Modelling rock slope behaviour and evolution with reference to Northern Spain and Southern Jordan

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Durham E-Theses

Modelling rock slope behaviour and evolution with

reference to Northern Spain and Southern Jordan

Nelis, Simon Brett

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Academic Support Oce, Durham University, University Oce, Old Elvet, Durham DH1 3HP e-mail: [email protected] Tel: +44 0191 334 6107

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MODELLING ROCK SLOPE BEHAVIOUR AND

EVOLUTION WITH REFERENCE TO NORTHERN SPAIN

AND SOUTHERN JORDAN

VOLUME 2

SIMON BRETT NELIS

A copyright of this thesis rests

with the author. No quotation

from it should be published

without his prior written consent

and information derived from it

should be acknowledged.

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Contents of Volume 2

List of Figures and Plates

The figures in this thesis include output from the UDEC computer simulation software and from the laboratory testing of rock. The output consists of two-dimensional block plots and filled contour block plots. The labelled notation (*1 0"1) indicates that the axes need to be multiplied by 10. On all UDEC plots, the horizontal and vertical axes are in meters. The plot legend includes an indication of the type of output plot, model cycle count, model time and also the contour intervals. In plots with displacement vectors, the scale presented is in meters. The notation 1 E 1 on the scale means that the scale is 1 *1 0 m long. The values of displacement relate to actual displacements in the rock mass in meters. Where plots of unbalanced forces are presented, the x-axis is model time (s) and they axis is force (kg m s·2).

Chapter 2

2.1

2.2

Chapter 4

Geomorphological interactions between processes, landforms and materials (Allison, 1996).

Basic failure mechanisms of rock masses under gravitational stress.

313

314

4.1 Hypothetical slope scales and examples of natural slopes at these 315 scales. 4.2 4.3 4.4 4.5 4.6

Stress boundary conditions imposed on each model.

Stress-strain response of unjointed 1 m rock masses to simulate the behaviour of intact material.

Stress-strain response of a 1 m sandstone rock mass with varying block sizes.

Stress-strain response of a 1 m limestone rock mass with varying block sizes.

Stress-strain response of a 1 m granite rock mass with varying block sizes. 316 317 318 319 320

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4.7 4.8 4.9 4.10a 4.10b 4.10c 4.10d 4.10e 4.10f 4.11a 4.11b 4.11c 4.11d 4.11e 4.11f 4.12a

Comparative axial strain curves for 1 m rock masses composed of different block sizes.

Joint normal closure magnitude for 1 m rock masses in limestone, sandstone and granite.

Deformation moduli for 1 m rock masses in limestone, sandstone and granite.

Strain zone development in a 1 m limestone rock mass with 0.05 m block size

Strain zone development in a 1 m limestone rock mass with 0.2 m block size.

Strain zone development in a 1 m sandstone rock mass with 0.05 m block size

Strain zone development in a 1 m sandstone rock mass with 0.1 m block size

Strain zone development in a 1 m sandstone rock mass with 0.2 m block size.

Strain zone development in a 1 m granite rock mass with 0.05 m block size. 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336

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4.12b 4.12c 4.12d 4.12e 4.12f 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22a 4.22b

Strain zone development in a 1 m granite rock mass with 0.1 m block size.

Joint shear magnitude for 1 m rock masses in limestone, sandstone and granite

Displacement vector plots for a 1m limestone rock mass with 0.05 and 0.1 m block edge length.

Stress-strain response of a 1 0 m sandstone rock mass with varying block sizes.

Stress-strain response of a 1 0 m granite rock mass with varying block sizes.

Deformation moduli during loading for 10 m limestone, sandstone and granite rock masses.

Joint normal closure during loading for 10 m limestone, sandstone and granite rock masses.

Strain zone development in a 1 m limestone rock mass with 1 m block size. 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352

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4.22c 4.22d 4.22e 4.22f 4.23a 4.23b 4.23c 4.23d 4.23e 4.23f 4.24a 4.24b 4.24c 4.24d 4.24e 4.24f

Strain zone development in a 1 m limestone rock mass with 2 m block size.

Strain zone development in a

1

m limestone rock mass with

3

m block size.

Strain zone development in a 1 0 m sandstone rock mass with

0.5

m block size.

1 0

m sandstone rock mass with

1

m block size.

1 0

m sandstone rock mass with

2

m block size.

Strain zone development in a 1 0 m sandstone rock mass with 3 m block size.

Strain zone development in a 1 0 m sandstone rock mass with 4 m block size

10

m granite rock mass with

0.5

m block size.

10

1

m block size.

1 0

2

m block size.

10

3

m block size.

Strain zone development in a 10 m granite rock mass with 4 m block size.

10

5

m block size. 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368

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4.25 4.26 4.27 4.28 4.29 4.30 4.31 4.32 4.33 4.34a 4.34b 4.34c 4.34d 4.34e 4.34f 4.35a

Block rotation magnitude for 10 m limestone, sandstone and granite rock masses.

