stressInducedPoint: Induced Stress due to Point Loads

In geotech: Geotechnical Engineering

Description

These functions calculate induced stresses due to a point load applied at the surface: induced.point performs this calculation at a specific depth, induced.point.profile performs this calculation at a series of depths.

Usage

induced.point(P, x, y, z, nu)
induced.point.profile(P, x, y, z = NA, nu)

Arguments

P	point load
x	horizontal distance from point load in the x direction
y	horizontal distance from point load in the y direction
z	depth(s) of interest
nu	Poisson's ratio

Details

The depth(s) of interest (z) should be a single value for induced.point, and a vector of values for induced.point.profile. For induced.point.profile, the default vector of z values is 1-ft or 1-m increments, to a maximum depth of 50 ft or 50 m.

Value

Function induced.point outputs a six-element list giving the induced stress at a specified depth using the Boussinesq (1885) theory.

• sigmaX = induced horizontal stress in the x direction

• sigmaY = induced horizontal stress in the y direction

• sigmaZ = induced vertical stress

• tauZX = induced shear stress on the ZX plane

• tauYX = induced shear stress on the YX plane

• tauYZ = induced shear stress on the YZ plane

Function induced.point.profile outputs a seven-element list containing seven vectors that display the depth variation of induced stresses using the Boussinesq (1885) theory.

• depth = depth

• sigmaX = induced horizontal stress in the x direction

• sigmaY = induced horizontal stress in the y direction

• sigmaZ = induced vertical stress

• tauZX = induced shear stress on the ZX plane

• tauYX = induced shear stress on the YX plane

• tauYZ = induced shear stress on the YZ plane

Author(s)

James Kaklamanos <[e-mail]> and Kyle Elmy <[e-mail]>

References

Boussinesq, J. (1885). "Application des Potentiels a L'Etude de L'Equilibre et du Mouvement des Solides Elastiques", Gauthier-Villars, Paris (in French).

See Also

stressInducedArea, stressVertical, stressHorizontal

Examples

##  Example code for Induced Stress due to a Point Load
induced.point(P = 100000, x = 5, y = 2, z = 6, nu = 0.35)

##  Example code for Induced Stress due to a Point Load: Profile
induced.point.profile(P = 100000, x = 5, y = 2, nu = 0.35)

Example output

$sigmaX
[1] 172.2196

$sigmaY
[1] 17.01116

$sigmaZ
[1] 302.7692

$tauZX
[1] 252.3077

$tauYX
[1] 46.62503

$tauYZ
[1] 100.9231

$depth
 [1]  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
[26] 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
[51] 50

$sigmaX
 [1] -119.2242737  140.6815930  296.9522181  332.6577112  294.6284330
 [6]  232.1261981  172.2196175  124.0845942   88.2941685   62.5994315
[11]   44.4068686   31.5614030   22.4631798   15.9800094   11.3264695
[16]    7.9609574    5.5094646    3.7122926    2.3877260    1.4074962
[21]    0.6802256    0.1402142   -0.2602036   -0.5559094   -0.7726395
[26]   -0.9295296   -1.0409099   -1.1175829   -1.1677417   -1.1976344
[31]   -1.2120498   -1.2146739   -1.2083551   -1.1953015   -1.1772289
[36]   -1.1554737   -1.1310774   -1.1048526   -1.0774325   -1.0493100
[41]   -1.0208675   -0.9924004   -0.9641356   -0.9362456   -0.9088600
[46]   -0.8820744   -0.8559575   -0.8305568   -0.8059029   -0.7820133
[51]   -0.7588952

