According to the employed constitutive model the material constants are chosen in such a way that they control different aspects of the mechanical behaviour of the soil, and as such they are independent. However, some empirical correlations turn out to exist and are of use. It was found that both the index quantities wL, wP and IP and the material constants (λ, κ, e100) depend linearly on the critical friction angle ϕc, which in turn depends linearly on the clay content CC. From a physical point of view, this is not surprising, since the mechanical properties must depend on granulometric properties (mineral content, grain shape and size distribution, ion content of the pore water).
The correlations between different parameters and/or index quantities given below may be helpful if parameters have to be estimated for comparable materials (cf. due to insufficient laboratory data. In order to enable a comparison the following tests were performed:
• Determination of clay minerals by means of roentgen diffractometry
• Determination of the grain size distribution (cf. Fig. A.6)
• Determination of the plastic and liquid limit (wP and wL)
• Determination of the calcite and dolomite content
• Determination of ignition loss (organic content)
• Oedometric compression tests with creep phases (Cc, Cs, ¯Cα, λ, κ)
• CIU triaxial compression tests with changes in the strain rate (ϕc)
The results of the soil mechanical investigations is summarized in Table 2.4. The outcome of the roentgen diffractometry tests is given in Table 2.5). The content of swellable clay minerals of all materials was less than 25%.
The laboratory results (OCT and TXC) were used to calibrate the viscohypoplastic pa-rameters for every material (Tab. A.3).
Consistency limits wL and wP
In the undesirable case when only the clay content CC is known from a sedimentation analysis, wL and wP can be estimated by (cf. Fig. 2.16)
2.5. Interrelations between Parameters and/or Index Quantities 27
Material#110#154#158#159#160#162#472#578 ClayContentin%3050688578192942 CaCO3Contentin%27.326.30.30.30.227.10.10.4 CaMg(CO3)2Contentin%7.65.00.00.00.07.70.00.2 IgnitionLossin%2.33.16.07.54.11.13.02.3 Graindensityρsing/cm3 2.7052.7522.6902.6542.7072.7442.7042.746 PlasticLimitwPin%16.920.923.128.925.316.822.718.7 LiquidLimitwLin%33.243.454.571.558.725.138.636.2 PlasticityIndexIPin%16.322.531.342.633.48.316.017.5 Symbol(USCS)CLCLCHCHCHCLCLCL Criticalfrictionangleϕc30.8◦ 26.1◦ 21.8◦ 24.0◦ 20.6◦ 35.0◦ 32.1◦ 27.0◦ CompressionindexCc0.2130.3320.5290.7350.6560.1650.2910.300 SwellingindexCs0.0330.0710.1080.1750.1520.0150.0270.063 Compressionindexλ0.0590.0860.1100.1270.1280.0450.0720.077 Swellingindexκ0.0090.0180.0240.0330.0310.0040.0070.017 CoefficientofCreep
¯ Cα 4.5·10−3 4.6·10−3 6.2·10−3 1.4·10−2 1.4·10−2 1.7·10−3 1.7·10−3 3.0·10−3 Table2.4:Summaryofthelaboratorytestresultsoftheinvestigatedmaterials.
Material#110#154#158#159#160#162#472#578Chlorite01010001Swellableclayminerals151010839253Mica112061719162250Kaolinite252844233316GypsumN.D.N.D.N.D.N.D.N.D.N.D.N.D.N.D.Quartz2116451341284126AnhydriteN.D.N.D.N.D.N.D.N.D.N.D.N.D.N.D.Feldspar53121872Calcite26290102401Dolomite940001210Sumnon-layeredsilicates7364563055724930ChemicallycombinedH2O5.146.5710.3113.1310.604.096.657.75CO215.4414.530.270.570.2415.910.590.52S0.010.040.020.160.060.030.010.01C*0.150.410.190.390.010.190.09-0.02
Table2.5:Mineralogiccontentinmasspercentagedeterminedwiththeaidofroentgendiffractometry.
2.5. Interrelations between Parameters and/or Index Quantities 29
Material ϕc λ κ e100 Dr in s−1 Iv βr 110 30.8◦ 0.055 0.010 0.68 10−6 0.025 0.70 154 26.1◦ 0.085 0.018 0.81 1.5·10−6 0.025 0.75 158 21.8◦ 0.106 0.024 1.05 10−6 0.020 0.55 159 24.0◦ 0.127 0.030 1.58 10−7 0.020 0.90 160 20.6◦ 0.127 0.027 1.29 10−6 0.020 0.66 162 35.0◦ 0.045 0.007 0.58 10−6 0.030 0.99 472 32.1◦ 0.067 0.010 0.75 10−6 0.020 0.99 578 27.0◦ 0.077 0.008 0.78 10−6 0.030 0.90 Table 2.6: Viscohypoplastic parameters of the investigated materials.
wL = 0.6048 · CC + 0.1415 (s = 0.040) (2.16) wP = 0.1498 · CC + 0.1415 (s = 0.022)
where s is the standard derivation.