Joint shear magnitude during loading for 10 m limestone, sandstone and granite rock masses.

Stress-strain response of a 100 m limestone rock mass with varying block sizes.

Stress-strain response of a 100 m granite rock mass with varying block sizes.

Deformation moduli during loading for 100 m limestone, sandstone and granite rock masses.

Joint normal closure during loading for 100 m limestone, sandstone and granite rock masses.

Joint shear magnitude during loading for 100 m limestone, sandstone and granite rock masses.

Block rotation magnitude for 100 m limestone, sandstone and granite rock masses.

Strain zone development in a 100 m limestone rock mass with 20m block size.

Strain zone development in a 1 00 m limestone rock mass with 30 m block size.

Strain zone development in a 1 00 m sandstone rock mass with 5 m block size. v 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384

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4.35b 4.35c 4.35d 4.35e 4.35f 4.36a 4.36b 4.36c 4.36d 4.36e 4.36f 4.37 4.38 4.39 4.40 4.41

Strain zone development in a 100 m sandstone rock mass with 20 m block size.

Strain zone development in a 100 m sandstone rock mass with 30m block size.

Stress-strain response of a 1 000 m limestone rock mass with varying block sizes.

Stress-strain in response of a 1 000 m sandstone rock mass with varying block sizes.

Deformation moduli for 1000 m limestone, sandstone and granite rock masses.

Joint normal closure for 1000 m limestone, sandstone and granite rock masses. 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400

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4.42 4.43 4.44a 4.44b 4.44c 4.44d 4.44e 4.44f 4.45a 4.45b 4.45c 4.45d 4.45e 4.45f 4.46a 4.46b

Joint shear displacement for 1000 m limestone, sandstone and granite rock masses.

Block rotation magnitudes for 1000 m limestone, sandstone and granite rock masses.

Strain zone development in a 1000 m limestone rock mass with 100m block size.

Strain zone development in a 1 000 m sandstone rock mass with 300m block size.

Strain zone development in a 1000 m granite rock mass with 100 m block size. 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416

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4.46c 4.46d 4.46e 4.46f 4.47 4.48 4.49 4.50 4.51 4.52 Chapter 5 5.1 5.2 5.3 5.4 5.5

Strain zone development in a 1 000 m granite rock mass with 300 m block size.

The stress-strain response of a rock mass compared to that commonly seen for intact rock.

Summary stress-strain response of the two failure mechanisms which develop due to block size effects in the simulated rock masses.

Comparison of joint shear magnitude for all scales and all lithologies (a). Block rotation magnitude for all scales and lithologies (b).

Link between theoretical modelling and slope form.

Comparison of joint normal closure and deformation modulus for all block sizes and lithologies at a range of outcrop scales.

Comparison of deformation moduli for all scales and all lithologies (a) and comparison of joint normal closure magnitude for all scales and lithologies (b).

Topographic setting of the Picas de Europa, northern Spain. Adapted from Smart (1984).

The main geological successions found in the Picas de Europa. Geological setting of the Andara region of the Eastern Massif of the Picas de Europa.

General geological setting of the Vega de Liordes.

Landscape component model depicting the most important landscape elements and linkages in the Picas de Europa mountains. 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431

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5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16a 5.16b 5.17 5.18a 5.18b 5.19a 5.19b 5.20a 5.20b 5.21a

Contoured polar projection of the discontinuities at Torre Olavarria, Picas de Europa, northern Spain.

Contoured polar projection for the discontinuities at Pico de Ia Padierna, Picas de Europa, northern Spain.

Contoured polar projection of the discontinuities at Tiro Pedabejo, Picas de Europa, northern Spain.

Contoured polar projections for the discontinuities at Canchorral de Hormas, Picas de Europa, northern Spain.

Contoured polar projection of the discontinuities at Algobras, Allende, Picas de Europa, northern Spain.

Contoured polar projection of the discontinuities at Los Montes, Picas de Europa, northern Spain.

Histograms and quantile plots of joint spacing with a fitted exponential distribution.

Histograms and quantile plots of joint spacing with compared with an ideal Weibull distribution.

Aggregated joint spacing data from all sites in the Picas de Europa. Cumulative probability distribution functions of joint spacing.

First two L-moments for joint spacing in the Picas de Europa. Skewness and kurtosis L-moments for joint spacing in the Picas de Europa.

Bedding spacing data compared with a lognormal distribution. Mohr's circles for Pico de Ia Padierna.

Sigma 1 I sigma 3 stress space with fitted Mohr-Coulomb failure envelope for Pico de Ia Padierna.

Mohr's circles for Tiro Pedabejo.

Sigma 1 I sigma 3 stress space with fitted Mohr-Coulomb failure envelope for Tiro Pedabejo.

Mohr's circles for Canchorral de Hormas.

Sigma 1 I sigma 3 stress space with fitted Mohr-Coulomb failure envelope for Canchorral de Hormas.

Mohr's circles for the Deva Gorge limestones.

