APPENDIX B

SETTLEMENT PREDICTIONS

B-1

SETTLEMENT PREDICTIONS Schmertmann strain influence methodology Originally proposed by Schmertmann (1970) and modified by Schmertmann, Hartmann, and Brown (1978), this method was developed to estimate foundation settlements in sands. To utilize this method, the subsurface is broken into layers. Each layer has a constant value of strain and soil modulus. Settlement is calculated by summing the influence of all layers, as calculated by equation B-1.

zEIpCCS

B4,B2

0 s

z21 ∆∆= ∑ (eq. B-1)

where: ∆p = net foundation pressure = bearing pressure minus initial effective

vertical stress Iz = vertical strain influence factor (from Figure B-1) Es = soil modulus of deformation ∆z = thickness of soil layer C1 = pressure change correction factor for effective overburden

p'5.01 vo

∆σ

−=

σ’vo = initial effective vertical stress at the base of footing C2 = time influence factor = 1 + (0.2)(log (t/0.1)) t = time of interest (in years) Schmertmann developed the diagram shown in Figure B-1 to determine the appropriate strain influence factor, Iz, for each layer within the profile. Two distributions are shown: one for square or circular footings (L/B=1), and a second for strip footings (L/B>10). Both are triangular distributions, and the one for square or circular footings begins at a value of 0.1 at the base of the footing, while the one for strip footings begins at a value of 0.2 at the base of the footing. The maximum strain factor, Izp, occurs at a depth equal to B/2 for square footings and B for strip footings, and can be calculated using equation B-2.

vpzp '

p1.05.0Iσ∆

+= (eq. B-2)

where: σ’vp = initial effective stress at the depth of maximum strain influence.

B-2

Figure B-1. Strain influence factor diagram (from Schmertmann et al., 1978). Values of soil modulus: The soil modulus, Es, can be determined from the following three in-situ tests:

Cone penetrometer test (CPT): Schmertmann (1978) developed a correlation between cone penetrometer tip resistance, qc which is measured continuously as the cone is advanced through the soil, and soil modulus, Es, for sands. The soil moduli for axi-symmetrical (i.e. square or circular) and plane-strain (i.e. strip) footings are calculated differently, as shown in equations B-3 and B-4.

Es (axisymmetrical) = 2.5qc (eq. B-3) Es (plane-strain) = 3.5qc (eq. B-4)

Pressuremeter test (PMT): Martin (1977) studied the correlation between the PMT modulus, EPMT, and the soil modulus, Es, specifically in the Piedmont region. He concluded that EPMT and Es are nearly equivalent, and later studies by Gambin and Rousseau (1982) reached the same conclusion. The most direct way to obtain EPMT is to perform pressuremeter tests at critical depths below the expected foundation level and calculate EPMT. Appendix A explains how to interpret pressuremeter test results. Standard penetration test (SPT): Soil moduli can also be obtained from correlations with SPT N-values. Martin (1977, 1987) developed a

B-3

correlation between EPMT, or Es, and SPT N-values for Piedmont residual soils, as shown in Figure B-2. Trendline #33 is the most conservative correlation, and N-values and their corresponding EPMT values from the trendline are shown in Table B-1. One other method of determining Es from SPT testing is to develop a site-specific EPMT versus log N chart from site explorations, and use it in the same manner as Figure B-2. It is important to note that Martin (1987) suggests reducing the calculated settlements by 40% when using Figure B-2. This is known as the ‘Martin correction,’ and the implications of applying the correction are discussed in the bias and reliability section below.

Figure B-2. Pressuremeter modulus (EPMT) vs. SPT N-values (from Martin, 1987).

Bias and Reliability: Only one case with two comparisons was available using Schmertmann’s CPT correlation, so reliability could not be computed for the CPT correlation. This method of estimating soil modulus is not complex (only one calculation is needed to determine soil modulus), and settlements can be estimated relatively quickly.

B-4

A total of 9 comparisons were made using PMT test data to obtain EPMT. Figure B-3 illustrates the bias and reliability of the Schmertmann method using PMT parameters to estimate soil modulus. From the cases reviewed, it appears this method generally predicts settlements close to those measured in the field, with a slight bias (about 10%) towards conservatism.

