basis of calculations - geotech master

8/18/2019 Basis of Calculations - Geotech Master

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Q-Systems Engineering LLC

Structural and Geotechnical Consultants

www.qsystemsengineering.net

Page 1 of 15 April 15, 2016

GEOTECH MASTER™ BY Q-SYSTEMS ENGINEERING

BASIS OF EVALUATION

1. SCOPE

Geotech Master ™ by Q-Systems Engineering, receives as input basic geotechnical information and

produces as output soil engineering properties and allowable foundation pressures. More specifically:

1. The input to Geotech Master ™ includes soil profile data from borehole logs and geotechnical

index testing.

a. The soil profile is typically divided in layers of assumed constant properties such as

Standard Penetration Test (SPT) blow-count, constant cone penetrometer test (CPT) tip

resistance, etc.b. For each layer, information includes some or all of the following (provide only the ones

that are available):

i. Soil type, e.g. SILTY SAND. Selected from a list provided by the software.

ii. USCS classification (e.g. SW-SM). Selected from a list provided by the software.

iii. Dry unit weight. For this to be meaningful, it must be obtained from

undisturbed samples. As such, this information is not always available.

iv. Density (for granular materials) of stiffness (for fines). For example MEDIUM-

DENSE. Selected from a list provided by the software.

v. SPT blows per foot. If you use SPT blow-count, Geotech Master ™ needs to know

if the values are uncorrected (N), corrected (N_60), or corrected and adjustedfor depth (N1_60). If the blow count data are not corrected, Geotech Master ™

guides you how to provide the proper information to correct them. All required

information should be included in the drilling report, or it can be obtained from

the driller.

vi. CPT data. If you have Cone Penetrometer Test data, Geotech Master ™ invites

you to provide average values per layer of the following (complete or partial):

Tip resistance qc, tip water pressure u2, side resistance qs, side water pressure

u3.

vii. Water content in percent (e.g. 18).

viii. Plasticity index in percent (e.g. 29).ix. Liquid limit in percent (e.g. 37).

c. Select the menu option File | Print Geotechnical Data to print the spreadsheet of the

geotechnical data.

2. The output of Geotech Master ™ includes the Mohr-Coulomb strength parameters for each layer.

a. For each layer you have the option to select drained or undrained parameters.

http://www.qsystemsengineering.net/http://www.qsystemsengineering.net/http://www.qsystemsengineering.net/


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b. For granular materials, the undrained option is not meaningful and should not be

selected.

c. For fine materials, such as silts and clays, drained and undrained parameters are

meaningful and represent long term versus short term capacity. The options that are

best suited for your project must be selected. Alternatively, you can evaluate bearing

capacity with either option and select the most critical

d. Drained strength parameters (cohesion and/or internal friction angle in degrees)can be evaluated based on SPT blow counts and/or CPT resistance data, OR they can be

provided by the user if more reliable tests, such as direct shear, or consolidated

undrained (CU) or consolidated drained (CD) triaxial tests have been performed on soil

specimens. When strength parameters are evaluated based on SPT blow counts, the

corrected blow counts, which are also adjusted for depth are used. Thus, both N_60

and N1_60 are listed.

e. The undrained strength parameters can be evaluated based on SPT blow counts, CPT

resistance data, the plasticity index PI, the logarithmic liquidity index (defined later), OR

they can by selected by the user if more reliable tests, such as unconsolidated

undrained (UU) triaxial tests have been performed on soil specimens. The evaluation

option based on PI is considered to be the least reliable (especially since it is heavily

relied on the overconsolidation ratio) and is not recommended if any of the other options

are available.

f. Select the menu option File | Print Strength Parameters to print the spreadsheet of the

evaluated strength parameters.

3. The output of Geotech Master™ includes recommendations for the bearing capacity of a shallow

foundation. The parameters that the user can select here are as follows:

a. A range of depth of embedment defined by the minimum and the maximum depth of

embedment. The software evaluates the allowable bearing capacity in one-foot

increments (or 0.3 meters) of the depth of embedment.

b. A range of foundation widths, defined by the minimum and maximum footing widths.