0.20 0.30 0.40 0.50 0.60 0.70 0.80
0.00 0.20 0.40 0.60 0.80 1.00
wL
clay content wL=f(CC)
0.15 0.20 0.25 0.30
0.00 0.20 0.40 0.60 0.80 1.00
wP
clay content wP=f(CC)
(a) (b)
Figure 2.16: Correlation between (a) wL and (b) wP and the clay content CC.
Critical friction angle ϕc
A linear correlation was observed between wL, wP, IP, CC and the critical friction angle ϕc in rad (cf. Fig. 2.17), viz
ϕc = 0.6920 − 0.4819 · wL (s = 0.054) (2.17)
0.20 0.40 0.60 0.80
ϕc in rad
0.15 0.20 0.25 0.30
ϕc in rad
0.00 0.10 0.20 0.30 0.40 0.50 ϕc in rad
0.00 0.20 0.40 0.60 0.80 1.00 ϕc in rad
CC ϕc=f(CC)
(c) (d)
Figure 2.17: Correlation between ϕc and (a) wL, (b) wP, (c) IP and (d) CC.
Compression and swelling index (λ and κ)
2.5. Interrelations between Parameters and/or Index Quantities 31
The virgin compression index λ and the swelling index κ both show a linear dependency on wL, wP, IP, ϕc and CC (cf. Fig. A.7 and Fig. A.8):
λ = 0.2407 − 0.3257 · ϕc (s = 0.013) (2.18)
= 0.1978 · wL− 0.0032 (s = 0.009)
= 0.6699 · wP − 0.0590 (s = 0.015)
= 0.2666 · IP + 0.0235 (s = 0.009)
= 0.1268 · CC + 0.0226 (s = 0.005)
κ = 0.0593 − 0.0896 · ϕc (s = 0.005) (2.19)
= 0.0584 · wL− 0.0096 (s = 0.003)
= 0.1942 · wP − 0.0253 (s = 0.005)
= 0.0792 · IP − 0.0018 (s = 0.003)
= 0.0366 · CC − 0.0016 (s = 0.003)
Reference Void Ratio e100
The reference void ratio e100also depends linearly on on wL, wP, IP, ϕcand CC (Eqn. (2.20) and Fig. 2.20). The associated reference creep rates were Dr ∈ [10−7; 10−6] s−1. The de-viations in e100 due to the choice of a different Dr are generally much smaller than the inaccuracy of the given estimates and can therefore be neglected.
e100 = 2.3530 − 2.9783 · ϕc (s = 0.234) (2.20)
= 2.1919 · wL− 0.0496 (s = 0.075)
= 7.5744 · wP − 0.7012 (s = 0.133)
= 2.9347 · IP + 0.2507 (s = 0.087)
= 1.3292 · CC + 0.2738 (s = 0.114)
0.040
0.20 0.40 0.60 0.80
λ
0.15 0.20 0.25 0.30
λ
0.00 0.10 0.20 0.30 0.40 0.50
λ
0.30 0.40 0.50 0.60 0.70
λ
0.00 0.20 0.40 0.60 0.80 1.00
λ
2.5. Interrelations between Parameters and/or Index Quantities 33
0.20 0.40 0.60 0.80
κ
0.15 0.20 0.25 0.30
κ
0.00 0.10 0.20 0.30 0.40 0.50
κ
0.30 0.40 0.50 0.60 0.70
κ
0.00 0.20 0.40 0.60 0.80 1.00
κ
0.40
0.20 0.40 0.60 0.80
e100
0.15 0.20 0.25 0.30
e100
0.00 0.10 0.20 0.30 0.40 0.50 e100
0.30 0.40 0.50 0.60 0.70 e100
0.00 0.20 0.40 0.60 0.80 1.00 e100
2.5. Interrelations between Parameters and/or Index Quantities 35
Viscosity Index Iv
Different to what was expected, no clear correlation between Ivand any of other quantities could be found. Krieg [24] e.g. found a correlation with wL, and Mesri and Castro [35] give Cα/Cc ≈ 0.04 ± 0.01 for inorganic soft clays and Cα/Cc≈ 0.06 ± 0.01 for highly organic plastic clays. In this study, the values range between 0.02 and 0.03 for the investigated materials (CL to CH).
