Monforte et al 2019a - Revision history

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 The last analysis of this work is the hydro-mechanical simulation of the cone penetration test in a Modified Cam Clay soil. A parametric analysis covers the effect of the permeability of the soil -from drained to undrained conditions- and the interface friction angle. The effect of these parameters on the cone resistance, sleeve friction and pore pressure at three potential measurement points is fully characterized. These numerical results are used to assess several techniques to estimate the permeability of soils from CPTu testing. Special attention is paid to on-the-fly techniques, in which permeability could be directly estimated from the CPTu data stream without the need for any stoppage.
-==PREFACE==
+==Preface==
 This monograph is a revised version of the doctoral dissertation of the first author, entitled ''Insertion Problems in Geomechanics with the Particle Finite Element Method''. The thesis was defended on November 5th 2018 in Barcelona.  The research was conducted under the supervision of Professors M. Arroyo, J. M. Carbonell and A. Gens.

@@ Line 9,284: / Line 9,284: @@
 |}
-<span id='citeF-155'></span>[[#cite-155|[155]]] published analytical solutions for the problem of consolidation beneath a smooth impermeable circular raft of finite stiffness. The normalized consolidation curve from that solution is compared with the numerical solutions in Figure [[#img-116|116]]. All numerical solutions plot very close to one another and the small differences with the analytical solution are likely due to the different mechanical interface condition (smooth contact vs perfect adherence). The use of stabilization in the mass conservation equation does not seem to produce any over-diffusive effect.
+Booker and Small <span id='citeF-155'></span>[[#cite-155|[155]]] published analytical solutions for the problem of consolidation beneath a smooth impermeable circular raft of finite stiffness. The normalized consolidation curve from that solution is compared with the numerical solutions in Figure [[#img-116|116]]. All numerical solutions plot very close to one another and the small differences with the analytical solution are likely due to the different mechanical interface condition (smooth contact vs perfect adherence). The use of stabilization in the mass conservation equation does not seem to produce any over-diffusive effect.
 <div id='img-118a'></div>

@@ Line 7,459: / Line 7,459: @@
 ===7.1.3 Strain history as a sampling disturbance measure===
-====7.1.3.1 Strain Path Method====
+====Strain Path Method====
 <div id='img-63'></div>
@@ Line 7,520: / Line 7,520: @@
 A more detailed parametric analysis assessing the influence of the area ratio, cutting-edge angles and inside clearance was performed by&nbsp;<span id='citeF-139'></span>[[#cite-139|[139]]] by means of a Strain Path method implemented via a finite element approach. In particular, the authors analyzed the effect of the area ratio, the cutting-edge angle and inside clearance on the sample disturbance, evaluated on the basis of the strains imposed on the center-line of the soil sample.
-====7.1.3.2 Shallow Strain Path Method====
+====Shallow Strain Path Method====
 <span id='citeF-146'></span>[[#cite-146|[146]]] developed an extension of the Strain Path method, the Shallow Strain Path method (SSPM), to explicitly include the effects of the stress free ground surface.  The authors concluded that shallow penetrations cause a heave at the ground surface, while settlements only occur in the region around the tip and in a thin region of material adjacent to the shaft of the penetrometer. At large penetrations, settlements only occur at all points below the tip of the tube.
@@ Line 7,560: / Line 7,560: @@
 Assuming that the displacement of this point is representative of the vertical displacements of the inner free surface  (the vertical displacement is not constant inside of the tube and may vary up to  a factor of 1.7 for very thin tubes, see Figure 12 of <span id='citeF-146'></span>[[#cite-146|[146]]]),  the specific recovery ratio may be computed for different wall thicknesses. Figure&nbsp;[[#img-66|66]] presents this curves in terms of the aspect ratio of the sampler.  The peak recovery takes place at very shallow penetrations, <math display="inline">z = \dfrac{\sqrt{2}}{2}\,\dfrac{B-t}{B}\, R</math>, and the maximum value decreases with the aspect ratio, <math display="inline">B/t</math>. Once the peak value is attained, the specific recovery ratio decreases until it reaches a steady state of 100%
-====7.1.3.3 Finite element simulations====
+====Finite element simulations====
 Very limited numerical work has been performed on the sampling process. The origins of these simulations may be traced back to <span id='citeF-147'></span>[[#cite-147|[147]]], that used the finite element method. The authors employ a viscoplastic flow approach: assuming that the elastic strains are negligible, the deformation process is comparable to that of a viscous fluid of non Newtonian kind; the viscosity is considered non-linear and depends on the assumed constitutive model for the soil. Nonetheless, <span id='citeF-148'></span>[[#cite-148|[148]]] claimed that  the  discretization used by <span id='citeF-147'></span>[[#cite-147|[147]]] was too coarse to provide sufficient accuracy: the finite element mesh consisted only of 50 quadrilateral elements.
@@ Line 7,566: / Line 7,566: @@
 <span id='citeF-148'></span>[[#cite-148|[148]]] performed a set of hydro-mechanical simulations of the sampling on normally consolidated Modified Cam Clay soil. The authors analyzed the effect of the penetration rate, sampler-soil interface friction and thickness of the tube; although the amount of disturbance varied due to these factors, in all the cases disturbance concentrated near the soil-sampler interface and at the top of the sample. Additionally, sampling disturbance due to friction at the soil-sampler interface increase as the sampler penetrates the soil: as such, long samples may result be seriously degraded. It is worth noting that the penetration of the sampler is simulated by splitting a group of nodes ahead of the penetration route up to a sufficient depth and applying incremental displacements to match the geometric configuration of the sampling tube;  the accuracy of this approach is not demonstrated. In all the cases, the obtained vertical strains in the centerline are in the same order of magnitude of those obtained by <span id='citeF-138'></span>[[#cite-138|[138]]]. A typical finite element mesh consists of 400 quadrilateral elements.
-====7.1.3.4 Physical modeling====
+====Physical modeling====
 In terms of physical evidences, <span id='citeF-149'></span>[[#cite-149|[149]]] and <span id='citeF-150'></span>[[#cite-150|[150]]] developed a small-scale physical modelling system to investigate the effect of tube sampling. The authors used an artificial, transparent soil with embedded seeding particles. The process of the penetration of  a glass sampler was recorded with digital photographies, that were analyzed by Particle Image Velocimetry (PIV).

