and second pile segments were subject to the limitation of 1.2, and the eighth through tenth pile segments were reduced by the ratio of N/15 as these SPT-N values were less than 15 (all shown as shaded areas of Column "G"). None of the pile segments were subjected to the lower limit of β ≥ 0.25.

   Table B.2. ASD Example Calculations for 18-inch Diameter CFA Pile in Cohesionless Soils

   	SPT-N Values, Pile Depths and Segment Lengths					Side Shear Resistance							End Bearing Resistance						Total Resistance
   	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T
   	SPT-N (blows / ft)	L(SPT-N) (ft)	L (ft)	L(mid) (ft)	Δ L (ft)	σ′v (psf)	β	fs (tsf)	ΔRs (kips)	Rs (kips)	SF	RS(Allow) (kips)	N(ave)		qp (ksf)	RS (kips)	SF	RB(Allow) (kips)	RT (kips)	RT(Allow) (kips)
   	16	2.0	3.25	1.63	3.25	0	1.20	0.00	0.0	0.0	2.5	0.0	21		24.80	43.8	2.5	17.5	43.8	17.5
   	27	4.5	5.75	4.50	2.50	0	1.20	0.00	0.0	0.0	2.5	0.0	23		28.00	49.5	2.5	19.8	49.5	19.8
   	19	7.0	8.25	7.00	2.50	58	1.20	0.07	0.8	0.7	2.5	0.3	23		27.20	48.1	2.5	19.2	48.8	19.5
   	24	9.5	10.75	9.50	2.50	202	1.25	0.25	3.0	3.7	2.5	1.5	24		28.40	50.2	2.5	20.1	53.9	21.6
   	25	12.0	13.25	12.00	2.50	346	1.17	0.40	4.8	8.5	2.5	3.4	24		28.20	49.8	2.5	19.9	58.3	23.3
   	22	14.5	17.00	15.13	3.75	526	1.09	0.57	10.1	18.6	2.5	7.4	24		28.80	50.9	2.5	20.4	69.5	27.8
   	26	19.5	22.00	19.50	5.00	778	1.00	0.78	18.4	37.0	2.5	14.8	18		21.00	37.1	2.5	14.8	74.1	29.6
   	9	24.5	27.00	24.50	5.00	1056	0.55	0.58	13.7	50.7	2.5	20.3	8		9.60	17.0	2.5	6.8	67.7	27.1
   	7	29.5	32.00	29.50	5.00	1334	0.39	0.53	12.4	63.1	2.5	25.2	8		9.00	15.9	2.5	6.4	79.0	31.6
   	8	34.5	37.00	34.50	5.00	1612	0.42	0.67	15.8	78.9	2.5	31.6	26		30.60	54.1	2.5	21.6	133.0	53.2
   	43	39.5	42.00	39.50	5.00	1967	0.72	1.41	33.3	112.2	2.5	44.9	54		64.20	113.5	2.5	45.4	225.7	90.3
   	64	44.5	47.00	44.50	5.00	2323	0.66	1.54	36.2	148.5	2.5	59.4	68		81.60	144.2	2.5	57.7	292.7	117.1
   	72	49.5	52.00	49.50	5.00	2678	0.61	1.63	38.5	186.9	2.5	74.8	75		89.40	158.0	2.5	63.2	344.9	138.0
   	77	54.5	57.00	54.50	5.00	3034	0.56	1.70	40.0	226.9	2.5	90.8	79		90.00	159.0	2.5	63.6	386.0	154.4
   	81	59.5	62.00	59.50	5.00	3389	0.51	1.74	40.9	267.9	2.5	107.1	79		90.00	159.0	2.5	63.6	426.9	170.8
   	76	64.5	67.00	64.50	5.00	3745	0.47	1.75	41.2	309.1	2.5	123.6	74		88.20	155.9	2.5	62.3	465.0	186.0
   	71	69.5	72.00	69.50	5.00	4100	0.42	1.74	41.0	350.1	2.5	140.0	SPT-N Values needed at least 2-Diameters Below Tip