432 433 434 435 436 437 438 439 440 441 442 442 443 444 444 445 445 446 446 447

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5.21b

5.22

5.23

5.24

5.25

Sigma 1 I sigma 3 stress space with fitted Mohr-Coulomb failure envelope for the Deva Gorge limestones.

Axial, lateral and volumetric stress-strain curves for Pica de Ia Padierna.

Axial, lateral and volumetric stress-strain curves for Tiro Pedabejo limestones.

Axial, lateral and volumetric stress-strain curves for Canchorral de Hormas limestones.

Axial, lateral and volumetric stress-strain curves for Deva Gorge limestones. 447 448 449 450 451

5.26 Comparative axial strain curves for Pica de Ia Padierna and Tiro 452 Pedabejo at 0, 10 and 15 Mpa confining pressures.

5.27 Comparative axial strain curves Canchorral de Hormas and Deva 453 Gorge limestones at 0 (UC), 10 and 15 MPa confining pressures.

5.28 Axial strain plotted against Confining pressure, P'o (MPa). 454

Chapter 6

6.1 Location of AI-Quwayra and Wadi Rum. 455

6.2 The broad geological setting of the Wadi Rum-AI-Quwayra area 456 6.3 Generalised geological section of the Wadi Rum-AI Quwayra 457

region of southern Jordan.

6.4 Extent of the sandstone inselbergs within the AI Quwayra Wadi 458 Rum study area.

6.5 Landscape component model showing the important geomorphic 459 features in the AI Quwayra Wadi Rum study area.

6.6

6.7

6.8

6.9

Contoured polar projection of the discontinuities at AL 1, Wadi Rum, Jordan.

Contoured polar projection of the discontinuities at AL2, Wadi Rum, Jordan.

460

461

462

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6.10 Contoured polar projection of the discontinuities at AL5, Wadi 464 Rum, Jordan.

6.13 Contoured polar projection of the discontinuities at ALB, Wadi 467 Rum, Jordan.

6.15 Contoured polar projection of the discontinuities at AL 10, Wadi 469 Rum, Jordan.

6.23 Dotplots of lumped joint spacing data for all sites examined in the 477 AI-Quwayra-Wadi Rum region of southern Jordan.

6.24 Quantiles of joint spacing compared with an ideal exponential 478 distribution.

6.25 Log normal distributions of lumped discontinuity data for all sites in 479 the AI-Quwayra and Wadi Rum areas of Jordan.

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6.26 6.27 6.28 6.29a 6.29b 6.30a 6.30b 6.31a 6.31b 6.32a 6.32b 6.33 6.34 6.35 6.36 Chapter

7

Quantiles of joint spacing compared with fitted Weibull distributions.

AL7 compared with randomly generated Weibull distributions given the same population mean.

Quantiles of joint spacing compared with a gamma distribution. First two L-moments for joint spacing.

Skewness and kurtosis L-moments for joint spacing. Mohr's circles for Red lshrin sandstone.

Sigma 1 I sigma 3 stress space with fitted Mohr-Coulomb failure envelope for Red lshrin sandstone.

Mohr's circles for Disi Sandstone.

Sigma 1 I sigma 3 stress space with fitted Mohr-Coulomb failure envelope for Disi sandstone.

Mohr's circles for Salib Arkosic sandstone.

Sigma 1 I sigma 3 stress space with fitted Mohr-Coulomb failure envelope for Salib Arkosic sandstone.

Axial, lateral and volumetric stress-strain curves for Red lshrin sandstones for specimens tested at 0 (UC), 10 and 15 MPa confining pressures.

Axial, lateral and volumetric stress-strain curves for Disi sandstones for specimens tested at 0 (UC), 10 and 15 MPa confining pressures.

Axial, lateral and volumetric stress-strain curves for Salib Arkosic sandstones for specimens tested at 0 (UC), 10 and 15 MPa confining pressures.

Axial strain plotted against Confining pressure, P'o (MPa) for the three sandstone types.

480 481 482 483 483 484 484 485 485 486 486 487 488 489 490

7.1 Figure 7.1 Block plot of the north section of the cirque wall of Torre 491 de Salinas, Picas de Europa at equilibrium.

7.2 Figure 7.1 Block plot of the north section of the cirque wall of Torre 492 de Salinas, Picas de Europa at equilibrium.

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7.3a 7.3b 7.3c 7.3d 7.4a 7.4b 7.4c 7.4d 7.4e 7.5 7.6a 7.6b 7.6c 7.6d 7.7a 7.7b

Displacement vectors for the north-south profile of the northern cirque wall of Torre de Salinas at 100 000 cycles.

3d Displacement vectors for the north-south profile of the northern cirque wall of Torre de Salinas at 600 000 cycles.

Horizontal displacement contours of the north section of the cirque wall of Torre de Salinas at equilibrium.

Horizontal displacement contours of the north section of the cirque wall of Torre de Salinas at 100 000 cycles.

Total unbalanced forces for the north-south profile of the northern cirque wall of Torre de Salinas at 600 000 cycles.

