Earth Retaining WallsCIVL455

CHAPTER II: LATERAL EARTH PRESSURE THEORY

Rankine’s Lateral Earth Pressure Theory

• Lateral pressure on walls can be evaluated for threeconditions;

At-rest condition Active condition

Passive condition

Ref: B. M. Das (2007)

At-rest lateral pressure

• Rankine’s lateral earth pressure theory based on a frictionlesswall and horizontal backfill. AT-REST (GEOSTATIC) CASE.

For most soils

For overconsolidated granular soils

For normally consolidated cohesive soils

For over-consolidated cohesive soils

Ref: B. M. Das (2007)

Active lateral pressure

• Rankine’s lateral earth pressure theory based on a frictionlesswall and horizontal backfill. ACTIVE CASE.

Drained

Undrained

Drained

DrainedUndrained

Undrained

Ref: B. M. Das (2007)

Active lateral pressure

• Rankine’s lateral earth pressure theory based on a frictionlesswall and inclined backfill. ACTIVE CASE.

Drained backfill with c’=0.

Drained backfill with c’>0.

Ref: B. M. Das (2007)

Passive lateral pressure

• Rankine’s lateral earth pressure theory based on a frictionlesswall and horizontal backfill. PASSIVE CASE.

Drained

Undrained

Passive lateral pressure

• Rankine’s lateral earth pressure theory based on a frictionlesswall and inclined backfill. PASSIVE CASE.

Drained backfill with c’=0.

Drained backfill with c’>0.

Ref: B. M. Das (2007)

Kp = Rankine's passive pressure coefficient

f () f

20 0.490 0.492 0.496 0.504 0.515 0.531 0.553 0.583 0.627 0.697 0.940 20 2.040 2.034 2.015 1.985 1.941 1.883 1.808 1.715 1.596 1.435 1.064

21 0.472 0.474 0.478 0.485 0.495 0.509 0.529 0.555 0.591 0.646 0.748 21 2.117 2.111 2.093 2.063 2.020 1.964 1.892 1.803 1.691 1.547 1.338

22 0.455 0.456 0.460 0.466 0.475 0.488 0.505 0.528 0.560 0.605 0.677 22 2.198 2.192 2.175 2.145 2.103 2.048 1.978 1.892 1.786 1.654 1.478

23 0.438 0.439 0.443 0.448 0.457 0.468 0.484 0.504 0.531 0.569 0.625 23 2.283 2.277 2.260 2.231 2.189 2.135 2.067 1.984 1.882 1.758 1.600

24 0.422 0.423 0.426 0.431 0.439 0.449 0.463 0.481 0.505 0.537 0.583 24 2.371 2.366 2.348 2.320 2.279 2.226 2.160 2.078 1.980 1.861 1.715

25 0.406 0.407 0.410 0.414 0.421 0.431 0.443 0.460 0.481 0.509 0.547 25 2.464 2.458 2.441 2.413 2.373 2.321 2.255 2.176 2.080 1.966 1.828

26 0.390 0.391 0.394 0.398 0.405 0.413 0.425 0.439 0.458 0.482 0.515 26 2.561 2.556 2.539 2.511 2.471 2.419 2.355 2.277 2.183 2.073 1.941

27 0.376 0.376 0.379 0.383 0.389 0.396 0.407 0.420 0.437 0.458 0.487 27 2.663 2.657 2.641 2.613 2.574 2.522 2.459 2.382 2.290 2.182 2.055

28 0.361 0.362 0.364 0.368 0.373 0.380 0.390 0.401 0.417 0.436 0.460 28 2.770 2.764 2.748 2.720 2.681 2.630 2.567 2.491 2.401 2.295 2.172

29 0.347 0.348 0.350 0.353 0.358 0.365 0.373 0.384 0.398 0.415 0.436 29 2.882 2.877 2.860 2.832 2.793 2.743 2.680 2.605 2.516 2.412 2.291

30 0.333 0.334 0.336 0.339 0.343 0.350 0.357 0.367 0.379 0.395 0.414 30 3.000 2.995 2.978 2.950 2.912 2.861 2.799 2.724 2.635 2.533 2.414

31 0.320 0.321 0.322 0.325 0.329 0.335 0.342 0.351 0.362 0.376 0.393 31 3.124 3.119 3.102 3.074 3.036 2.985 2.923 2.848 2.761 2.659 2.542