   Table B.3. ASD Example Calculations for 18-inch Diameter Drilled Displacement Pile in Cohesionless Soils

   	SPT-N Values, Pile Depths and Segment Lengths					Side Shear Resistance							End Bearing Resistance						Total Resistance
   	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T
   	SPT-N (blows / ft)	L(SPT-N) (ft)	L (ft)	L(mid) (ft)	Δ L (ft)	σ′v (psf)	WS (ksf)	fs (tsf)	ΔRs (kips)	Rs (kips)	SF	RS(Allow) (kips)	N(ave)	WT (ksf)	qp (ksf)	RS (kips)	SF	RB(Allow) (kips)	RT (kips)	RT(Allow) (kips)
   	16	2.0	3.25		3.25		0.00	1.60	24.5	0.0	2.50	0.0	SPT-N Values needed Approximately 4-Diameters Above Tip
   	27	4.5	5.75		2.50		0.00	2.70	31.8	0.0	2.50	0.0	22	0	84.36	149.1	2.50	59.6	149.1	59.6
   	19	7.0	8.25		2.50		0.00	1.90	22.4	20.1	2.50	8.1	23	0	88.92	157.1	2.50	62.9	177.3	70.9
   	24	9.5	10.75		2.50		0.00	2.40	28.3	48.4	2.50	19.4	23	0	88.16	155.8	2.50	62.3	204.2	81.7
   	25	12.0	13.25		2.50		0.00	2.50	29.5	77.9	2.50	31.1	21	0	80.56	142.4	2.50	56.9	220.2	88.1
   	22	14.5	17.00		3.75		0.00	2.20	38.9	116.7	2.50	46.7	21	0	77.90	137.7	2.50	55.1	254.4	101.8
   	26	19.5	22.00		5.00		0.00	2.60	61.3	178.0	2.50	71.2	16	0	60.80	107.4	2.50	43.0	285.5	114.2
   	9	24.5	27.00		5.00		0.00	0.90	21.2	199.2	2.50	79.7	13	0	47.50	83.9	2.50	33.6	283.2	113.3
   	7	29.5	32.00		5.00		0.00	0.70	16.5	215.7	2.50	86.3	17	0	63.65	112.5	2.50	45.0	328.2	131.3
   	8	34.5	37.00		5.00		0.00	0.80	18.8	234.6	2.50	93.8	31	0	115.90	204.8	2.50	81.9	439.4	175.7
   	43	39.5	42.00		5.00		1.00	4.30	101.3	335.9	2.50	134.4	47	28	178.00	314.6	2.50	125.8	650.4	260.2
   	64	44.5	47.00		5.00		1.00	4.40	103.7	439.5	2.50	175.8	64	28	178.00	314.6	2.50	125.8	754.1	301.6
   	72	49.5	52.00		5.00		1.00	4.40	103.7	543.2	2.50	217.3	74	28	178.00	314.6	2.50	125.8	857.8	343.1
   	77	54.5	57.00		5.00		1.00	4.40	103.7	646.9	2.50	258.8	77	28	178.00	314.6	2.50	125.8	961.4	384.6
   	81	59.5	62.00		5.00		1.00	4.40	103.7	750.6	2.50	300.2	76	28	178.00	314.6	2.50	125.8	1065.1	426.0
   	76	64.5	67.00		5.00		1.00	4.40	103.7	854.2	2.50	341.7	SPT-N Values needed Approximately 4-Diameters Below Tip
   	71	69.5	72.00		5.00		1.00	4.40	103.7	957.9	2.50	383.2

   Figure B.2: ASD Example for CFA Pile in Cohesionless Soils

   

   Figure B.3: ASD Example for Drilled Displacement Pile in Cohesionless Soils

   

   Figure B.4: Comparison of Ultimate Resistances of 18 inch Diameter CFA Pile and Drilled Displacement Pile for Cohesionless Soil Example

   