Undrained Strength Ratio (cu/p00)
The so-called undrained strength ratio cu/p00, where p00 denotes the initial in situ effective mean pressure, is often used in practice for the estimation of cu of normally consolidated soils [25]. In order to determine this ratio for the different soft soils examined here, numerical simulations of CIU triaxial tests were performed for different initial isotropic mean pressures p00 and OCR and an axial strain rate ˙ε1 = 10−5/s.
Figure 2.21a depicts exemplarily the results for material #110. For each OCR the ratio cu/p00 is constant. Figure 2.21b shows cu/p00 = f (OCR) with f (OCR) = a · OCRb as an appropriate fitting function. This yields
cu = p00· a · OCRb. (2.21)
The material constants a and b were determined for all materials (Tab. A.4). A linear correlation between those two parameters and ϕc in rad was found (cf. Fig. 2.22):
a = 0.5558 · ϕc+ 0.0679 (s = 0.023) (2.22) b = 0.1670 · ϕc+ 0.8676 (s = 0.016) (2.23)
0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
0.30 0.40 0.50 0.60 0.70
a, b
ϕc in rad a b
Figure 2.22: Parameters a and b vs. ϕc.
The factor a, which in the case of OCR = 1 is equal to cu/p00, ranges between 0.262 and 0.408. This is in very good agreement with e.g. cu/p00 ∈ [0.3 ± 0.1] given by Lambe [25]
”for many remoulded clays”. These results are another indication, that the mechanical behaviour of clayey soils can be simulated realistically with the aid of the viscohypoplastic constitutive equation.
Equation (2.21) is also used in Chapter 4.3.3 for the determination of the so-called cone factor Nkt which relates CPT penetration resistance with cu.
Chapter 3
Benchmarking of CPT Interpretation Methods for Calcareous Sands
3.1 Introduction
When offering soil improvement measures such as vibro compaction geotechnical con-tractors often face the problem that clients demand cone penetration resistances after compaction, which sometimes cannot be achieved even if the material was well densified.
For the performance control of deep vibratory compaction it is also of importance to develop interpretation methods based on scientific investigations in order to replace inap-propriate ones, which transfer empirical findings to other materials without an adequate physical base.
The cone penetration resistance depends not only on the state of the soil (density and stress) but also on the granulate properties (grain hardness, shape and size distribution).
In practice calcareous sands often cause problems: Their grains are much softer and more breakable than quartz grains (calcite: Mohs’ hardness 3; quartz: Mohs’ hardness 7). Even for a comparable grain size distribution and grain shape and the same initial pressure and density, the penetration resistances of these materials can differ substantially [40].
On behalf of Keller Grundbau GmbH (Offenbach/Germany) CPT calibration chamber tests (Sec. 3.2) were performed at IBF in order to examine the influence of different mass fractions of a calcareous sand in a mixture with a quartz sand with respect to the attainable cone penetration resistances. The test facility allows the preparation of granular samples with a desired density in a calibration chamber. It is possible to simulate different stress states and densities and to get reproducible CPT results.
37
Material CaCO3 ρs d10 d60 CU emin emax ϕc content in g/cm3 in mm in mm = d60/d10
Dubai sand 90% 2.805 0.13 0.53 4.1 0.762 1.223 36.0◦
Karlsruhe sand ≈ 0% 2.647 0.14 0.31 2.2 0.531 0.875 31.0◦ Table 3.1: Index properties of the original materials.
The interpretation of the calibration chamber tests is performed applying a semi-empirical method after Cudmani [7], which is described in Section 3.4. It is based on a hypoplastic constitutive equation, which mathematically describes the mechanical behaviour of gran-ular materials [51]. All material constants are obtained from standard laboratory tests on disturbed samples. For a given stress state the only state variable is the void ratio (or the density) which can be indirectly determined from CPT results. However, one premise of hypoplasticty is the permanence of the grains. In reality CPT may lead to grain frac-turing even with quartz [3] [7]. Since calcite is more breakable than quartz, the purpose of the present investigation is to clarify how far the interpretation method after Cudmani is applicable to calcareous granular materials. In addition the tests are evaluated using a procedure proposed by the German code DIN 4094 as well as one by Schmertmann [45]
(Sec. 3.3) for comparison. The performance of the different methods is benchmarked in Section 3.5. Section 3.6 addresses the influence of two different mass fractions of gravel and stones (d > 4 cm) in a quartz/shell sand mixture on the cone penetration resistance.