scholarly journals Modeling parameters of structured clays as a multivariate normal distribution

2012 ◽  
Vol 49 (5) ◽  
pp. 522-545 ◽  
Author(s):  
Jianye Ching ◽  
Kok-Kwang Phoon
Keyword(s):  
Shear Strength ◽  
Probability Distribution ◽  
Normal Distribution ◽  
Multivariate Normal Distribution ◽  
Undrained Shear Strength ◽  
Multivariate Distribution ◽  
Soil Parameters ◽  
Multivariate Normal ◽  
Multivariate Probability Distribution ◽  
Undrained Shear

This study explores the possibility of modeling liquidity index, undrained shear strength, remolded undrained shear strength, preconsolidation stress, and vertical effective stress of structured clays (sensitive or quick clays) as a multivariate normal distribution. The literature is replete with correlation equations between two soil parameters. Consistent synthesis of more than two soil parameters through construction of a multivariate probability distribution function is rare, despite obvious practical usefulness of such an approach. This study compiles a large database of structured clays to construct the multivariate probability distribution among the aforementioned five soil parameters. This multivariate distribution is then used to simulate the correlations between soil parameters of interest and to derive useful equations for Bayesian inference. This constructed multivariate distribution and equations are further validated by another independent database of structured clays as well as by empirical equations proposed in the literature.

Modeling piezocone cone penetration (CPTU) parameters of clays as a multivariate normal distribution

2014 ◽  
Vol 51 (1) ◽  
pp. 77-91 ◽  
Author(s):  
Jianye Ching ◽  
Kok-Kwang Phoon ◽  
Chih-Hao Chen
Keyword(s):  
Shear Strength ◽  
Normal Distribution ◽  
Multivariate Normal Distribution ◽  
Undrained Shear Strength ◽  
Soil Parameters ◽  
Multivariate Normal ◽  
Cone Penetration ◽  
Overconsolidation Ratio ◽  
Data Points ◽  
Undrained Shear

This study examines the possibility of modeling piezocone cone penetration (CPTU) cone tip resistance, excessive pore pressure behind the cone, undrained shear strength, and overconsolidation ratio of lightly overconsolidated clays as a multivariate normal distribution. This is part of a continuing study to develop a multivariate distribution that could be used to simulate common soil parameters at a clay site. This study compiles a large database consisting of 535 data points in which the CPTU parameters, undrained shear strength, and overconsolidation ratio are simultaneously measured in close proximity. A multivariate normal distribution is then used to capture the correlations between soil parameters of interest and to derive useful equations for Bayesian inference. This constructed multivariate normal distribution and equations are further validated by another independent database consisting of 594 data points as well as by empirical equations proposed in literature. The most useful outcome of this study is to provide a systematic and analytical method for updating the distributions of the normalized undrained shear strength and the overconsolidation ratio in the presence of CPTU parameters.

Multivariate distribution for undrained shear strengths under various test procedures

2013 ◽  
Vol 50 (9) ◽  
pp. 907-923 ◽  
Author(s):  
Jianye Ching ◽  
Kok-Kwang Phoon
Keyword(s):  
Shear Strength ◽  
Test Procedure ◽  
Undrained Shear Strength ◽  
Multivariate Distribution ◽  
Strain Rates ◽  
Test Procedures ◽  
Strength Based ◽  
Multivariate Probability Distribution ◽  
Stress States ◽  
Undrained Shear

The undrained shear strength (su) of a clay is not a constant. In particular, su values of a clay evaluated by different test procedures are different because these tests may have different stress states, stress histories, degrees of sampling disturbance, and strain rates. This study constructs the multivariate probability distribution of su from various test procedures based on a large clay database. This multivariate distribution provides an estimation of the normalized undrained shear strength based on four factors: test mode, overconsolidation ratio, strain rate, and plasticity. Once this multivariate distribution is constructed, interesting questions can be answered systematically using simple Bayesian analysis, e.g., given the su value for one test procedure, what is the updated mean and coefficient of variation of the su value for another test procedure?

scholarly journals A Random Forest Model for the Prediction of Spudcan Penetration Resistance in Stiff-Over-Soft Clays