Block plot of the east-west profile of the central cirque headwall for Torre de Salinas, Picas de Europa, at equilibrium

Displacement vectors for the east-west profile of the central cirque wall of Torre de Salinas at 100 000 cycles.

Horizontal displacement contours for the east-west profile of the cirque headwall for Torre de Salinas at equilibrium.

Horizontal displacement contours for the east-west profile of the cirque headwall for Torre de Salinas 100 000 cycles.

493

494

495

496

497

498

499

500 501 502 503

504

505 506 507

508

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7.7c 7.7d 7.8 7.9a 7.9b 7.9c 7.9d 7.10a 7.10b 7.10c 7.11a 7.11 b 7.12 7.13a

Total unbalanced forces for the east-west profile of the central cirque wall of Torre de Salinas at 500 000 cycles.

Block plot of the east-west profile of the southern cirque headwall for Torre de Salinas, Picas de Europa, at equilibrium.

Displacement vectors of the east-west profile of the southern cirque headwall for Torre de Salinas, Picas de Europa, at 200 000 cycles.

Horizontal displacement contours for the east-west profile of the southern cirque headwall for Torre de Salinas at equilibrium. Horizontal displacement contours for the east-west profile of the southern cirque headwall for Torre de Salinas at 200 000 cycles. Horizontal displacement contours for the east-west profile of the southern cirque headwall for Torre de Salinas at 400 000 cycles. Block plot of the north-south profile of the far western section for the ridge of Pica de La Padierna at equilibrium.

Displacement vectors of the north-south profile of the far western section for the ridge of Pica de La Padierna at 530 000 cycles. Horizontal displacement contours for the north-south profile of the far western section of the ridge of Pica de La Padierna at 530 000 cycles.

Block plot of the north-south profile of the central ridge of Pica de La Padierna at equilibrium. 509 510 511 512 513 514 515 516 517 518 519 520 521 522

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7.13b 7.13c 7.14 7.15a 7.15b 7.15c 7.16 7.17a 7.17b 7.18 7.19 7.20a 7.20b 7.21 7.22a 7.22b

Displacement vectors for the north-south profile of the central ridge of Pica de La Padierna at 150 000 cycles.

Displacement vectors for the north-south profile of the central ridge of Pica de La Padierna at 550 000 cycles.

Block plot of the north-south profile of the central ridge of Pica de La Padierna at 500 000 cycles.

Horizontal displacement contours for the north-south profile of the central ridge of Pica de La Padierna at equilibrium.

Horizontal displacement contours for the north-south profile of the central ridge of Pica de La Padierna at 150 000 cycles.

Horizontal displacement contours for the north-south profile of the central ridge of Pica de La Padierna at 550 000 cycles.

Total unbalanced forces for the north-south profile of Pica de Ia Padierna at equilibrium.

Block plot of the north-south profile of the far eastern section for the ridge of Pica de La Padierna at equilibrium.

Displacement vectors for the north-south profile of the far eastern section for the ridge of Pica de La Padierna at 500 000 cycles. Block plot of the north-south profile of the far eastern section for the ridge of Pica de La Padierna at 500 000 cycles.

Total unbalanced forces for the north-south of the eastern section of Pica de Ia Padierna at 500 000 cycles.

Figure 7.20a Block plot of the north-south profile for Tiro Pedabejo, Picas de Europa, at equilibrium.

Displacement vectors for the north-south profile for Tiro Pedabejo, Picas de Europa, at 500 000 cycles.

Total unbalanced forces for the north-south profile of Tiro Pedabejo at 500 000 cycles.

Horizontal displacement contours for the north-south profile of Tiro Pedabejo at equilibrium.

Horizontal displacement contours for the north-south profile of Tiro Pedabejo at 500 000 cycles. 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538

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7.23a 7.23b 7.23c 7.23d 7.24a 7.24b 7.24c 7.25 7.26a 7.26b 7.26c 7.26d 7.27a 7.27b 7.27c 7.28

Block plot of the east-west profile for Tiro Pedabejo, Picas de Europa, at equilibrium.

Horizontal displacement contours for the east-west profile of Tiro Pedabejo at 201 000 cycles

Horizontal displacement contours for the east-west profile of Tiro Pedabejo at 351 000 cycles.

24c Horizontal displacement contours for the east-west profile of Tiro Pedabejo at 601 000 cycles.

Total unbalanced forces for the north-south profile of Tiro Pedabejo at 601 000 cycles.

Block plot of the north-south profile of Canchorral de Hormas, Picas de Europa at equilibrium.

Displacement vectors of the north-south profile of Canchorral de Hormas at 100 000 cycles.

26c Displacement vectors of the north-south profile of Canchorral de Hormas at 250 000 cycles.

Block plot of the north-south profile of Canchorral de Hormas, Picas de Europa at 500 000 cycles.

Horizontal displacement contours for the north-south profile of Canchorral de Hormas at equilibrium

Horizontal displacement contours for the north-south profile of Canchorral de Hormas at 100 000 cycles.