The software evaluates the allowable bearing capacity in ½ foot (or 0.15 meters)

increments.

c. The type of footing shape (square, rectangular, long). If the rectangular footing is

selected, you are asked to provide a (Long Side)/(Short Side), L/B ratio. Circular footings

of diameter

can be approximated as square footings with width

0.8⋅

d. The desired factor of safety.

e. For each depth of embedment, plots are generated that provide the allowable bearing

capacity (pressure) versus footing width.

f. You can select the option to plot the allowable load versus width rather than the

bearing pressure.



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a. The calculations of bearing capacity versus depth of embedment, as well as footing

width, are also presented in a spreadsheet, next to the plot.

b. Select the menu option File | Print BC Graph to print the graph of the calculated bearing

capacities.

c. Select the menu option File | Print BC Sheet to print the spreadsheet of the calculated

bearing capacities.

2. Evaluation of Strength Parameters

2.1.

SPT Energy Efficiency correction

The recorded SPT blow counts N, if not corrected, must be adjusted as follows:

Where /0.60 = Hammer efficiency correction factor.

= Hammer efficiency =Borehole diameter correction. = Sampler correction.= Rod length correction

The software provides you recommendations for these corrections based on: A.W. Skempton, 1986,

Standard Penetration Test Procedures and the Effects in Sands of Overburden Pressure, Relative Density,

Particle Size, Aging and Overconsolidation: Geotechnique, v. 36:3, p. 425-447 ;

2.2.

SPT Overburden correction

An added correction to the SPT data is provided to account for the overburden pressure.

Multiple studies have been published on this subject. Geotech Master ™ uses a correction that is based

on the recommendations of five studies, as shown in the figure that follows:



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The references of the five studies are as follows:

Peck, R.B. & Bazaraa, A.R.S.S. 1969. Discussion of paper by D’Appolonia et al, Journal of the Soil

Mechanics and Foundations Division, ASCE, 95(3): 305-309

Peck, R.B., Hanson, W.E. and Thombum, T.H., 1974. Foundation Engineering. John Wiley & Sons,N.Y.

Seed, H. B., Evaluation of Soil Liquefaction Effects on Level Ground During Earthquakes, in Liquefaction

Problems in Geotechnical Engineering, Preprint 2752, ASCE National Convention, Philadelphia, PA, 1976,

pp. 1– 104.

Tokimatsu, K and Yoshimi, Y (1983 ), “Empirical correlation of soil liquefaction based on SPT N-Value and

fines content.” Soils and Foundations, JSSMFE, Vol. 23, No. 4, December, pp. 56-74

Liao, S. S. C. AND Whitman, R. V., 1986, Overburden correction factors for SPT in sand: Journal

Geotechnical Engineering, Vol. 112, No. 3, pp. 373– 377.

2.3.

Evaluation of Unit Weights

If SPT data is available, then the unit weight of a layer is evaluated based on reference Design of Sheet

Pile Walls, U.S. Army Corps of Engineers, Engineer Manual 1110-2-2504, 1994:



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Soil Density

Description

SPT Blow Count

NMoist

γm

Submerged

γsub

Very Loose 0 to 4 < 100 < 60

Loose 5 to 10 95 to 125 55 to 65

Medium Dense 11 to 30 110 to 130 60 to 70

Dense 31 to 50 110 to 140 65 to 85

Very Dense > 51 >130 >75

Unit Weight

(pcf)

NON-COHESIVE SOILS

If no SPT data is available, then the unit weight of each layer is evaluated based on NAVFAC DM 7.01,

1982

Soil Consistency

Description

SPT Blow Count

N

Saturated

Unit Weight pcf

Very Soft 0 to 2 100 110

Soft 3 to 4 100 to 120

Firm 5 to 8 110 to 125

Stiff 9 to 16 115 to 130

Very Stiff 16 to 32 120 to 140

Hard >32 >130

COHESIVE SOILS



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2.4.

Evaluation of friction angle for drained conditions

2.4.1. Drained Conditions

If SPT data is available, the friction angle is evaluation based on Bowles 1977 , as recommended byCALTRANS geotechnical manual:

If CPT data is available instead, then the method by Senneset et al is adapted (Senneset, K., R. Sandven,and N. Janbu, “Evaluation of Soil Parameters from Piezocone Tests,” Transportation Research Record

1235, Transportation Research Board, National Research Council, Washington, D.C, 1989, pp. 24– 37.)