2020 ◽  
Vol 27 (4) ◽  
pp. 130-138
Author(s):  
Pan Gao ◽  
Zhihui Liu ◽  
Ji Zeng ◽  
Yiting Zhan ◽  
Fei Wang
Keyword(s):  
Shear Strength ◽  
Random Forest ◽  
Penetration Resistance ◽  
Undrained Shear Strength ◽  
Soil Parameters ◽  
Good Prediction ◽  
Resistance Profile ◽  
Soft Clays ◽  
Centrifuge Tests ◽  
Undrained Shear

AbstractPunch-through is a major threat to the jack-up unit, especially at well sites with layered stiff-over-soft clays. A model is proposed to predict the spudcan penetration resistance in stiff-over-soft clays, based on the random forest (RF) method. The RF model was trained and tested with numerical simulation results obtained through the Finite Element model, implemented with the Coupled Eulerian Lagrangian (CEL) approach. With the proposed CEL model, the effects of the stiff layer thickness, undrained shear strength ratio, and the undrained shear strength of the soft layer on the bearing characteristics, as well as the soil failure mechanism, were numerically studied. A simplified resistance profile model of penetration in stiff-over-soft clays is proposed, divided into three sections by the peak point and the transition point. The importance of soil parameters to the penetration resistance was analysed. Then, the trained RF model was tested against the test set, showing a good prediction of the numerical cases. Finally, the trained RF was validated against centrifuge tests. The RF model successfully captured the punch-through potential, and was verified using data recorded in the field, showing advantages over the SNAME guideline. It is supposed that the trained RF model should give a good prediction of the spudcan penetration resistance profile, especially if trained with more field data.

scholarly journals The Distribution of the Ratio of Two Quadratic Forms

1955 ◽  
Vol 8 (3) ◽  
pp. 402 ◽  
Author(s):  
GS Watson
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Quadratic Forms ◽  
Multivariate Normal Distribution ◽  
Linear Functions ◽  
Multivariate Normal ◽  
Exact Probability ◽  
Exact Probability Distribution ◽  
Integral Order

The exact probability distribution of the ratio of two quadratic forms is given in the case where the quadratic forms and the multivariate normal distribution of the variables is such that the ratio is a ratio of linear functions of gamma variables of integral order.

The Evaluation of Probabilities in a Normal Multivariate Distribution, with Special Reference to the Correlation Ratio

1949 ◽  
Vol 8 (3) ◽  
pp. 95-100 ◽  
Author(s):  
M. H. Quenouille
Keyword(s):  
Special Reference ◽  
Normal Distribution ◽  
Multivariate Normal Distribution ◽  
Multivariate Distribution ◽  
Frequency Function ◽  
Correlation Ratio ◽  
Multivariate Normal ◽  
Symmetrical Case ◽  
Independent Observations ◽  
Image Position

This paper deals with the multivariate normal distribution in the symmetrical case when the frequency function may be reduced toThis is the usual distribution occurring for a series of similar independent observations or for the firing of shots at a target.

scholarly journals Site Investigations of the Lacustrine Clay in Taihu Lake, China, Using Self-Boring Pressuremeter Test

Sensors ◽  
2021 ◽  
Vol 21 (18) ◽  
pp. 6026
Author(s):  
Bin Wang ◽  
Kang Liu ◽  
Yong Wang ◽  
Quan Jiang
Keyword(s):  
Shear Strength ◽  
Shear Modulus ◽  
Normal Distribution ◽  
Taihu Lake ◽  
Undrained Shear Strength ◽  
Plasticity Index ◽  
Lake Area ◽  
Site Investigations ◽  
Lacustrine Clay ◽  
Undrained Shear