32 0.307 0.308 0.309 0.312 0.316 0.321 0.328 0.336 0.346 0.358 0.374 32 3.255 3.249 3.233 3.205 3.166 3.116 3.053 2.979 2.892 2.791 2.675

33 0.295 0.295 0.297 0.299 0.303 0.307 0.313 0.321 0.330 0.342 0.355 33 3.392 3.387 3.370 3.342 3.303 3.253 3.190 3.116 3.029 2.928 2.813

34 0.283 0.283 0.285 0.287 0.290 0.294 0.300 0.307 0.315 0.325 0.338 34 3.537 3.532 3.515 3.487 3.448 3.397 3.335 3.260 3.173 3.072 2.958

35 0.271 0.271 0.273 0.275 0.278 0.282 0.287 0.293 0.301 0.310 0.322 35 3.690 3.685 3.668 3.640 3.600 3.549 3.486 3.412 3.324 3.224 3.109

36 0.260 0.260 0.261 0.263 0.266 0.270 0.274 0.280 0.287 0.296 0.306 36 3.852 3.846 3.829 3.801 3.761 3.710 3.647 3.571 3.483 3.383 3.268

37 0.249 0.249 0.250 0.252 0.254 0.258 0.262 0.267 0.274 0.282 0.291 37 4.023 4.017 4.000 3.971 3.931 3.879 3.816 3.740 3.651 3.550 3.435

38 0.238 0.238 0.239 0.241 0.243 0.246 0.250 0.255 0.261 0.268 0.277 38 4.204 4.198 4.181 4.152 4.111 4.059 3.995 3.918 3.829 3.727 3.611

39 0.228 0.228 0.229 0.230 0.232 0.235 0.239 0.244 0.249 0.256 0.263 39 4.395 4.390 4.372 4.343 4.302 4.249 4.184 4.106 4.016 3.913 3.797

40 0.217 0.218 0.219 0.220 0.222 0.225 0.228 0.232 0.237 0.243 0.250 40 4.599 4.593 4.575 4.546 4.504 4.450 4.384 4.306 4.215 4.111 3.993

Lateral earth pressure coefficients for vertical frictionless wall with inclined backfill

Wall friction

• Coulomb’s method for walls with inclined back, inclined backfill andfriction.

Ref: B. M. Das (2007)

Active Case

Passive Case

Wall friction

• Simplified solution for Coulomb’s graphical method for lateralearth pressure for walls with inclined back, inclined backfilland friction.

Ref: B. M. Das (2007)

d/f 0.667

f ()

20 0.438 0.474 0.524 0.604 0.907 0.474 0.515 0.570 0.659 0.990 0.514 0.560 0.623 0.721 1.089 0.559 0.612 0.683 0.795 1.208 0.611 0.672 0.754 0.882 1.355

21 0.421 0.455 0.501 0.572 0.736 0.457 0.496 0.548 0.626 0.807 0.498 0.542 0.600 0.689 0.890 0.544 0.594 0.661 0.761 0.989 0.596 0.655 0.732 0.847 1.109

22 0.405 0.437 0.480 0.543 0.670 0.442 0.478 0.526 0.597 0.738 0.483 0.524 0.579 0.659 0.817 0.529 0.577 0.639 0.731 0.911 0.581 0.637 0.710 0.816 1.023

23 0.390 0.420 0.459 0.516 0.621 0.427 0.461 0.506 0.570 0.687 0.468 0.507 0.558 0.631 0.764 0.514 0.560 0.619 0.703 0.854 0.567 0.621 0.690 0.787 0.962

24 0.375 0.403 0.440 0.491 0.581 0.412 0.444 0.486 0.545 0.645 0.453 0.491 0.539 0.606 0.720 0.500 0.544 0.599 0.677 0.807 0.553 0.605 0.670 0.761 0.913

25 0.361 0.387 0.421 0.468 0.546 0.398 0.429 0.467 0.521 0.609 0.440 0.475 0.520 0.582 0.682 0.486 0.528 0.581 0.652 0.768 0.540 0.589 0.651 0.736 0.870

26 0.347 0.372 0.403 0.446 0.514 0.385 0.413 0.450 0.499 0.576 0.426 0.460 0.502 0.559 0.648 0.473 0.513 0.563 0.629 0.732 0.527 0.575 0.633 0.712 0.833

27 0.334 0.357 0.386 0.426 0.486 0.371 0.399 0.433 0.478 0.547 0.413 0.445 0.485 0.538 0.618 0.460 0.498 0.545 0.608 0.701 0.515 0.560 0.616 0.690 0.800

