Mohr-Coulomb Model

1 Steven F. Bartlett, 2010 Mohr-Coulomb ModelTuesday, September 11, 201212:43 PM Mohr-Coulomb Model Page 1 Steven F. Bartlett, 2011 The angle of dilationcontrols an amount of plastic volumetric strain developed during plastic shearing and is assumed constant during plastic yielding. The value of =0 corresponds to the volume preserving deformation while in (regardless of overconsolidated layers) are characterized by a very low amount of dilation ( 0). As for sands, the angle of dilation depends on the angle of internal friction. For non-cohesive soils (sand, gravel) with the angle of internal friction >30 the value of dilation angle can be estimated as = -30.

2 A negative value of dilation angle is acceptable only for rather loose sands. In most cases, however, the assumption of = 0 can be from < > How does dilatancy affect the behavior of soil?No dilatancy, dilatancy angle = 0. Note that the unit square has undergone distortion during shear. Note that the unit square has undergone distortion and volumetric strain (change in volume).Post-Failure -Dilation AngleWednesday, August 17, 201112:45 PM Mohr-Coulomb Model Page 2 Steven F. Bartlett, 2011 Soils dilate (expand) or contract upon shearing and the degree of this dilatancy can be explained by the dilatancy angle.

3 The dilatancy angle can be calculated from the Mohr's circle of strain, or from the triaxial test, see later. It can also be estimated from the following formulas, if the volumetric and maximum shear strain increments are element is dilating during shear. This is plastic behavior.(Salgado: The Engineering of Foundations, p. 132)(Salgado: The Engineering of Foundations, p. 132)Post-Failure -Dilation Angle (cont.)Wednesday, August 17, 201112:45 PM Mohr-Coulomb Model Page 3 Steven F. Bartlett, 2010(Flac v. 5 User Manual)(Flac v. 5 User Manual)Post-Failure Behavior, Dilation Angle from Triaxial TestTuesday, September 11, 201212:43 PM Mohr-Coulomb Model Page 4 Steven F.

4 Bartlett, 2010(Salgado: The Engineering of Foundations, p. 132)Plane strain conditions p- c= p P= peak friction angle (used in FLAC as command friction= C= critical state friction angle ( approx. 28 to 36 degrees quartz sand) P= peak dilation angle (used in FLAC as dilation =)Triaxial ( , axisymmetrical) conditions p- c= pPost-Failure Behavior, Dilation Angle from Triaxial TestTuesday, September 11, 201212:43 PM Mohr-Coulomb Model Page 5 Steven F. Bartlett, 2011 Plane StrainTriaxial Strain(See Eq. 5-16 in book to relate pand c) p = peak friction angle C = critical state friction angleValid only for a confining stress of 1 atm(Salgado: The Engineering of Foundations)Plane Strain vs.)

5 Triaxial Strain ConditionsWednesday, August 17, 201112:45 PM Mohr-Coulomb Model Page 6 Steven F. Bartlett, 2011If we know the critical state friction angle of a soil, the horizontal earth pressure coefficient Ko, and the relative density of the deposits, we can estimate the peak friction angle. This is valuable for design because most often, the peak friction angle is used to define the strength of the soil in foundation calculations. Practical application Iteration to estimate peak friction angle from stress state and void ratioThe mean effective stress (in situ) was used to calculate the average consolidation stress for the sample because the soil has been anisotrophically consolidated in situ.

6 Anisotropic consolidation better represents the actual conditions. Such consolidaton is also called Ko stress at the end of consolidation phase for Ko condition(Salgado: The Engineering of Foundations)Estimation of the peak friction angle from critical state friction angleWednesday, August 17, 201112:45 PM Mohr-Coulomb Model Page 7 Steven F. Bartlett, 2011 Note that in the above example, the peak friction angle calculate from the above equation, is not consistent with the assumed value of 40 degrees. Thus, the mean stress of is somewhat inconsistent with the calculated peak friction angle of degrees.

7 Hence, another iteration is required. This is done by adjusting the assumed peak friction angle to degrees and recalculating the mean stress and resulting friction angle until convergence is reached. In practice, friction angles are usually reported to the nearest whole number, so once the iteration converges to a stable whole number value, then iteration can can use the charts on the next page to estimate the difference between the peak and critical state friction angle as a function of effective confining stress.(Salgado: The Engineering of Foundations)Estimation of the peak friction angle from critical state friction angleWednesday, August 17, 201112:45 PM Mohr-Coulomb Model Page 8 Steven F.

8 Bartlett, 2011(Salgado: The Engineering of Foundations)Estimation of the peak friction angle from critical state friction angleWednesday, August 17, 201112:45 PM Mohr-Coulomb Model Page 9 Steven F. Bartlett, 2010 Initial StateDeformed StateMohr - coulomb Model in FLACT uesday, September 11, 201212:43 PM Mohr-Coulomb Model Page 10 Steven F. Bartlett, 2010 Axial Stress versus Axial StrainDoes this relationship show the correct values of:Cohesion at failure? 's modulus? these questions by used the above plot to confirm that cohesion and Young's modulus have been appropriately - coulomb Model in FLACT uesday, September 11, 201212:43 PM Mohr-Coulomb Model Page 11 Steven F.

9 Bartlett, 2010configset = large; large strain modegrid 18,18; for 18" x 18" EPS blockmodel mohrprop density = 20 bulk = shear = cohesion=50e3 friction=0 dilation=0 tension = 100e3; EPS properties;ini x mul ; makes x grid dimension equal to m or 1 inchini y mul ; makes y grid dimension equal to m or 1 inch;fix y j 1; fixes base in y direction onlyfix x y j 1 ;fixes base in x and y direction only;fix y i 8 12 j 1 ; fixes only part of basehis unbal 999;apply yvelocity from 1,19 to 19,19 ;applies constant downward velocity to simulate a strain-controlled testapply yvelocity xvelocity=0 from 1,19 to 19,19 ;applies constant downward velocity to simulate a strain-controlled testdef verticalstrain; subroutine to calculate vertical strain whilestepping avgstress = 0 avgstrain = 0 loop i (1,izones) loop j (1,jzones) vstrain = ((0-ydisp(i,j+1) -(0 -ydisp(i,j))) )*100 ; percent strain vstress = syy(i,j)*(-1) avgstrain = avgstrain + vstrain/18/18 avgstress = avgstress + vstress/18/18 end_loop end_loopendhis avgstrain 998his avgstress 997.

10 Step 3000history 999 unbalancedcycle 3000 FLAC Code for ModelTuesday, September 11, 201212:43 PM Mohr-Coulomb Model Page 12