Table B-1. Pressuremeter modulus (EPMT) and N-values for trendline #3 (after Martin, 1987).

N EPMT N EPMT N EPMT N EPMT N EPMT N EPMT

1 15 21 128 41 205 61 272 81 332 100/6 (200) 627

2 24 22 132 42 209 62 275 82 334 100/4 (300) 834

3 33 23 137 43 212 63 278 83 337 100/2 (600) 1359

4 40 24 141 44 216 64 281 84 340

5 47 25 145 45 219 65 284 85 343

6 53 26 149 46 223 66 287 86 346

7 59 27 153 47 226 67 290 87 349

8 65 28 157 48 229 68 293 88 351

9 71 29 161 49 233 69 296 89 354

10 76 30 165 50 236 70 299 90 357

11 81 31 169 51 239 71 302 91 360

12 86 32 172 52 243 72 305 92 363

13 91 33 176 53 246 73 308 93 365

14 96 34 180 54 249 74 311 94 368

15 101 35 184 55 252 75 314 95 371

16 106 36 187 56 256 76 317 96 374

17 110 37 191 57 259 77 320 97 376

18 115 38 195 58 262 78 323 98 379

19 119 39 198 59 265 79 326 99 382

20 124 40 202 60 268 80 329 100 385

N in blows/foot EPMT in tons/ft2

A total of 23 comparisons were made using SPT correlations to EPMT, as shown in Figure B-2 and Table B-1. The bias and reliability of calculating settlement using the correlation between SPT N-values and Es is shown in Figure B-4. From the bias calculated from Figure B-4, it was determined that this method overpredicts settlement by almost 80%. However, when Martin’s correction (a 40% reduction) is applied, the bias drops considerably, to less than 10%, as shown in Figure B-5. The SPT correlation method to estimate the soil modulus appears to be the quickest and easiest to use, since it does not require in-situ testing beyond the widely used SPT. At the very least, it can be used as a check of more complex methods used to estimate settlement.

B-5

Figure B-3. Reliability of Schmertmann strain influence method with PMT test data.

Figure B-4. Reliability of Schmertmann strain influence method with EPMT - SPT N-value correlation test data.

B-6

Figure B-5. Reliability of Schmertmann strain influence method with EPMT - SPT N-value correlation test data, corrected per Martin.

Spreadsheet for Schmertmann’s strain influence method The writers have developed a spreadsheet that performs settlement calculations using Schmertmann's strain influence methodology. A copy of the spreadsheet is on the floppy diskette included with this report. In order to use the program, the following information is required:

• Footing width, B, in feet • Elevation of ground surface, base of footing and water table, in feet • Unit weight of water, γw, in pcf • Net bearing pressure, ∆p, in psf • Total unit weight of soil above base of footing, in pcf • Time, t, at which to calculate settlement beyond end of construction, in years • Elevation of top and bottom of layer, in feet • Soil modulus, Es, in tsf • Total unit weight of soil, γT, in pcf

All calculations are completed for both the axisymmetric and plane-strain cases. Immediate settlement and settlement at time t (entered in input) is calculated. Values computed included:

B-7

• Initial effective vertical stress at the base of the footing, σ'vo • Elevation of Izp • Initial effective vertical stress at the depth of maximum strain influence factor, σ'vp • Maximum strain influence factor, Izp • Pressure change correction factor, C1 • Time influence correction factor, C2 • Thickness of layer and elevation of the center of the layer • Iz at the center of each layer • Strain at the center of each layer • Change in thickness at the center of each layer

Example calculation: Settlement was monitored for the First American Bank Building in Tyson’s Corner, Virginia (Law Engineering Testing Company, 1986). Cone penetrometer data and SPT N-values were used to characterize the site on which the construction of a 17-story office building was proposed. This sample calculation is for the estimated settlement of the proposed new office building. Seven SPT and three CPT explorations were completed in the area of the new building. However, complete data is only available for five of the SPT explorations. Figure B-6 summarizes the results of the SPT and CPT tests, as well as the resulting soil modulus profiles. A fill layer was encountered in 3 of the 5 borings (FAB-6, FAB-5, FAB-8). This fill consists of clay, silt and sand ranging in thickness from 9 to 11 feet. The fill was only encountered along the northernmost wall of the building and is overlain by a course gravel base and asphalt. Beneath the fill are silts and silty sands with blow counts ranging from 5 to 100, as shown in Figure B-6. Beneath the silty sands is a layer of decomposed rock at a depth of about 80 feet. Decomposed rock was defined for this project as samples with N-values greater than 60 blows/foot. Procedure for using spreadsheet: 1. Clear spreadsheet of existing input by pressing clear input button on the right. 2. Enter project information in the upper left corner. 3. Enter global input data:

