Determining 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 the conventional combination of the consolidation coefficient (C-c) and void ratio (e-0) are mathematically identical. However, the modulus number approach is much to be preferred as it provides only one value and allows the engineer to develop a mental experience base for the soils normally encountered. In contrast, the conventional approach requires both C c and e0 and it is not possible to develop a useful experience reference when two variables have to 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 stresscompression behavior --- soil compressibility, be it mud and peat, or clay, silt, and sand, or gravel and tills can be expressed in dimensionless modulus numbers ranging from 1 through 1,000. For reference see Janbu's papers listed below. See also, Chapter 3, Sections 3.5 through 3.7 in the Red Book ( Fellenius 2014), which summarizes the Janbu Tangent modulus method and gives the mathematical relations for determining the consolidation coefficient (Cc), the void ratio (e0), the Compression ratio (CR), and the Janbu Modulus Number (m). Computer programs available on the market do not normally produce the Janbu modulus numbers. Although, the "m" is easily determined from the conventional values, the here offered 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 conventional consolidation tests, As the name implies, the first sheet is for stress-strain input and the second sheet is for stress-void ratio input. The input data is intended to be written in the white background columns. Cells with blue and green background are for entry of coordinates of certain cells and may have to be 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 from an example used by Arthur Casagrande for examination of his graduate students in the The 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 to the 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 stressstrain 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 values and the degree of saturation per the options provided above the table. References Fellenius, 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 Foundation Engineering, 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, Norwegian University of Science and Technology, Geotechnical Institution, Bulletin 35, 86 p. . 73 12.667 1.STRESS CC = Cc/(1 + e0) = e1 = e2 = 0.60 p1 = p2 = 40 124 Ccr = 0.00 12.333 13.50 19.463 6.080 764 64 d(p-ave) (kPa) wn = 80.158 VOID RATIO .045 e1 = e2 = 2.23 8.38 9.000 14.732 1.38 11.3 3.220 wn = 80.2 MODULUS vs.144 2.240 e (.111 1. STRESS 300 1200 5.59 11.111 13.3 2.180 2.778 9.19 mr = m= 20 40 80 124 186 277 435 729 0.3 M (kPa) Strain (%) Rho-s = 0.28 6.696 1.21 20.00 15. AVERAGE STRESS MODULUS vs.000 2800 e0 = 2.00 10 163.00 2.010 6.188 2.010 4.-) 2.STRESS CR = Ccr/(1 + e0) = 0.Enter values or cell references in white cells Example of data given as Stress-Strain Post glacial clay from a depth of 8 m ρw = 1. STRESS for reference points 100 Stress (kPa) log 2.500 8.696 11.463 11.014 277 753 2.0 wn = 79.862 15.0 # p' (kPa) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 10 20 40 80 124 186 277 435 729 1.333 2.000 12.762 5 10 15 30 42 53 77 125 Strain % S = 100.743 .201 2.158 2.8 STRAIN vs.681 VOID RATIO .00 p1 = 277 p2 = 1.0 e0 = 2.857 1.92 4.500 1.180 2.92 13.00 10.046 m= 3.169 2.681 1.16 14.430 Cc = 0.60 1.997 1.37 13.778 3.62 12.111 1.220 2.111 1.430 98 30 p-ave (kPa) 5 15 30 60 102 155 232 356 582 1.743 16. 00 15.00 2.000 2.900 15.000 10.00 10.00 1.600 1.700 5.00 4.20.200 Strain ( % ) Void Ratio (.000 14.00 10.000 10.000 ss (kPa) logarithmic scale 10.00 8.00 16.000 10.000 0.000 6.000 Stress (kPa) logarithmic scale 100 1.00 1.000 0 0 200 400 600 800 1.800 1.000 Average Stress (kPa) 1 .00 10 100 1.000 5.300 2.-) 2.000 Stress (Kka) linear scale Modulus (KPa) Strain (%) Stress (kPa) log scale 20.000 1.000 12.000 0 500 1.000 0.500 10 100 1.100 2. 