Determining Compressibility & Modulus Numbers
Background TextDetermining Janbu Modulus Values from Results of
Consolidation TestsBengt H. Fellenius, Dr.Tech., P.Eng.January 4,
2001 (Updated January 2014)The results of settlement calculation
using the Janbu Janbu Modulus Number (m) and theconventional
combination of the consolidation coefficient (C-c) and void ratio
(e-0) aremathematically identical. However, the modulus number
approach is much to be preferred asit provides only one value and
allows the engineer to develop a mental experience basefor the
soils normally encountered. In contrast, the conventional approach
requires both Ccand e0 and it is not possible to develop a useful
experience reference when two variables haveto be considered. Of
course, the MIT Compression Ratio (CR) can serve that same
purpose.Moreover, the Janbu approach works also for silts and sand,
even soil exhibiting linear stress-compression behavior --- soil
compressibility, be it mud and peat, or clay, silt, and sand,
orgravel and tills can be expressed in dimensionless modulus
numbers ranging from 1through 1,000.For reference see Janbu's
papers listed below. See also, Chapter 3, Sections 3.5 through3.7
in the Red Book ( Fellenius 2014), which summarizes the Janbu
Tangent modulus methodand gives the mathematical relations for
determining the consolidation coefficient (Cc), thevoid ratio (e0),
the Compression ratio (CR), and the Janbu Modulus Number
(m).Computer programs available on the market do not normally
produce the Janbu modulusnumbers. Although, the "m" is easily
determined from the conventional values, the hereoffered template
can be of interest to the geotechnical engineer. The two sheets
named"Strain Data" and "Void Ratio Data" are intended for input of
results from conventionalconsolidation tests, As the name implies,
the first sheet is for stress-strain input and thesecond sheet is
for stress-void ratio input.The input data is intended to be
written in the white background columns. Cells withblue and green
background are for entry of coordinates of certain cells and may
have tobe changed to get the plotting right. Cells with yellow
background must not be touched.The sheet named "Casagrande
Original" is a copy of a table reproduced by Nilmar Janbu froman
example used by Arthur Casagrande for examination of his graduate
students in theThe test itself is from the early 1930's. Janbu
quoted the test in his summary of his method(Janbu 1998), which
publication every geotechnical engineer would appreciate
reading.The sheet named Casagrande Data shows the Casagrande
original test data entered tothe Strain Data Table. The Casagrande
Plot shows the plot of the Casagrande data.To use the spread sheet
for your own work, save it under a changed name, then,delete the
sheets that are redundant. You may want to re-size the diagrams.The
diagrams showing void ratio vs. stress and strain vs. stress do not
need explanation.To benefit from and to understand the purpose of
the diagrams showing linear stress-strain and Tangent Modulus vs.
Average Stress, you will need to read Janbu's 1998 paper.To whet
your appetite, the Janbu Tangent Modulus diagram (the one in the
fourth quarter position)offers an alternative method for
determining the preconsolidation stress.Notice, when you have input
the lab data, you should check the void ratio and density valuesand
the degree of saturation per the options provided above the
table.ReferencesFellenius, B. H., 2014. Basics of foundation
design. Revised Electronic Edition.[www.Fellenius.net], 410
p.Janbu, N., 1963. Soil compressibility as determined by oedometer
and triaxial tests.European Conference on Soil Mechanics and
Foundation Engineering, Wiesbaden,Vol. 1, pp. 19-25, and Vol. 2,
pp. 17-21.Janbu, N., 1965. Consolidation of clay layers based on
non-linear stress-strain.Proceedings 6th International Conference
on Soil Mechanics and FoundationEngineering, Montreal, Vol. 2, pp.
83-87.Janbu, N., 1967. Settlement calculations based on the tangent
modulus concept.University of Trondheim, Norwegian Institute of
Technology, Geotechnical Institution,Bulletin 2, 57 p.Janbu, N.,
1998. Sediment deformations. University of Trondheim,
NorwegianUniversity of Science and Technology, Geotechnical
Institution, Bulletin 35, 86 p.