28 0.321 0.343 0.370 0.406 0.460 0.359 0.385 0.416 0.458 0.521 0.401 0.431 0.469 0.518 0.590 0.448 0.484 0.529 0.587 0.671 0.503 0.546 0.599 0.668 0.769

29 0.309 0.330 0.355 0.388 0.436 0.347 0.371 0.401 0.440 0.496 0.389 0.417 0.453 0.499 0.564 0.436 0.471 0.513 0.567 0.645 0.491 0.533 0.583 0.648 0.741

30 0.297 0.316 0.340 0.371 0.414 0.335 0.358 0.386 0.422 0.473 0.377 0.404 0.438 0.480 0.540 0.425 0.458 0.497 0.548 0.620 0.479 0.519 0.568 0.629 0.714

31 0.286 0.304 0.326 0.354 0.394 0.324 0.345 0.371 0.405 0.451 0.366 0.392 0.423 0.463 0.518 0.413 0.445 0.483 0.530 0.596 0.468 0.507 0.553 0.611 0.690

32 0.275 0.292 0.312 0.338 0.374 0.313 0.333 0.357 0.389 0.431 0.355 0.379 0.409 0.446 0.497 0.402 0.432 0.468 0.513 0.574 0.457 0.494 0.538 0.593 0.667

33 0.264 0.280 0.299 0.323 0.356 0.302 0.321 0.344 0.373 0.412 0.344 0.367 0.395 0.430 0.477 0.392 0.420 0.454 0.497 0.553 0.447 0.482 0.524 0.576 0.645

34 0.254 0.269 0.287 0.309 0.339 0.292 0.310 0.331 0.358 0.394 0.334 0.356 0.382 0.415 0.458 0.381 0.409 0.441 0.481 0.534 0.437 0.471 0.511 0.560 0.624

35 0.244 0.258 0.275 0.295 0.323 0.282 0.299 0.319 0.344 0.377 0.323 0.345 0.370 0.400 0.440 0.371 0.397 0.428 0.466 0.515 0.427 0.459 0.498 0.544 0.604

36 0.235 0.248 0.263 0.282 0.307 0.272 0.288 0.307 0.331 0.361 0.314 0.334 0.357 0.386 0.423 0.362 0.387 0.416 0.451 0.497 0.417 0.448 0.485 0.529 0.586

37 0.226 0.238 0.252 0.270 0.293 0.263 0.278 0.296 0.317 0.345 0.304 0.323 0.346 0.373 0.407 0.352 0.376 0.404 0.437 0.480 0.408 0.438 0.473 0.515 0.568

38 0.217 0.228 0.242 0.258 0.279 0.253 0.268 0.285 0.305 0.331 0.295 0.313 0.334 0.360 0.392 0.343 0.366 0.392 0.424 0.464 0.398 0.427 0.461 0.501 0.551

39 0.208 0.219 0.231 0.246 0.265 0.245 0.258 0.274 0.293 0.317 0.286 0.303 0.323 0.347 0.377 0.334 0.356 0.381 0.411 0.448 0.389 0.417 0.449 0.487 0.534

40 0.200 0.210 0.221 0.235 0.253 0.236 0.249 0.264 0.281 0.303 0.277 0.294 0.312 0.335 0.363 0.325 0.346 0.370 0.398 0.433 0.381 0.407 0.438 0.474 0.518

Active earth pressure coefficients for a rough wall with inclined backfill

Passive earth pressure coefficients for a rough wall with inclined backfill

d/f 0.100

f ()

20 2.144 2.444 2.780 3.167 3.626 2.016 2.288 2.586 2.922 3.310 1.921 2.174 2.445 2.746 3.085 1.854 2.093 2.348 2.624 2.930 1.810 2.043 2.287 2.547 2.831

21 2.233 2.554 2.916 3.337 3.842 2.093 2.381 2.701 3.064 3.487 1.987 2.254 2.544 2.866 3.234 1.912 2.164 2.433 2.728 3.058 1.861 2.105 2.363 2.639 2.943

22 2.327 2.670 3.061 3.519 4.074 2.173 2.479 2.822 3.214 3.676 2.057 2.338 2.647 2.993 3.391 1.972 2.237 2.523 2.838 3.192 1.915 2.170 2.442 2.736 3.061

23 2.426 2.793 3.214 3.713 4.324 2.256 2.583 2.950 3.373 3.877 2.129 2.426 2.755 3.127 3.558 2.035 2.314 2.617 2.953 3.334 1.970 2.238 2.524 2.836 3.184