Site investigations of the soils are considered very important for evaluation of the site conditions, as well as the design and construction for the project built in it. Taihu tunnel is thus far the longest tunnel constructed in the lake in China, with an entire length of over 10 km. However, due to the very insufficient site data obtained for the lacustrine clay in the Taihu lake area, a series of self-boring pressuremeter (SBPM) field tests was therefore carried out. Undrained shear strengths were deduced from the SBPM test, with the results showing generally higher than those obtained from the laboratory tests, which may be attributed to the disturbance to the soil mass during the sampling process. Degradation characteristics of the soil shear modulus (Gs) were mainly investigated, via a thorough comparison between different soil layers, and generally, the shear modulus would cease its decreasing trends and become stable when the shear strain reaches over 1%. Meanwhile, it was found that a linear relationship between the plasticity index and the shear modulus, and between the decay rate of the shear modulus and the plasticity index as well, could be developed. Further statistical analysis over the undrained shear strength and shear modulus distribution of the soils shows that the undrained shear strength of the soils follows a normal distribution, while the shear modulus follows a log-normal distribution. More importantly, the spatial correlation length of the shear modulus is found much smaller than that of the undrained strength.

Investigation of bearing capacity factor of T-bar penetrometer at shallow depths in clayey soils

2013 ◽  
Vol 1 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Márcio S.S. Almeida ◽  
José Renato M.S. Oliveira ◽  
Khader I. Rammah ◽  
Pablo C. Trejo
Keyword(s):  
Shear Strength ◽  
Offshore Structures ◽  
Analytic Solutions ◽  
Undrained Shear Strength ◽  
Soil Parameters ◽  
Geotechnical Centrifuge ◽  
Fine Grain ◽  
Centrifuge Tests ◽  
Undrained Strength ◽  
Undrained Shear

The T-bar penetrometer is normally used in both in-situ and on the centrifuge to establish profiles of the undrained shear strength of fine-grain soils. However, adequate measurement of the undrained shear strength at shallow depths requires understanding the failure mechanism at these depths. For onshore and offshore structures such as pipelines, the assessment of soil parameters, in particular the undrained shear strength at shallow depth can be very critical to achieve both efficient and economic design. However, this requires the evaluation of the value of T-bar bearing factor (Nb) corresponding to both shallow and very shallow depths. This paper describes a series of geotechnical centrifuge tests undertaken using three different sizes of the T-bar penetrometer on two types of clayery soil. The results of the undrained strength obtained from each T-bar were compared with the results obtained from the bigger T-bars. The curves that describes the variation of the T-bar factor (Nb) versus the penetration depth were established from the comparison of all results obtained from the three different sizes of the T-bar. The results of (Nb) obtained in this study were compared with results obtained from both numerical and analytic solutions proposed in the literature. Generally, the experimental data obtained in this study presented Nb values higher than those predicted by others authors for all H/D ratios. However, the comparison indicates that the Nb values obtained in this study showed relatively reasonable agreement with those values obtained from the literature by adopting a non-homogenous strength profile.

Modelling spatial variability of soil parameters

1990 ◽  
Vol 27 (5) ◽  
pp. 617-630 ◽  
Author(s):  
M. Soulié ◽  
P. Montes ◽  
V. Silvestri
Keyword(s):  
Shear Strength ◽  
Spatial Variability ◽  
Undrained Shear Strength ◽  
Geostatistical Analysis ◽  
Earth Dam ◽  
Soil Parameters ◽  
Bay Area ◽  
Measurements Errors ◽  
Weak Zones ◽  
Undrained Shear

The purpose of this study is to show that geostatistics can help in finding the structure of the spatial variability of the undrained shear strength within a clay deposit. The site under study, B-6, owes its name to the earth dam that will be constructed on it; the site is located on the shore of the Broadback River in the James Bay area of Quebec. The geostatistical analysis is carried out on the unaltered zone of the B-6 clay; it shows an anisotropic structure for the spatial variability. The knowledge of the structure (variogram) of the undrained shear strength is used in the kriging theory to compute estimations at points of the deposit where experimental measurements are not available. Kriging is also used to identify weak zones within the B-6 clay. The geostatistical analysis of the B-6 clay gives the opportunity to test the capability of the method. Even if the errors of measurements were small, the variogram has permitted detection and correction of a bias that affected a certain number of vane profiles. Key words: clay, geostatistics, undrained shear strength, variogram, measurements errors, kriging.

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