Horizontal displacement contours for the north-south profile of Canchorral de Hormas at 500 000 cycles.

Total unbalanced forces for the north-south profile of Canchorral de Hormas, Picas de Europa, at 500 000 cycles.

539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554

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7.29a 7.29b 7.29c 7.29d 7.30a 7.30b 7.30c 7.31 7.32a 7.32b 7.33 7.34 7.35a 7.35b 7.35c 7.36a

Block plot of the east-west profile of Canchorral de Hormas, Picas de Europa at equilibrium.

Displacement vectors for the east-west profile of Canchorral de Hormas, Picas de Europa at 1 00 000 cycles.

Displacement vectors for the east-west profile of Canchorral de Hormas, Picas de Europa at 200 000 cycles.

Displacement vectors for the east-west profile of Canchorral de Hormas, Picas de Europa at 500 000 cycles.

Horizontal displacement contours for the east-west profile of Canchorral de Hormas at equilibrium.

Horizontal displacement contours for the east-west profile of Canchorral de Hormas at 100 000 cycles.

Horizontal displacement contours for the east-west profile of Canchorral de Hormas at 200 000 cycles.

Total unbalanced forces for the east-west profile of Canchorral de Hormas at 500 000 cycles.

Block plot of the east-west profile of Los Montes, Picas de Europa at equilibrium.

Displacement vector plot for the east-west profile of Los Montes, Picas de Europa at 300 000 cycles.

Total unbalanced forces for the east-west profile of Los Montes at 300 000 cycles.

Horizontal displacement contours for the east-west profile of Los Montes at 300 000 cycles.

Block plot of the east-west profile of Los Montes, Picas de Europa with a simulated road cut at equilibrium.

Displacement vectors for the east-west profile of Los Montes, Picas de Europa at 1 00 000 cycles.

Displacement vectors for the east-west profile of Los Montes, Picas de Europa at 300 000 cycles.

Horizontal displacement contours for the east-west profile of Los Montes with simulated road cut at 1 00 000 cycles.

555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570

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7.36b 7.37a 7.37b 7.37c 7.38a 7.38b 7.39a 7.39b 7.39c 7.39d 7.40a 7.40b 7.40c 7.41 7.42a 7.42b

Horizontal displacement contours for the east-west profile of Los Montes with simulated road cut at 300 000 cycles

Block plot of the north-south profile of Los Montes, Picas de Europa at equilibrium.

Displacement vectors for the north-south profile of Los Montes, Picas de Europa at 100 000 cycles.

Displacement vectors for the north-south profile of Los Montes, Picas de Europa at 300 000 cycles.

Horizontal displacement contours for the north-south profile of Los Montes at 100 000 cycles.

Horizontal displacement contours for the north-south profile of Los Montes at 300 000 cycles.

Block plot of the east-west profile of Allende, Picas de Europa at equilibrium.

Displacement vectors for the east-west profile of Allende at 100 000 cycles.

Displacement vectors for the east-west profile of Allende at 250 000 cycles.

Displacement vectors for the east-west profile of Allende at 500 000 cycles

Horizontal displacement contours for the east-west profile of Allende at 100 000 cycles.

Total unbalanced forces for the east-west profile of Allende, Picas de Europa, at 500 000 cycles.

Block plot of the north-south profile of Allende, Picas de Europa at equilibrium.

Displacement vectors for the north-south profile of Allende, Picas de Europa at 100 000 cycles. 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586

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7.42c

7.42d

7.43a

7.43b

7.46

7.47

7.48

7.49

7.50

7.51

7.52

7.53

7.54

7.55

Displacement vectors for the north-south profile of Allende, Picas de Europa at 300 000 cycles.

Displacement vectors for the north-south profile of Allende, Picas de Europa at 401 040 cycles.

Horizontal displacement contours for the north-south profile of Allende at 1 00 000 cycles.

Horizontal displacement contours for the north-south profile of Allende at 300 000 cycles.

Compariosn of the half-way time for all failures in the Picas de Europa models.

Exponential asymptotic model (dashed line) applied to x-displacement data for the failures at Torre de Salinas.

Exponential asymptotic model (dashed line) applied to x-displacement data for the failure on the north-south profile of Pica de Ia Padierna.

Exponential asymptotic model (dashed line) applied to x-displacement data for the failures at Los Montes.

Exponential asymptotic model (dashed line) applied to x-displacement data for the failures at Allende.

Summary of the two main patterns of failure in f...-t space associated with brittle, catastrophic failure and self-stabilising flexural toppling failure.

Results of erosion rate modelling on the samples selected for 36_CL dating.

Calculated 36CI dates for rock slope failures in the Picas de Europa.

587

588

589

590

591

592

593

594

595

596

597

598

599

600

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7.56

7.57

Chapter 8

Exhaustion model for paraglacial rock slope failure in the Picas de Europa, compared with data from Cruden and Hu (1993) in the Canadian Rockies.

Proposed model of paraglacial rock slope evolution for the Picas de Europa based on UDEC modelling, assessment of paraglacial exhaustion models and cosmogenic dating.