24 2.530 2.922 3.377 3.921 4.593 2.344 2.691 3.085 3.543 4.092 2.204 2.519 2.869 3.269 3.735 2.100 2.394 2.715 3.074 3.484 2.027 2.308 2.610 2.942 3.313

25 2.640 3.060 3.551 4.144 4.885 2.437 2.805 3.227 3.723 4.323 2.282 2.616 2.989 3.419 3.924 2.168 2.477 2.818 3.201 3.642 2.087 2.381 2.699 3.052 3.449

26 2.756 3.206 3.737 4.384 5.200 2.533 2.926 3.379 3.915 4.570 2.365 2.717 3.116 3.577 4.124 2.239 2.564 2.925 3.335 3.809 2.149 2.457 2.793 3.167 3.592

27 2.878 3.360 3.935 4.641 5.542 2.635 3.053 3.539 4.120 4.836 2.451 2.824 3.249 3.745 4.338 2.313 2.656 3.039 3.476 3.986 2.213 2.536 2.891 3.288 3.743

28 3.008 3.525 4.146 4.918 5.915 2.742 3.188 3.710 4.339 5.122 2.541 2.936 3.390 3.923 4.567 2.390 2.751 3.157 3.625 4.174 2.280 2.618 2.993 3.415 3.901

29 3.145 3.699 4.373 5.218 6.321 2.855 3.330 3.891 4.574 5.431 2.635 3.055 3.539 4.113 4.811 2.470 2.851 3.282 3.782 4.373 2.349 2.704 3.100 3.549 4.069

30 3.290 3.886 4.616 5.542 6.764 2.973 3.480 4.084 4.825 5.765 2.734 3.179 3.696 4.314 5.072 2.554 2.956 3.414 3.948 4.586 2.422 2.794 3.212 3.689 4.245

31 3.444 4.085 4.877 5.893 7.250 3.099 3.640 4.290 5.095 6.126 2.838 3.310 3.863 4.529 5.353 2.642 3.066 3.552 4.124 4.811 2.497 2.888 3.329 3.837 4.433

32 3.607 4.297 5.158 6.274 7.784 3.231 3.809 4.510 5.385 6.519 2.947 3.448 4.040 4.758 5.655 2.734 3.181 3.698 4.310 5.052 2.575 2.986 3.453 3.992 4.631

33 3.780 4.524 5.461 6.689 8.373 3.371 3.989 4.745 5.697 6.945 3.062 3.594 4.228 5.003 5.980 2.830 3.302 3.853 4.508 5.309 2.657 3.089 3.582 4.157 4.841

34 3.965 4.768 5.789 7.141 9.023 3.518 4.180 4.996 6.035 7.411 3.183 3.749 4.428 5.265 6.330 2.931 3.430 4.016 4.718 5.584 2.742 3.196 3.718 4.330 5.064

35 4.162 5.029 6.143 7.636 9.745 3.675 4.384 5.266 6.400 7.920 3.310 3.912 4.640 5.546 6.709 3.036 3.564 4.188 4.942 5.879 2.831 3.309 3.861 4.513 5.302

36 4.372 5.309 6.527 8.179 10.548 3.841 4.601 5.556 6.796 8.478 3.444 4.086 4.867 5.847 7.120 3.147 3.706 4.370 5.180 6.195 2.924 3.427 4.012 4.707 5.554

37 4.597 5.612 6.944 8.776 11.445 4.017 4.833 5.868 7.225 9.091 3.586 4.269 5.109 6.171 7.566 3.263 3.855 4.564 5.434 6.535 3.021 3.551 4.171 4.913 5.824

38 4.837 5.938 7.399 9.435 12.451 4.204 5.082 6.204 7.693 9.767 3.735 4.465 5.367 6.521 8.051 3.385 4.013 4.769 5.706 6.901 3.123 3.681 4.339 5.131 6.111

39 5.094 6.290 7.896 10.164 13.586 4.403 5.348 6.567 8.204 10.515 3.893 4.672 5.644 6.898 8.580 3.514 4.179 4.988 5.996 7.296 3.229 3.818 4.516 5.363 6.419

40 5.370 6.671 8.439 10.973 14.870 4.615 5.633 6.960 8.763 11.345 4.061 4.893 5.941 7.306 9.159 3.649 4.355 5.220 6.308 7.724 3.341 3.962 4.703 5.609 6.749