8. Ultimate Unit Side Shear (f_S) - the product of columns "G" and "F" (f_S = β σ′_v), note that none of the pile segments exceeded the limit of 2 tsf.
9. Ultimate Side Shear for Pile Segment (Δ R_S) - the product of column "H" and the peripheral area of the pile segment (Δ R_S = f_S A_peripheral = f_S π D_diameter Δ L).
10. Ultimate Side Shear (R_S) - the sum of the pile segment ultimate side shear values (Σ Δ R_S) to the pile embedment depth.
11. The Safety Factor (SF) - given in problem statement as 2.5.
12. The Allowable Side Shear Resistance (R_S(Allow)) - column "F"divided by column "G".
13. Average SPT-N Value Below Pile Tip (N_(ave)) - the average of column "A" from the pile tip to a depth of 2 to 4 pile diameters below the pile tip (in this example 4 to 8 ft), depending upon the frequency of SPT-N values with depth and soil layering. Note that the 14th and 15th pile segments have N_(ave) > 75 (shown as shaded areas of column "M), and the resulting q_p has been limited as described for column "O".
14. Intentionally left Blank - for easy comparison of example calculations of CFA piles (Table B.2) to drilled displacement piles (Table B.3).
15. Ultimate Unit End-Bearing (q_p) - columns "M" multiplied by 0.6 (q_p = 0.6 N_(ave)) to get q_p in tsf, and multiplied by 2 to convert units to ksf. Note that the 14th and 15th pile segments have been subject to the upper limit of 90 ksf (shown as shaded areas of column "O").
16. Ultimate End-Bearing (R_B) - the product of column "O" and the cross-sectional area of the pile (R_B = q_p A_{(cross-section)} = q_p (π/4) D_(diameter)²).
17. The Safety Factor (SF) - given in problem statement as 2.5.
18. The Allowable End-Bearing Resistance (R_B(Allow)) - Column "P" divided by column "Q".
19. Ultimate Total Resistance (R_T) - sum of columns "J" and "P" (R_T = R_S + R_B).
20. The Allowable Total Resistance (R_T(Allow)) - sum of columns "L" and "R". Note this could be calculated as the product of column "S" and the safety factor, as only an overall safety factor was specified.

The following list details the drilled displacement pile calculations in Table B.3 (column-by-column)

The calculations for the static axial capacity of the single drilled displacement pile differs from that for the CFA pile only in the estimation of the ultimate unit side shear and ultimate unit end-bearing resistances. Thus details for the drilled displacement pile calculations (column-by-column) are as described above for the CFA pile, with the following exceptions noted to follow.

1. Unit Side Shear Constant (W_s) - as specified by the recommended method detailed in Section 5.4.2. W_s = 0 ksf for the top two layers (Well rounded, and poorly graded material), and W_s = 1 ksf (0.5 tsf) for the bottom layer (angular, and well graded).
2. Ultimate Unit Side Shear (f_S) - as specified by the recommended method detailed in Section 5.4.2., (0.05 N (2 ksf / 1 tsf) + W_s), where SPT-N is from Column "A"and W_s is from Column "G". Note that the 12th through the 17th pile segments exceeded the limit of 4.4 ksf (2.2 tsf), and thus were set to this limiting value (shown as shaded areas of column "H").
3. Average SPT-N Value Below Pile Tip (N_(ave)) - the average of column "A" from the pile tip to a depth of approximately 4 pile diameters above and below the pile tip (in this example 4 to 8 ft), depending upon the frequency of SPT-N values with depth and soil layering. Note that the 12th through 15th pile segments have N_(ave) > 50 (shown as shaded areas of column "M"), and the resulting q_p will be limited in column "O".
4. Unit End-Bearing Constant (W_T) - as specified by the recommended method detailed in Section 5.4.2. W_s = 0 ksf for the top two layers (Well rounded, and poorly graded material), and W_s = 28 ksf (14 tsf) for the bottom layer (angular, and well graded).
5. Ultimate Unit End-Bearing (f_S) - as specified by the recommended method detailed in Section 5.4.2., (1.9 N_(ave) (2 ksf / 1 tsf) + W_T), where N_(ave) is from Column "M" and W_s is from Column "N". Note that the 11th through the 15th pile segments exceeded the limit of 178 ksf (89 tsf), and thus were set to this limiting value (shown as shaded areas of column "O").