601

602

8.1 Block plot of the north-south profile of AL9 at equilibrium. 603 8.2 Total unbalanced forces for the north-south profile of AL9 at 604

equilibrium.

8.3a Displacement vectors for the north-south profile of AL9 at 15 000 605 cycles.

8.3b Displacement vectors for the north-south profile of AL9 at 17 000 606 cycles.

8.3c Displacement vectors for the north-south profile of AL9 at 40 000 607 cycles. 8.4 8.5a 8.5b 8.5c 8.5d 8.6a 8.6b 8.7 8.8a

Total unbalanced forces for the north-south profile of AL9 at 40 000 cycles.

Horizontal displacement contours for the north-south profile of AL9 at equilibrium.

Horizontal displacement contours for the north-south profile of AL9 at 15 000 cycles.

Block plot of the east-west profile of AL9 at equilibrium.

Displacement vectors for the east-west profile of AL9 at 50 000 cycles.

Total unbalanced forces for the east-west profile of AL9 at 50 000 cycles.

Block plot of the north-south profile of AL 12 at equilibrium.

608 609 610 611 612 613 614 615 616

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8.8b 8.8c 8.8d 8.9 8.10a 8.10b 8.10c 8.11a 8.11 b 8.12 8.13a 8.13b 8.13c 8.13d 8.14a 8.14b 8.14c

Displacement vectors for the north-south profile of AL 12 at 12 000 cycles

Displacement vectors for the north-south profile of AL 12 at 15 000 cycles.

Total unbalanced forces for the north-south profile of AL 12 at 25 000 cycles

Horizontal displacement contours for the north-south profile of AL 12 at 12 000 cycles.

Block plot of the east-west profile of AL 12 at equilibrium.

Displacement vectors for the east-west profile of AL 12 at 100 000 cycles.

Horizontal displacement contours for the east-west profile of AL 12 at 100 000 cycles.

Displacement vectors for the north-south profile of AL 1 0 at 15 000 cycles.

Horizontal displacement contours for the north-south profile of AL 10 at 21 000 cycles. 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633

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8.15 8.16a 8.16b 8.17 8.18a 8.18b 8.19 8.20 8.21a 8.21b 8.21c 8.22a 8.22b 8.23 8.24a 8.24b 8.24c 8.24d

Total unbalanced forces for the north-south profile of AL 10 at 21 000 cycles.

Displacement vectors for the east-west profile of AL 1 0 at 1 00 000 cycles.

Displacement vectors for the north-south profile of AL 11 at 1 00 000 cycles.

Total unbalanced forces for the north-south profile of AL 11 at 100 000 cycles.

Total unbalanced forces for the east-west profile of AL 11 at 40 000 cycles.

Block plot of the north-south profile of AL3 at equilibrium

Displacement vectors for the north-south profile of AL3 at 13 000 cycles.

Displacement vectors for the north-south profile of AL3 at 20 000 cycles. 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651

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8.25a Horizontal displacement contours for the north - south profile of 652 AL3 at 13 000 cycles.

8.25b Horizontal displacement contours for the north - south profile of 653 AL3 at 20 000 cycles.

8.26a Block plot of the east-west profile of AL3 at equilibrium. 654 8.26b Displacement vectors for the east-west profile of AL3 at 20 000 655

cycles.

8.26c Displacement vectors for the east-west profile of AL3 at 150 000 656 cycles.

8.27a Horizontal displacement contours for the east-west profile of AL3 at 657 20 000 cycles.

8.27b Horizontal displacement contours for the east-west profile of AL3 at 658 150 000 cycles.

8.28 Total unbalanced forces for the east-west profile of AL3 at 150 000 659 cycles.

8.29a Block plot of the north-south profile of AL2 at equilibrium. 660 8.29b Displacement vectors for the north-south profile of AL2 at 20 000 661

cycles.

8.29c Displacement vectors for the north-south profile of AL2 at 68 502 662 cycles.

8.30a Horizontal displacement contours for the north-south profile of AL2 663 at 20 000 cycles.

8.30b Horizontal displacement contours for the north-south profile of AL2 664 at 68 502 cycles.

8.31 Total unbalanced forces for the north-south profile of AL2 at 68 502 665 cycles.

8.32a Block plot of the east-west profile of AL2 at equilibrium. 666 8.32b Displacement vectors for the east-west profile of AL2 at 1 00 000 667

cycles.

8.33 Horizontal displacement contours for the east-west profile of AL2 at 668 100 000 cycles.

(27)

8.34b 8.34c 8.34d 8.35a 8.35b 8.36a 8.36b 8.36c 8.36d 8.37a 8.37b 8.37c 8.38a 8.38b 8.38c 8.38d 8.39

Block plot of the east-west profile of AL7 at equilibrium.

Displacement vectors for the east-west profile of AL7 at 20 000 cycles.

Horizontal displacement contours for the east-west profile of AL7 at 13 000 cycles.