$sigmaY
 [1] 119.2242737 111.1508030  95.3489991  72.8547369  49.8294893  30.8031073
 [7]  17.0111554   7.7832118   1.9232151  -1.6492942  -3.7351067  -4.8784458
[13]  -5.4340194  -5.6283592  -5.6047511  -5.4534002  -5.2309043  -4.9726118
[19]  -4.7004173  -4.4276807  -4.1623394  -3.9088879  -3.6696422  -3.4455510
[25]  -3.2367177  -3.0427372  -2.8629124  -2.6963934  -2.5422655  -2.3996042
[31]  -2.2675093  -2.1451238  -2.0316446  -1.9263266  -1.8284838  -1.7374876
[37]  -1.6527643  -1.5737910  -1.5000923  -1.4312360  -1.3668297  -1.3065167
[43]  -1.2499731  -1.1969043  -1.1470424  -1.1001435  -1.0559853  -1.0143651
[49]  -0.9750980  -0.9380148  -0.9029608

$sigmaZ
 [1]   0.000000   9.685861  61.058555 144.825874 224.952112 278.526807
 [7] 302.769237 304.788797 293.092008 274.275618 252.619639 230.616987
[13] 209.589667 190.155314 172.531818 156.722327 142.622874 130.082942
[19] 118.938413 109.028659 100.204712  92.332507  85.293516  78.984050
[25]  73.313959  68.205130  63.589973  59.410015  55.614638  52.159960
[31]  49.007874  46.125223  43.483089  41.056195  38.822389  36.762216
[37]  34.858540  33.096238  31.461926  29.943734  28.531109  27.214645
[43]  25.985946  24.837494  23.762549  22.755052  21.809547  20.921112
[49]  20.085297  19.298073  18.555785

$tauZX
 [1]   0.000000  48.429307 152.646388 241.376457 281.190141 278.526807
 [7] 252.307697 217.706284 183.182505 152.375343 126.309820 104.825903
[13]  87.329028  73.136659  61.618506  52.240776  44.569648  38.259689
[19]  33.038448  28.691752  25.051178  21.983930  19.384890  17.170446
[25]  15.273742  13.641026  12.228841  11.001855   9.931185   8.993097
[31]   8.167979   7.439552   6.794233   6.220636   5.709175   5.251745
[37]   4.841464   4.472465   4.139727   3.838940   3.566389   3.318859
[43]   3.093565   2.888081   2.700290   2.528339   2.370603   2.225650
[49]   2.092218   1.969191   1.855578

$tauYX
 [1] -725.01584412 -484.29306928 -196.00541316  -31.68003178   33.21516376
 [6]   49.30467973   46.62503141   38.63533430   30.40691444   23.46759757
[11]   18.02914058   13.89142967   10.77540572    8.43014694    6.65711109
[16]    5.30713794    4.27060527    3.46757318    2.83976514    2.34453514
[21]    1.95048397    1.63432189    1.37863522    1.17029552    0.99932263
[26]    0.85806736    0.74062025    0.64238051    0.55973965    0.48984725
[31]    0.43043635    0.37969227    0.33615335    0.29863531    0.26617313
[36]    0.23797628    0.21339377    0.19188693    0.17300790    0.15638268
[41]    0.14169760    0.12868849    0.11713202    0.10683867    0.09764701
[46]    0.08941910    0.08203662    0.07539784    0.06941493    0.06401193
[51]    0.05912288

$tauYZ
 [1]   0.0000000  19.3717228  61.0585552  96.5505829 112.4760562 111.4107226
 [7] 100.9230789  87.0825134  73.2730019  60.9501373  50.5239278  41.9303613
[13]  34.9316111  29.2546638  24.6474025  20.8963103  17.8278593  15.3038755
[19]  13.2153792  11.4767010  10.0204712   8.7935721   7.7539560   6.8681782
[25]   6.1094966   5.4564104   4.8915364   4.4007419   3.9724742   3.5972386
[31]   3.2671916   2.9758209   2.7176931   2.4882542   2.2836700   2.1006980
[37]   1.9365856   1.7889858   1.6558909   1.5355761   1.4265554   1.3275437
[43]   1.2374260   1.1552323   1.0801159   1.0113356   0.9482412   0.8902601
[49]   0.8368874   0.7876764   0.7422314

geotech documentation built on May 1, 2019, 9:09 p.m.