• Square mat foundation dimensions = 150 feet • Thickness of mat foundation = 4.5 feet • Average net bearing pressure = 3260 psf • Elevation of ground surface = 500.5 • Groundwater was not detected in explorations; say elevation = 0 • Unit weight of water = 62.4 pcf • Unit weight of soil above footing base = 120 pcf • Settlement calculated at t = 1 year

B-8

Figure B-6. Site exploration summary and soil modulus profile (after Law Engineering, 1986).

4. Separate subsurface into sublayers and calculate the value of Es for each layer.

The subsurface profile was broken into 5 sublayers. The unit weight, average cone tip resistance, and average N-value and Es using both correlations were determined at the center of each layer. See Table B-2 for the layer input. Input elevations of the top of the layer and bottom of the layer, total unit weight, and soil modulus into the spreadsheet. This example will be done twice: once using the soil modulus obtained from the CPT data, and once using the soil modulus correlated from the SPT data. To obtain the soil modulus from the CPT data, equation B-3 was used, and to correlate the SPT data to a soil modulus, Table B-1 was used. Figure B-5 shows the determined soil modulus profile versus depth.

B-9

Table B-2. Example problem information for input into spreadsheet.

Data from CPT Data from SPT Layer

Top Elev. (ft)

Bottom Elev. (ft)

∆z (ft)

γt (pcf) qc

(kg/cm2) Es

1

(tsf) N-value

(blows/ft) Es

(tsf) 1 496 485 11 120 110 287 17 110 2 485 479.5 5.5 115 109 285 23 137 3 479.5 468 11.5 115 72 188 14 96 4 468 462 6 110 102 266 16 106 5 462 421 41 110 ---2 2663 51 239

Note: 1 Use equation B-3 since the mat foundation is axisymmetric 2 No data available beyond 32.5 feet in depth 3 Assume that Es is equal to or larger than layer 4 because N-values continue to increase. 1 kg/cm2 ≈ 1.044 tsf

5. Page down to see the calculated settlement. Table B-3 compares the measured and

calculated settlements, and the completed spreadsheets for this example are shown in Figures B-7 and B-8.

In this particular case, the use of the Schmertmann strain influence method using CPT test data to estimate soil modulus overpredicts the settlement at the time of construction completion. However, the estimated settlement at 1 year after construction is within the range of observed settlements. It should be noted that more than 60% of the settlement would come from layers at depths in which no CPT data is available, therefore limiting the usefulness of the CPT correlation in this case. The original correlation of SPT to Es also overpredicts the measured settlements. The calculated settlement at the end of construction is twice the maximum measured settlements. However, the calculated settlement after 1 year is equal to the maximum measured settlement. It is interesting to note that when the Martin correction is applied, the immediate settlement estimation is close to the maximum measured settlement, yet when comparing settlements after 1 year, the Martin correction underestimates the maximum settlement, by almost 50%.

Table B-3. Comparison of measured and calculated settlements using Schmertmann’s strain influence

method for an office building in Tyson’s Corner, VA.

Time Measured

settlements (inches)

Calculated settlements

using CPT soil modulus (inches)

Calculated settlements

using SPT soil modulus (inches)

Calculated settlements using SPT soil modulus

with Martin correction (inches)

Upon completion of construction 0.25-1.25 1.7 2.5 1.5

After 1 year 0.78-3.0 2.1 3.0 1.8

B-10

Project Name: 17-story office bldg using CPT dataProject Location: Tyson's Corner, VAProject Number: Foundation settlement exampleCalculations By: Angelle DucoteDate: 2/23/00