Total unbalanced forces for the east-west profile of AL 17 at 404 360 cycles. 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686

(28)

8.40a 8.40b 8.40c 8.41 8.42 8.43 8.44 8.45 8.46 8.47 8.48 8.49

Out of balance forces with loess smoothing function applied to pick out the main trends in unbalanced forces.

Comparison of failure mechanisms compared with the out of balance forces for models simulating the sandstone inselbergs of the Wadi Rum region.

Exponential asymptotic model (dashed line) applied to x-displacement data for the toppling failure on the north face of AL9. Exponential asymptotic model (dashed line) applied to x-displacement data for the toppling failure on the north face of AL12.

Exponential asymptotic model (dashed line) applied to x-displacement data for the toppling failure on the south face of AL 10.

Exponential asymptotic model (dashed line) applied to x-displacement data for the toppling failure on the south face of AL 11.

Exponential asymptotic model (dashed line) applied to x-displacement data for the failures on the east (a) and south (b) faces.

Exponential asymptotic model (dashed line) applied to x-displacement data for the failures on the east (a) and south (b) faces. 687 688 689 690 691 692 693 694 695 696 697 698

(29)

8.50 8.51 8.52 8.53 8.54 8.55

Exponential asymptotic model (dashed line) applied to x-displacement data for the failures on the east (a) and south (b) faces.

Results of erosion rate modelling on the samples selected for 10Be dating. As the erosion rate increases, the applied erosion rate correction increases the ages of the boulder.

10

Be ages estimates for selected rock slope failures in the Wadi Rum region.

Smoothed total unbalanced forces for AL2. 10Be ages and a1 error have been overlaid on the graph, based on one year representing

1.5 model cycles.

Smoothed total unbalanced forces for AL7 10Be ages and a1 error have been overlaid on the graph, based on one model cycle representing 1.5 years.

Smoothed total unbalanced forces for AL 1010Be ages and a1 error have been overlaid on the graph, based on one model cycle representing 2.3 years.

699

700 701 702 703 704

(30)

List of Plates

Chapter 5

5.1 Incision of the Cares Gorge has divided the Central and Western 706 Picas in to two separate massifs.

5.2 A relict rock glacier in the Vega de Liordes formed through the 707 downslope transport of failed slope debris.

5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 Chapter 6 6.1 6.2 6.2

Debris flow system in the bottom left of the picture with the Government guesthouse of Fuente De just above.

The large debris flow system originating at Canchorral de Hormas. The cirque headwalls of Torre de Salinas, viewed from the Vega de Liordes.

The east-west trending face of Pica de Ia Padierna. The north face of Tiro Pedabejo.

The large block field forming the deposition area for failed material from the headwalls of Canchorral de Hormas.

The rock slope investigated at Los Montes in the Deva Gorge. The rock slope investigated at the crags of Algebras, Allende in the Deva Gorge.

Triaxial testing of rock cores in a Hoek Cell (inset) inserted in to a stiff loading frame (A). Confining pressure is applied with a hand pump. Uniaxial testing of cores for defining the unconfined compressive strength (B).

Tafoni weathering and case hardening on the sandstone inselbergs of Wadi Rum.

Example of rockfall event on the sandstone inselbergs in Wadi Rum.

A natural rock bridge formed through weathering of the sandstones. 708 709 710 711 712 713 714 715 716 717 718 719

(31)

6.4 Disi and Red lshrin Sandstone inselbergs. The Red lshrin Sandstone is much stronger than the Disi, supporting vertical slopes and much higher inselbergs

720

6.5 Rounded domes are characteristic of inselbergs developed in the 721 Disi sandstones.

6.6 Preferential weathering of 'master' joints leads to the development 722 of columnar inselbergs.

6.7 Example of tensile failure of sandstone caused by basal slope 723 sapping.

Chapter 7

7.1 Torre de Salinas. The UDEC model meshes were designed to 724 capture the main features of each of the cirque headwall features.

7.2 Pica de Ia Padierna. (A) is a view of the whole ridge, (B) the 725 central section, (C) the western portion and (D) the eastern end.

7.3 (A) The north face of Tiro Pedabejo (B) the south-west face of 726 Tiro Pedabejo from the Canal de Pedabejo. The full free face is

7.4 7.5 7.6 7.7 7.8 7.9

just off the picture.

Canchorral de Hormas. (A) View of the boulder field (B) View of the site from the end of the Deva Gorge. The red circle marks its location.

(A) General view of Allende from the south showing the west, south and east faces (B) View of the south face of Allende.

The north face of Torre de Salinas from the Collado de Jermoso, Picas de Europa.

View of Pena Remona.

Sampling for cosmogenic isotope analysis at Pica de Ia Padierna.

727 728 729 730 731 732

(32)

7.10

7.11

7.12

Chapter 8

Sampling of boulders for cosmogenic isotope analysis at Tiro Pedabejo. (A) General geomorphic setting of boulders of boulder 2, with an exposure age of 7459 ± 214 (B) close up view of boulder 1, with a calculated exposure age of 7824 ± 403 yrs BP.