In this method, two coefficients, and , are evaluated as follows: / and /′_ Where = recorded water pressure at the base or middle of the cone tip,

=the hydrostatic water pressure at the cone tip;

=the corrected cone resistance= the total overburden pressure at the cone tip=the effective overburden pressure at the cone tip

The effective friction angle ′ is then evaluated as follows:



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29.5 ().(0.256 0.336 log).If < 0.1 (granular materials, where no significant excess water pressure develops), then the frictionangle is evaluated as:

0.10.38

Where the tip resistance and are measured in atmospheres.

2.4.2. Undrained Conditions

If SPT data is available, the undrained shear strength is evaluated based on the recommendations by

NAVFAC (NAVFAC DM-7.1, “Soil Mechanics,” Design Manual 7.1, Department of the Navy, May 1982).

If CPT data is available, the undrained shear strength is evaluated based on the following equation:

/ With ranging from 11.9 to 32.1 with an average magnitude of 23.3 ( Zsolt Rémai (2013) Correlationof undrained shear strength and CPT resistance. Periodica Polytechnica Civil Engineering 57(1):39– 44)

The undrained shear strength may also be calculated based on PI values. The equation adopted in

Geotech Master ™ is ⋅ 0.11 0.0037 × . This equation was proposed by Skempton(Skempton A. W. 1957, “The planning and design of New Hong Kong Airport”, Proceedings,, the Institute

of Civil Engineers, London, Vol. 7, pp. 305-307.) The equation is valid for normally consolidated (NC)

clays, and needs to be corrected for overconsolidated clays. Q-Systems Engineering, considers the



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approach of evaluating the undrained shear strength as a function of PI to be less reliable than the other

methods covered here. As such, this approach is not recommended.

If the water content and the Atterberg limits are available, the undrained shear strength can beestimated based on the liquidity index LI = (w-PL)/PI. Geotech Master ™ uses the logarithmic liquidity

index (Koumoto, T., and Houlsby, G.T. 2001. Theory and practice of the fall cone test. Géotechnique,

51(8): 701– 712), which produces more reliable statistical correlations

The logarithmic liquidity index is defined as:

nwPL

n

Geotech Master ™ evaluates the undrained shear strength based on the large data base regression

anllysis presented by Vardanega. and Haigh , (Vardanega, P. and Haigh, S. (2014). "The undrainedstrength – liquidity index relationship." Canadian Geotechnical Journal, 51: 1073– 1086, 2014)



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3.

Evaluation of Compressibility Parameters

3.1. Modulus of Elasticity

Based on Bowles (Joseph E. Bowles, Foundation Analysis and Design, Fifth Edition, McGraw-Hill 1996):

Value Range for Modulus of Elasticity of Soils Es

Soil Es (MPa)

Clay

Very Soft 2-15

Soft 5-25

Medium 15-50

Hard 50-100

Sandy 25-250

Glacial Till

Loose 10-150

Dense 150-720

Very Dense 500-1440Loess 15-60

Sand

Silty 5-20

Loose 10-25

Dense 50-81

Sand and

Gravel

Loose 50-150

Dense 100-200

Shale 150-5000

Silt 2-20

From the same reference, if SPT data is available

Modulus of Elasticity based on SPT (N55)Soil Sand (norm. consolidated) 50015

7000√ 6000 18000 Sand (saturated) 25015 Sands, all (norm. consol.) 2750 Sand (overconsolidated) 40000 1050

,√ Gravelly sand 1200 6

600 6, ≤ 15 600 6 2000, > 15 Clayey sand 32015 Silts, sandy silt, or clayey silt 300 6

Also from the same reference, if CPT data is available



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Page 10 of 15 April 15, 2016

Finally, also from the same reference

Modulus of Elasticity of Soils based on Undrained Shear Strength Soil Condition (Units of )Clay and Silt > 30 100 500 Silty, Sandy clay < 30 500 1500 Clay

4200142.54 1.73 0.0071

3.2. Evaluation of the Overconsolidation Ratio (OCR)

Based on the work by Mayne and Kemper (Mayne, P. W., and Kemper, J. B., (1988). “Profiling OCR in

stiff clays by CPT and SPT,” Geotechnical Testing Journal, 11(2), 139-147.) the overconsolidation ratio

OCR is evaluated as a function of SPT blowcounts based on:

0.193 .