000 Average Stress (kPa) 1.000 1.400 .500 Stress (Kka) linear scale 0 400 600 800 1.200 1.500 1. 428 2.0 0 200 400 600 800 Average Stress (kPa) 1.0 Stress (kPa) linear scale 40.000 2.427 3 13 23 38 75 150 300 0.00 1.18 p-ave (KPa) 3 15 38 75 150 300 600 500 103 3 0 0 0 d(p-ave) (KPa) e (.46 m=5 2.109 6.76 1.87 30.219 2.109 6.270 16.00 1.42 69.52 25.138 1.04 31.STRESS CR = Ccr/(1 + eo) = 200 544 1.000 30.00 10.400 Strain (%) p' (KPa) Modulus (kPa) 2800 2.245 2.270 2.00 m= 5.4622 0.00 2.800 1.0 50.000 95. AVERAGE STRESS MODULUS vs.96 5.3 STRAIN vs.0 1000 Stress (KPa) log scale 2.0 Stress (kPa) logarithmic scale e1 = e2 = 30.894 10 100 e1 = e2 = 20.51 p1 = p2 = 50 200 Ccr = 0.000 77.STRESS CC = Cc/(1 + eo) = 20.00 10.16 1.28 0.700 4.0 MODULUS vs.037 1.4 1. STRESS m= 200 800 25 50 100 200 400 800 4.400 Strain ( % ) ρw = Rho-s = e-0 = Void Ratio (.138 1.000 p'c 0 100.00 m=5 10.0 1.350 5.56 4.-) Strain % 2.288 4.000 3.Example of data given using Stress-VOID RATIO w-n = 77.04 18.700 5.0 500.000 6.0543 m= 42.228 VOID RATIO .00 0.478 0.265 2.0 100.428 2.15 0.000 m=5 4.228 1.0 24.0 200.0 p1 = p2 = 200 800 Cc = 1.350 5.0 25.00 1.78 69.00 43.000 .261 2. STRESS for reference points 16.42 69.0 10.-) Sample of Champlain Sea Clay from depth of 5 m 1000.600 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 5.5 S= wn = 40.037 1.42 M (kPa) Enter values or cell references in white cells 0.0 400.138 VOID RATIO .42 69.27 p'c 2.00 0.0 800.0 200.680 1.200 CC = 0.272 1.288 4.200 8.894 1000.0 5.00 2.0 0.245 2.00 w-n = 77 e-0 = 2. 810 16 0.23 13.227 567 15.480 128 0.293 1.114 142 7.460 1.531 0 0.60 0.496 32 0.20 -568 -0.00 M (KPa) 0.502 89.63 772 -0.466 256 0.00 5.722 128 0.046 36 3.959 425.50 71 2.76 37.35 0.031 18 2.Original Data Table 2.162 0 10.754 64 0.33 0.3 -10.00 -283 -0.80 0.50 568 4.03 0.672 256 0.80 1135.00 283 4.07 871 9.89 16.598 106.615 0.02 1.00 9.53 106.015 213..00 Void Ratio d-stress d-strain (KPa) (%) Original void ratio = 0 0.93 5.135 19.Janbu-Casagrande 1934 Example --.00 18 1.456 512 0.166 284 11.00 35 1.09 0.50 -142 -0.73 2.537 1.024 0.00 -106 -1.135 19.00 3.#5 Strain (i.500 851.136 213.00 0.78 1.417 851.43 0.50 142 3.87 0.00 8.000 0 0.260 142 17.231 36 15.285 567 19.00 -36 -4.e.073 71 4.773 32 0.00 .00 0 0. #6 and #7) 18 2.00 0.43 4.24 0.765 27.00 STRESS (KPa) STRAIN (%) 6.10 0.53 0.237 425.274 284 18.00 LOAD DIAL (kg) (in) Area = 90.290 1.07 0.1 cm^2 4.966 53.145 0 0 7.#4 Stress and Col.810 ave-stress (KPa) The data in Columns 4 and 5 and in Columns 8 and 9 are intended for the plotting to the STRAIN sheet Calculated using Col.07 6.024 0.610 512 0. 610 0.722 0.135 e1 = e2 = Cc = 0.14 m= 16.460 0.977 2. STRESS for reference points 1.040 15.531 Rho-w = 1.350 15.3 p1 = p2 = 284 1.466 0.754 0.STRESS 0.765 1.04 17.128 6.0 2.7 MODULUS vs.770 870 1.2 CR = Cc/(1 + e0) = 284 772 2.96 16.810 wn = wn = 81.070 3.090 4.230 17. STRESS m= 500 1050 36 71 142 284 567 1.135 1.010 18.135 567 11.460 0 0 .135 851 426 213 89 d(p-ave) (kPa) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 36 71 142 284 567 1135 1135 567 284 142 36 0.600 11.480 0.537 0.098 9 18 27 53 107 213 426 284 e (.268 Strain % M (kPa) 2.410 10.000 14.330 19.9 81.456 0.8 5.810 0.560 19.953 13.460 Enter values or cell references in white cells 0.7 STRAIN vs.591 4. AVERAGE STRESS MODULUS vs.00 22.860 7.610 0.200 16.0 wn = 28.-) 0.953 13.110 19.128 6.000 S= 100.672 0.460 VOID RATIO .591 4.765 1.773 0.0 e0 = p' (kPa) p-ave (kPa) 9 27 54 107 213 426 851 1.Example of data given as Stress-Strain Post glacial clay from a depth of 8 m # Rho-s = 2800 e0 = 0.977 2.496 0. 600 5.000 100 1000 10000 Stress (kPa) logarithmic scale 0 0 500 1.700 10.-) Example of data given as Stress-Strain 20.000 Average Stress (kPa) 1.000 Modulus (kPa) Strain (%) 25.000 0 10.500 .00 1000 1500 15.000 m = 17 10.CR = 0.800 Strain ( % ) Void Ratio (.00 15.000 0.00 10 500 Stress (kPa) linear scale Stress (kPa) log scale 5.500 0.00 20.400 10 100 1.000 15.000 0.000 10.000 0.00 m = 17 5.14 m = 17 0.000 0.00 0.