Footing Width, B 150.0 feetElevation of Ground Surface 500.5 feetElevation of Base of Footing 496.0 feetElevation of Water Table 0.0 feetUnit Weight of Water, γw 62.4 pcfNet Bearing Pressure, ∆P 3260 psfSoil Unit Weight Above Footing Base 120 pcf

years

Layer No.Elev. Of Top of layer (ft)

Elev. Of Bottom of layer (ft)

Soil Modulus Es

(tsf)

Total Unit Weight, γt

(pcf)1 496.0 485.0 287 1202 485.0 479.5 285 1153 479.5 468.0 188 1154 468.0 462.0 266 1105 462.0 421.0 266 1206789

1011 121314151617181920

Note: The depth of the water table must be a layer boundary.

Input Global Data

Input Layer Data

Settlement Calculated at end of construction and at time t 1

Figure B-7 (a). Settlement spreadsheet example – soil modulus based on CPT – input data.

B-11

σ'vo at Elevation 496.0 540 psfElev. of Izp 421.0 feetσ'vp at elevation 421.0 9395 psfIzp 0.559C1 0.92C2 1.20

Computed Axisymmetrical Layer Information

Layer No. Elev. Of Top of layer (ft)

Elev. Of Bottom of layer (ft)

Soil Modulus Es (tsf)

Total Unit Weight, γT

(pcf)∆z (ft)

Elev. Of Center of Layer (ft)

Iz ε∆H

(inches)

1 496 485 287 120 11 490.5 0.13 0.07% 0.092 485 479.5 285 115 5.5 482.25 0.18 0.10% 0.063 479.5 468 188 115 11.5 473.75 0.24 0.19% 0.264 468 462 266 110 6 465 0.29 0.16% 0.125 462 421 266 120 41 441.5 0.43 0.24% 1.206789

1011121314151617181920

Immediate Settlement 1.7 inches

Settlement After 1 year 2.1 inches

Compute Global Values for Axisymmetrical Case

Figure B-7 (b). Settlement spreadsheet example – soil modulus based on CPT – axisymmetric condition.

B-12

σ'vo at Elevation 496 540 psfElev. of Izp 346 feetσ'vp at elevation 346 18395 psfIzp 0.542C1 0.92C2 1.20

Computed Plane Strain Layer Information

Layer No. Elev. Of Top of layer (ft)

Elev. Of Bottom of layer (ft)

Soil Modulus Es (tsf)

Total Unit Weight, γT

(pcf)∆z (ft)

Elev. Of Center of Layer (ft)

Iz ε∆H

(inches)

1 496 485 287 120 11 490.5 0.21 0.11% 0.152 485 479.5 285 115 5.5 482.25 0.23 0.12% 0.083 479.5 468 188 115 11.5 473.75 0.25 0.20% 0.284 468 462 266 110 6 465 0.27 0.15% 0.115 462 421 266 120 41 441.5 0.32 0.18% 0.906789

1011121314151617181920

Immediate Settlement 1.5 inches

Settlement After 1 year 1.8 inches

Compute Global Values for Plane Strain Case

Figure B-7 (c). Settlement spreadsheet example – soil modulus based on CPT – plane strain condition.

B-13

Project Name: 17-story office bldg using SPT dataProject Location: Tyson's Corner, VAProject Number: Foundation settlement exampleCalculations By: Angelle DucoteDate: 2/23/00

Footing Width, B 150.0 feetElevation of Ground Surface 500.5 feetElevation of Base of Footing 496.0 feetElevation of Water Table 0.0 feetUnit Weight of Water, γw 62.4 pcfNet Bearing Pressure, ∆P 3260 psfSoil Unit Weight Above Footing Base 120 pcf

years

Layer No.Elev. Of Top of layer (ft)

Elev. Of Bottom of layer (ft)

Soil Modulus Es

(tsf)

Total Unit Weight, γt

(pcf)1 496.0 485.0 110 1202 485.0 479.5 137 1153 479.5 468.0 96 1154 468.0 462.0 109 1105 462.0 421.0 239 12067891011 121314151617181920

Note: The depth of the water table must be a layer boundary.

Input Global Data

Input Layer Data

Settlement Calculated at end of construction and at time t 1

Figure B-8 (a). Settlement spreadsheet example – soil modulus based on SPT – input data.