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 In order to understand the effect of the constitutive parameters, this particular problem has been reanalyzed. The elastic parameters are listed in Table&nbsp;[[#table-24|24]], where case MCC1 coincides with the reference one. Additionally, the following parameters have been assumed: <math display="inline">M = 1</math>, <math display="inline">\lambda ^{\ast } / \kappa ^{\ast } = 10</math>, <math display="inline">p_0=1</math> MPa; as a consequence of the assumed material parameters and based on the reported maximum vertical load and interpreted <math display="inline">K_0 =0.53</math>&nbsp;<span id='citeF-43'></span>[[#cite-43|[43]]], the initial preconsolidation stress is set to <math display="inline">p_{c0}= 6.8065</math> MPa.
-====B.3.1.1 Attainable stress ratio====
+====Attainable stress ratio====
 Figure&nbsp;[[#img-157|157]] shows the constant volume trajectories in the triaxial plane assuming elasticity; as a reference, the Critical State Line and initial yield surface are also depicted. Using the combination MCC3, these trajectories are straight lines, since there is no coupling between the volumetric and deviatoric elastic response. For the MCC1 constitutive parameters, the limit stress ratio is <math display="inline">q/(-\pi ) < 1.424</math>; once the stress state reaches this limit, the determinant of the elastic stiffness matrix becomes negative and the stress ratio drastically reduces as deviatoric strains increase.
@@ Line 11,874: / Line 11,874: @@
 |}
-====B.3.1.2 Undrained triaxial tests====
+====Undrained triaxial tests====
 Results of undrained triaxial tests at a broad range of overconsolidation ratios are presented Figure&nbsp;[[#img-159|159]]. The axial load vs axial displacement results are not reported here since these simulations have been calculated with an independent Matlab code and some simplifications have been made. For instance, for undrained triaxial tests, the stress path from the p-axis to the yield surface is obtained imposing a sequence of volume preserving strains; once the point reaches the yield surface, using Matlab non-linear solver a new stress-strain point is found such that (i) the yield surface is zero, (ii) there is no variation of volume and (iii) the Lode angle is <math display="inline">\theta _L = -30^{\circ }</math> (triaxial compression test) and (iv) the stress path tends to the Critical State line.  Since the problem is solved in this manner, some information regarding the deviatoric plastic strains are lost. In order to validate this implementation, some simulations have been run using this the code and the one that is used to compute boundary valued problems and exactly the same stress paths have been found.
@@ Line 11,912: / Line 11,912: @@
 |}
-====B.3.1.3 Drained triaxial tests====
+====Drained triaxial tests====
 Figure&nbsp;[[#img-160|160]] shows the results of the simulation of drained triaxial tests. Using the set of parameters MCC1, the traixial test with the lowest OCR could not be simulated since the stress state reaches first the limit of attainable  stress ratios before reaching the yield surface.  However, the rest of simulations of MCC1 could be computed.