Where the overburden pressure is measured in MPa.The OCR can also be evaluated based on CPT tip resistance based on:

0.37 .

Modulus of Elasticity based on CPTSoil Sand (norm. consolidated) 2 4

8000

1.23 2 1

Sand (saturated) 1.0 3.5 0.6 7.0

Sand (overconsolidated) 6 30 Clayey sand 3 6 Silts, sandy silt, or clayey silt 1 2 < 2500 2.5 2500 < < 5000

then 4 5000, where −+−

Soft clay or clayey silt

3 8



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Page 11 of 15 April 15, 2016

3.3. Compression Index The compression index is estimated based on the following recommendations:Terzaghi and Peck 1967: 0.009 10 Azzouz et al 1976: 0.37 0.003 0.0004 0.34

Rendon-Herrero (1983): 0.141 .

Nakase et al 1988: 0.046 0.0104 Koppula 1986: 0.009 0.005 References

Terzaghi, K and R. B. Peck (1967) Soil Mechanics in Engineering Practice. 2nd ed. John Wiley & Sons, New

York.

Azzouz, A. S. et al. (1976) “Regression Analysis of Soil Compressibility,” Soils and Foundations, Tokyo,

Vol. 16, No. 2, pp. 19-29.

Rendon-Herrero, O. (1983) “Closure: Universal Compression Index Equation,” JGED, ASCE, Vol. 109, GT5,

May pp. 755-761.

Nakase, A., Kamei, T., and Kusakabe, O. (1988). "Constitutive Parameters Estimated by Plasticity Index."

J. Geotech. Engrg., vol. 114, No. 7, pp. 844-858.

Koppula, S.D. (1986) "Discussion: Consolidation parameters derived from index tests", Geotechnique, Vol. 36, No. 2,

June, pp. 291-292

3.4.

Recompression Index

The compression index is estimated based on the following recommendations:

Nagaraj and Murthy 1985 : 0.000463 Nakase et al 1988: 0.00194 4.6 Bowles 1996: 0.05 0.1 if no other information is availableReferences:



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Page 12 of 15 April 15, 2016

Nagaraj TS, Murthy BRS (1985). A critical reappraisal of compression index equations. Geotechnique

36(1): 27-32.

Nakase, A., Kamei, T., and Kusakabe, O. (1988). "Constitutive Parameters Estimated by Plasticity Index."J. Geotech. Engrg., vol. 114, No. 7, pp. 844-858.

Joseph E. Bowles, Foundation Analysis and Design, Fifth Edition, McGraw-Hill 1996.

4.

Evaluation of Allowable Bearing Pressure

The allowable bearing pressure is evaluated based on Meyerhof’s equations:

1

2

Where:

The coefficients, , and are evaluated as shown here.The overburden pressure is evaluated based on the weight of the layersabove the depth of embedment.

If the footing carries an overturning moment , in addition to the axialcompression , then the user must provide this information as an expressionof eccentricity /.The effect of eccentricity is accounted for by introducing a reduction in the

effective width: 2, thus reducing the effective footing area from × to × .The calculated allowable bearing capacity is adjusted by the factor /. Thus, the allowed load iscalculated by multiplying the calculated bearing capacity by the total footing area × .