B-14

Figure B-8 (b). Settlement spreadsheet example – soil modulus based on SPT – axisymmetric condition.

B-15

Figure B-8 (c). Settlement spreadsheet example – soil modulus based on SPT – plane strain condition.

B-16

Modified Meyerhof SPT methodology Duncan and Buchignani (1976) modified Meyerhof’s (1965) original method of estimating settlement. This method correlates settlement to bearing pressure, SPT N-values and footing width, as shown by equation B-5.

BC)5.1'N(p5S

−= (eq. B-5)

where: S = instantaneous settlement, in inches p = bearing pressure, tsf N’ = average of minimum SPT N-value. For SPT N-values

greater than 15 blows/foot in silty sands below the water table:

N’ = 15 + 0.5(N-15) (eq. B-6)

otherwise: N’ = N

CB = width correction factor, see Table B-4 To calculate settlement after a period of time, equation B-5 should be multiplied by a time rate factor, Ct, which is shown in Table B-5. The average SPT N-value is determined for each boring, over the interval between the base of the footing and a depth equal to the width of the footing, B. The minimum average N-value should be used, and N-values greater than 15 blows/foot in silty sands below the water table should be corrected per equation B-6.

Table B-4. Width correction factor, CB (from Duncan and Buchignani, 1976).

Footing Width, B (feet) CB ≤ 4 1.00 6 0.95 8 0.90

10 0.85 ≥ 12 0.80

Table B-5. Time rate factor, Ct (from Duncan and Buchignani, 1976).

Time Ct 1 month 1.0 4 months 1.1

1 year 1.2 3 years 1.3

10 years 1.4 30 years 1.5

B-17

Bias and Reliability: A total of 19 comparisons were made using this method, and its reliability and bias are shown in Figure B-9. On average, this method overpredicts settlement by about 40%.

Figure B-9. Reliability of Modified Meyerhof SPT method.

Example calculation: Settlement was measured for a one million gallon on-ground storage tank (tank #2) in Atlanta, Georgia (Barksdale et al., 1986). Although the 40-foot diameter tank is supported by a concrete ringwall approximately 2 feet deep and 4 feet wide, it is more appropriate to consider the tank as uniform load. The subsurface conditions, shown in Figure B-10, consist of 6 to 10 feet of firm to very firm slightly micaceous clayey sand, underlain by 24 to 27 feet of loose to very firm micaceous silty sand. A 5-foot thick layer of partially weathered bedrock, which grades into bedrock, underlies the silty sand. No groundwater was encountered at the site. When completely filled, the tank applied a pressure of 7.2 ksf to the soil through the foundation, however settlements were also recorded for an applied pressure of 4.5 ksf. This example will estimate the immediate settlement for the 4.5 ksf load. Procedure to estimate settlement:

1. Calculate N’, which equals the minimum average N-value in any boring over the depth B below the footing elevation. In this case, B equals 40 feet, however the residual soil layer is only 30 feet thick, so the average SPT N-value over the 30-foot thick soil profile is used:

B-18

NB6&7 = (20+15+12+15+14+18+56+15+50+26)/10 = 24 blows/foot NB2 = (20+12+7+12+10+15)/6 = 13 blows/foot NB5 = (21+15+13+12+16+15+23)/7 = 16 blows/foot so N’ = 13 blows/foot.

2. Determine CB. Given a footing width of 40 feet, from Table B-4, CB = 0.8.

Figure B-10. Subsurface profile at one million gallon on-ground storage tank in Atlanta, GA (from

Barksdale et al., 1986).

3. Determine Ct. For immediate settlement, Ct = 1.0 from Table B-5.

4. Calculate settlement, S.

inches 1.22 1.5)(0.8)-(13

(2.25tsf))(5 (1.0) S ==

Table B-6 compares the measured and computed settlements for the example problem. In this particular case, the modified Meyerhof SPT method underpredicted the measured settlement by almost 50%. Although in this example the modified Meyerhof method underpredicted the measured settlement, review and analysis of applicable published settlements in the Piedmont shows that the method generally overpredict settlements by about 40%, as shown in Figure B-9.

B-19

Table B-6. Comparison of measured and calculated settlements using modified Meyerhof SPT method for a one million gallon on-ground storage tank in Atlanta, GA.