@@ Line 13,481: / Line 13,481: @@
 In this  appendix, the effect of the constitutive parameters of the <span id='citeF-42'></span>[[#cite-42|[42]]] hyperleastic model has been assessed. In particular, the effect of the value of the parameters that govern the elastic deviatoric response has been assessed in a boundary value problem: the cone penetration test.  Three different sets of constitutive parameters have been used; all of them share a common treat: they try to mimic the ones used by&nbsp;<span id='citeF-123'></span>[[#cite-123|[123]]]. Two of them have a shear modulus almost proportional to the mean effective stress and coupling between the elastic and deviatoric response, whereas the third has a constant shear modulus and uncoupled elastic-deviatoric response. Results of the cone penetration test in drained and undrained conditions reveal that almost coincident results in terms of the net cone resistance and water pressure are obtained irrespectively of the constitutive paremeters. A detailed look at the calculated stress and strain fields reveals that almost unnoticeable differences appear.
-=F Additional results: three-dimensional simulations and hypo-elastic plastic large strain models=
+=Appendix F. Additional results: three-dimensional simulations and hypo-elastic plastic large strain models=
 Numerical simulation of large displacement problems in geomechanics has attracted the interest of many researchers over the past decades. In many circumstances these problems can be treated as two dimensional: plane stress or axisymmetric. However, some problems -such as the penetration of a square foundation or the dilatometer test (DMT)- do not enjoy any of these conditions. This appendix presents the extension to three dimensions of a numerical code for the simulation of large displacement fluid-saturated porous media at large strains. The proposal relies, on the one hand, on the Particle Finite Element Method, known for its capability to tackle large deformations and rapid changing boundaries, and, on the other hand, on constitutive descriptions well established in current geotechnical analyses. The performance of the method is assessed in several benchmark examples, ranging from the insertion of a rigid square footing to a rough ball penetrometer.
@@ Line 13,769: / Line 13,769: @@
 Additionally, the two main frameworks to describe elasto-plastic models at large strains (namely, hypoelastic-based and hyperelastic-based models) have been numerically assessed in the penetration of a footing in a single-phase quasi-incompressible medium and in a coupled-hydromechanical case. Rigid body rotations were relatively small in both problems; as such, both constitutive models predicted similar results.
-===References===
+=References=
 <div id="cite-1"></div>

← Older revision	Revision as of 07:05, 26 August 2019
(No difference)

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 Results assuming a rough interface behavior have also been presented.  It has been found that the maximum bearing capacity factor is in the order of <math display="inline">N_0=11.5</math> irrespectively of the contact adhesion; this capacity factor decreases until it reaches a value approximately of <math display="inline">N_0=10.3</math> once the structure is plugged.
-=E Additional results of the hydro-mechanical simulation of the Cone Penetration Test=
+=Appendix E. Additional results of the hydro-mechanical simulation of the Cone Penetration Test=
 ==E.1 Introduction==

@@ Line 13,037: / Line 13,037: @@
 Due to the high complexity of the formulation and, as mentioned early, the linearization has different terms in plane strain and three-dimensional analysis, the matrix form is not presented. The interested reader is referred directly to the developed numerical implementation&nbsp;<span id='citeF-37'></span>[[#cite-37|[37]]].
-=D Bearing capacity factors of close-ended piles and tubes=
+=Appendix D. Bearing capacity factors of close-ended piles and tubes=
 ==D.1 Introduction==