Nc Nq Nγ

0 5.10 1.00 0.00

1 5.38 1.09 0.00

2 5.63 1.20 0.01

3 5.90 1.31 0.02

4 6.19 1.43 0.04

5 6.49 1.57 0.07

6 6.81 1.72 0.11

7 7.16 1.88 0.15

8 7.53 2.06 0.21

9 7.92 2.25 0.28

10 8.34 2.47 0.37

11 8.80 2.71 0.47

12 9.28 2.97 0.60

13 9.81 3.26 0.74

14 10.37 3.59 0.92

15 10.98 3.94 1.13

16 11.63 4.34 1.37

17 12.34 4.77 1.66

18 13.10 5.26 2.00

19 13.93 5.80 2.40

20 14.83 6.40 2.87

21 15.81 7.07 3.42

22 16.88 7.82 4.07

23 18.05 8.66 4.82

24 19.32 9.60 5.72

25 20.72 10.66 6.77

26 22.25 11.85 8.00

27 23.94 13.20 9.46

28 25.80 14.72 11.19

29 27.86 16.44 13.24

30 30.14 18.40 15.67

31 32.67 20.63 18.56

32 35.49 23.18 22.02

33 38.64 26.09 26.17

34 42.16 29.44 31.15

35 46.12 33.30 37.15

36 50.59 37.75 44.43

37 55.63 42.92 53.27

38 61.35 48.93 64.07

39 67.87 55.96 77.33

40 75.31 64.20 93.69

41 83.86 73.90 113.99

42 93.71 85.37 139.32

43 105.11 99.01 171.14

44 118. 37 115. 31 211. 41

45 133. 87 134. 87 262. 74

Angle φ

(Degrees)

Meyerhof

Bear ing Capac i ty Factors

for General Shear fai lure



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The layers of soil that are influenced by the foundation failure are within a depth of /2 ⋅45/2 .

If more than one layer is included within this zone, then the bearing capacity is evaluate using averagevalues for cohesion and frictional coefficients , within the zone influenced by bearing capacityfailure. This approach has been recommended by Bowles (Bowles J.E. Foundation analysis and design,

4th

Ed., McGraw-Hill, New York, N.Y., 1988).

5. Evaluation of Static Footing Settlements.

5.1.

Settlements of Footings on Granular Soils

The approach adapted in the current version of Geotech Master™ is based on the vertical strain

influence factor , which was introduced by Schmertmann originally in 1970 and subsequently in 1978.(1. Schmertmann, J.H. 1970. Static cone to compute static settlement over sand. Journal of the Soil

Mechanics and Foundations Division, ASCE, 96(3) pp 1011-1043; 2. Schmertmann, J.H., Hartmann, J.P. &

Brown, P.R. 1978. Improved strain influence factor diagrams. Journal of the Geotechnical Engineering

Division, ASCE, 104(8) pp 1131-1135.)

The footing settlement is evaluated as the sum of the contributions of sublayers underneath thefoundation, each of which has a thickness Δ:

∑

Δ

=

Where

= Applied foundation pressure; = Effective overburden pressure at the elevation of the bottom of the footing BEFORE the excavation

and placement of the footing.

Δ = Net foundation pressure increase at bottom of footing.

1 0.5

= Correction factor for depth of embedment.

1 0.2 log . = Correction for secondary creep settlements = The modulus of elasticity of the granular soil (see section 3.1) for layer . = Strain influence factor at the center-height of sublayer . See the figure that follows:



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Page 14 of 15 April 15, 2016

5.2. Settlement of Footings on Fine-Grained Soils

The settlement o footings on fine grained soils are evaluated based on 1-D consolidation equations:

5.2.1.

Normally Consolidated Fine Grade Soil

The consolidation settlement for normally consolidated (NC) clays is evaluated as:

∑ 1 log

Δ

=

Where



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Page 15 of 15 April 15, 2016

The compression layer is divided in sublayers, and all quantities above are defined at the mid-depth ofeach layer.

= initial effective overburden pressure at the midpoint of sublayer, before the excavation andplacement of the footing.Δ = the increase of the vertical pressure at the midpoint of sublayer due to the footing placement.

5.2.2. Overconsolidated Fine Grade Soil

For the case of overconsolidated clays, we define the current effective overburden pressure asdefined earlier, and the precompression stress , which is the maximum effective overburdenpressure that the soil has experienced in the past.

Case where Δ ≤

∑

1 log

Δ

=

Case where Δ >

∑

1 log

= ∑ 1

log Δ

=

5.3. Settlement of Footings on Layered Granular and Fine-Grained Soils

Where layers of both granular and fine-grained materials are within the influence zone of the footing

increase pressures, the equations for both materials are combined, where each equation provides input

only in the layers where each equation is valid

basis of calculations - geotech master

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