Measured settlement

(inches)

Calculated settlement

(inches) Range 1.4 – 2.0

Average 1.7 1.22

Peck, Hanson, and Thornburn SPT methodology Originally developed by Terzaghi and Peck in 1948 and published by Peck, Hanson, and Thornburn (1953), this method uses a chart, as shown in Figure B-11, to correlate allowable bearing pressure to footing width and SPT N-value. Given a footing width and an average SPT N-value, an allowable bearing pressure can be estimated for a maximum settlement of 1”. However, assuming that settlement is linearly proportional to bearing pressure, the chart can be used to estimate settlement, as shown in equation B-7.

Figure B-11. Chart correlating settlement, bearing capacity, footing width, and SPT N-value (from Peck et

al., 1953).

The average N-value to be used is the minimum N-value in any boring within a depth B below the footing. SPT N-values should be corrected for hammer energy and silt content. SPT N-values greater than 15 blows/foot in silty sands below the water table should be corrected per equation B-6. Peck et al. note that if groundwater is near or above the bottom of the footing, the allowable bearing pressure should be reduced by a factor of

B-20

one-half. For groundwater levels between the bottom of the footing and a depth B below the footing, interpolation should be used to determine an appropriate reduction.

inches) (in settlement of1"for pressureBearing

pressurebearing AppliedS = (eq. B-7)

Bias and Reliability: A total of 13 comparisons were made with this method, and its reliability and bias are shown in Figure B-12. The results of our analysis indicate that this method generally predicts about 3 times the measured settlement in the Piedmont.

Figure B-12. Reliability of Peck, Hanson, and Thornburn SPT method.

Example calculation: The case study presented in the modified Meyerhof method example calculation is presented herein. The relevant information for the Peck, Hanson, and Thornburn SPT method is: Minimum SPT N-value, N = 13 blows/foot;

Footing width, B = 40 feet; and Applied bearing pressure = 4.5 ksf.

B-21

Procedure to estimate settlement: 1. Determine bearing pressure for 1” of settlement.

Given N = 13 and B = 40 feet, Figure B-11 yields a bearing pressure of 1 tsf for 1” of settlement.

2. Calculate settlement, S.

inches 2.25 tsf)(1.0 tsf)(2.25S ==

Table B-7 compares the measured and computed settlements for the example problem. In this particular case, the Peck, Hanson, Thornburn SPT method predicted the maximum settlement fairly accurately (within 10%). However, review and analysis of 13 case histories in the Piedmont revealed that the Peck, Hanson, and Thornburn SPT method tends to overpredict settlement, by almost a factor of 3. Table B-7. Comparison of measured and calculated settlements using Peck, Hanson, and Thornburn SPT

method for a one million gallon on-ground storage tank in Atlanta, GA.

Measured settlement

(inches)

Calculated settlement

(inches) Range 1.4 – 2.0

Average 1.7 2.25

One-dimensional consolidation methodology This method is the conventional means of determining the compressibility of cohesive soils based on laboratory consolidation tests. Bias and Reliability: A total of 27 comparisons were made using this method, and its reliability and bias are shown in Figure B-13. On average, this method overpredicts settlement by almost a factor of 2.

B-22

Figure B-13. Reliability of one-dimensional consolidation method.

Menard PMT methodology Originally proposed by Menard and Rousseau (1962) and modified by Baguelin, Jezequel and Shields (1978), this method is a PMT modulus-based settlement computation. Menard developed equations to calculate settlement for five different subsurface conditions: two for homogeneous soils and three for heterogeneous soils. Baguelin et al. (1978) modified three of Menard’s five equations by reducing them by a factor of one-half. A full description and examples of the method can be found in Menard and Rousseau (1962), Baguelin et al. (1978), Barksdale et al. (1986), and Wilson (1988).

Bias and Reliability: A total of 13 comparisons were made using this method of estimating settlement, and all were for homogenous profiles. The reliability and bias of this method are illustrated in Figure B-14. Based on the cases reviewed, the tendency of this method is to underestimate settlement by approximately 25%.

B-23

Figure B-14. Reliability of Menard PMT method (using equations by Baguelin et al., 1978).