Strain DataExample of data given as Stress-StrainEnter values or
cell references in white cellsPost glacial clay from a depth of 8
mRho-s =2800w =1,000e0 =2.220wn =80.0S =100.0wn =80.0e0 =2.240wn
=79.3#p'p-aved(p-ave)eStrainM(kPa)(kPa)(kPa)(-
-)%(kPa)2.220110552.2010.601,66722015102.1881.002,50034030152.1801.238,69648060302.1691.5911,1115124102422.1581.9213,3336186155532.1442.3713,7787277232772.1113.389,01084353561251.9976.924,46397295821.85711.286,743101,4301,0801.68116.7312,86211987641.73215.161230641.76214.2113141516p1
=277e1 =2.111p2 =1,430e2 =1.681VOID RATIO - STRESSCc =0.60CC =
Cc/(1 + e0) =0.19m =12.3p1 =40e1 =2.180p2 =124e2 =2.158VOID RATIO -
STRESSCcr =0.045CR = Ccr/(1 + e0) =0.014mr =163.82773.38753STRAIN
vs. STRESS11.502,04619.62m =12.33003,0001200MODULUS vs. AVERAGE
STRESS14,00012.2202,50040MODULUS vs. STRESS8,69680for reference
points11,11112413,33318613,7782779,0104354,4637296,743
Strain Data
Test DataCc-LineStress (kPa) log scaleVoid Ratio (- -)
Void Ratio Data
Test CurveFitted lineStress (kPa) logarithmic scaleStrain
(%)
Casagrande ORIGINAL
Stress (Kka) linear scaleStrain ( % )
Casagrande DATA
Modulus vs Stressm-lineReference pointsAverage Stress
(kPa)Modulus (KPa)
Casagrande Plot
Test CurveFitted lineStress (kPa) logarithmic scaleStrain
(%)
Example of data given using Stress-VOID RATIOSample of Champlain
Sea Clay from depth of 5 mRho-s =2800w =1,000e-0 =2.27w-n =77.00S
=95.5w-n =77e-0 =2.16wn
=77.4p'p-aved(p-ave)eStrainM(KPa)(KPa)(KPa)(-
-)%(kPa)2.2700.00Enter values or cell references in white
cells15.0332.2650.153,270225.015132.2610.2816,350350.038232.2450.765,1094100.075382.2191.566,2885200.0150752.1384.044,0376400.03001501.68018.041,4287800.06003001.22831.872,8948200.05001.27230.5295.01031.42725.7810369.4211069.4212069.4213069.42141516p1
=200e1 =2.138p2 =800e2 =1.228VOID RATIO - STRESSCc =1.51CC = Cc/(1
+ eo) =0.4622m =5.0p1 =50e1 =2.245p2 =200e2 =2.138VOID RATIO -
STRESSCcr =0.18CR = Ccr/(1 + eo) =0.0543m =42.32004.0544STRAIN vs.
STRESS24.001,47843.96m =5.02001,700800MODULUS vs. AVERAGE
STRESS4,7005.02516,35050MODULUS vs. STRESS5,109100for reference
points6,2882004,0374001,4288002,894
p'c
Test DataCc-LineStress (KPa) log scaleVoid Ratio (- -)
CC = 0.46 m = 5p'cStress (kPa) linear scaleStrain ( % )Test
CurveFitted lineStress (kPa) logarithmic scaleStrain (%)
Janbu-Casagrande 1934 Example --- Original Data
Table2.003.004.005.006.007.008.009.00The data in Columns 4 and 5and
in Columns 8 and 9 areLOADDIALSTRESSSTRAINVoid
Ratiod-stressd-strainMave-stressintended for the
plotting(kg)(in)(KPa)( % )(KPa)( % )(KPa)(KPa)to the STRAIN
sheetArea = 90.1 cm^2Original void ratio =0.810Calculated using
Col.#4 Stress00.00000.000.810and Col.#5 Strain (i.e., #6 and
#7)182.078719.00160.031182.070.773181.021,76527.00320.046363.090.754351.781,96653.50640.073714.870.722712.732,598106.501280.1141427.600.6721423.434,136213.002560.16628411.030.6102834.076,959425.505120.22756715.100.5375684.2313,417851.001,0240.2901,13519.330.46000.201135.001,0240.2931,13519.530.456-568-0.53106,500851.005120.28556719.000.466-283-0.7637,237425.502560.27428418.240.480-142-0.8916,015213.001280.26014217.350.496-106-1.935,50289.00320.2313615.430.531-36-4.6377200.162010.800.615-0.3-10.800.14500
p'cm = 5Modulus vs Stressm-lineReference pointsAverage Stress
(kPa)Modulus (kPa)m = 5
Example of data given as Stress-StrainPost glacial clay from a
depth of 8 mRho-s =2800Rho-w =1,000e0 =0.810wn =81.0S =100.0wn
=81.0e0 =2.268wn =28.9#p'p-aved(p-ave)eStrainMEnter values or cell
references in white cells(kPa)(kPa)(kPa)(-
-)%(kPa)0.810118990.7732.07087023627180.7543.0901,76537154270.7224.8601,9774142107530.6727.6002,59152842131070.61011.0404,12865674262130.53715.1106,953711358514260.46019.33013,460811351,1352840.45619.56095678510.46619.010102844260.48018.230111422130.49617.3501236890.53115.410130.310.770141516p1
=284e1 =0.610p2 =1,135e2 =0.460VOID RATIO - STRESSCc =0.2CR = Cc/(1
+ e0) =0.14m =16.728411.04772STRAIN vs. STRESS17.002,09822.96m
=16.85005,0001050MODULUS vs. AVERAGE
STRESS14,20016.7361,76571MODULUS vs. STRESS1,977142for reference
points2,5912844,1285676,9531,13513,4601,13505670
CR = 0.14 m = 17m = 17m = 17
Example of data given as Stress-Strain
0.810.610.770.460.750.720.670.610.540.460.460.470.480.500.530.30
Test DataCc-LineStress (kPa) log scaleVoid Ratio (- -)
2.073.094.867.6011.0415.1119.3319.5619.0118.2317.3515.4110.77
Stress (kPa) linear scaleStrain ( % )
11.042.0717.003.0922.964.867.6011.0415.1119.3319.5619.0118.2317.3515.4110.77
Test CurveFitted lineStress (kPa) logarithmic scaleStrain
(%)
5000.001764.71869.5714200.001977.401764.712591.241977.404127.912591.246953.324127.9113459.726953.320.0013459.720.001135.00851.00425.50213.0089.00
Modulus vs Stressm-lineReference pointsAverage Stress
(kPa)Modulus (kPa)
CR = 0.14 m = 17m = 17m = 17