Boulders selected for cosmogenic sampling at Allende. (A) Geomorphic setting of boulder 1, with a calculated exposure age of 6540 ± 636 and (B) boulder 2, with a 36CI exposure age of 6575 ± 242 yrs BP.

Evidence that the south face of Pico de Ia Padierna still represents an overdip slope and that future failures are likely.

733

734

735

8.1 Evidence that the south face of Pico de Ia Padierna still represents 736 an overdip slope and that future failures are likely.

8.2 8.3 8.4 8.5 8.6 8.7 8.8

Evidence that the south face of Pico de Ia Padierna still represents an overdip slope and that future failures are likely.

North-south profile of AL 10 from the west face (A) and the north-south profile showing a large failure on the north-south face from the eastern end of the inselberg (B).

North-south profile of AL 1 0 from the west face (A) and the north-south profile showing a large failure on the north-south face from the eastern end of the inselberg (B).

East-west profile of AL3, taken from the south face (A). Close up view of the failure on the west face of the inselberg (B). The inselberg is composed entirely of Salib Arkosic sandstone, pushed up due to normal faulting.

West face of AL2 (B) showing a small cap of Disi sandstone on the upper part of the inselberg. The north face of AL2 is shown in (B). South face of AL7 showing a large failure and preferential weathering of joints, producing the 'tower' morphology.

The west face of AL 17, in the Barra Canyon, showing evidence of large-scale slope collapse.

737 738 739 740 741 742 743

(33)

8.9

8.10

View from the top of the rockfall debris on the west face of AL 17, with the Barra Canyon located in the centre of the picture.

Boulders being sampled for cosmogenic dating from failed rock slopes in Wadi Rum, Jordan.

744

(34)

list of Appendices

All appendices are to be found on the disk which is attached to the back cover of

Volume 2 of this thesis. The appendices are chapter ordered and the filename

corresponds to the appendix number. For the UDEC input files, where the letter 'v' is

used, values are varied for the different model runs.

Chapter 3

3.1

Chapter 4 4.1 4.2

Basic program for calculating the angle of intersection between a joint plane and a UDEC mesh.

A FISH function to calculate strain accumulation at gridpoints. UDEC input file for a 1 m sandstone rock mass with variable joint spacing. A 'v' indicates that the block size parameter was varied. 4.3 UDEC input file for a 1 m limestone rock mass with variable joint

spacing. A 'v' indicates that the block size parameter was varied. 4.4 UDEC input file for a 1 m granite rock mass with variable joint

spacing. A 'v' indicates that the block size parameter was varied. 4.5 UDEC input file for a 10 m sandstone rock mass with variable joint

spacing. A 'v' indicates that the block size parameter was varied. 4.6 UDEC input file for a 10 m limestone rock mass with variable joint

spacing. A 'v' indicates that the block size parameter was varied. 4.7 UDEC input file for a 10 m granite rock mass with variable joint

spacing. A 'v' indicates that the block size parameter was varied. 4.8 UDEC input file for a 100 m sandstone rock mass with variable

joint spacing. A 'v' indicates that the block size parameter was varied.

4.9 UDEC input file for a 100 m limestone rock mass with variable joint spacing. A 'v' indicates that the block size parameter was varied. 4.10 UDEC input file for a 100 m granite rock mass with variable joint

spacing. A 'v' indicates that the block size parameter was varied. 4.11 UDEC input file for a 1000 m sandstone rock mass with variable

joint spacing. A 'v' indicates that the block size parameter was varied.

(35)

4.12

UDEC input file for a

1000

m limestone rock mass with variable joint spacing. A 'v' indicates that the block size parameter was varied.

4.13

UDEC input file for a

1000

m granite rock mass with variable joint spacing. A 'v' indicates that the block size parameter was varied.

Chapter 7

7.1

UDEC input command file used to simulate the northern cirque headwall at Torre de Salinas.

7.2

UDEC input command file used to simulate the central cirque headwall at Torre de Salinas.

7.3 UDEC input command file used to simulate the southern cirque headwall at Torre de Salinas.

7.4 UDEC input command file used to simulate the north-south profile of the western section of Pica de Ia Padierna.

7.5 UDEC input command file used to simulate the north-south profile of the central section of Pica de Ia Padierna.

7.6

UDEC input command file used to simulate the north-south profile of the eastern section of Pica de Ia Padierna.

7.7

UDEC input command file used to simulate the north-south profile of Tiro Pedabejo.

7.8

UDEC input command file used to simulate the east-west profile of Tiro Pedabejo.

7.9

UDEC input command file used to simulate the north-south profile of Canchorral de Hormas.

7.10

UDEC input command file used to simulate the east-west profile of Canchorral de Hormas.

7.11

UDEC input command file used to simulate the east-west profile of Los Montes with no simulated road-cut.

7.12

UDEC input command file used to simulate the east-west profile of Los Montes with simulated road-cut.

7.13 UDEC input command file used to simulate the north-south profile of Los Montes.

7.14

UDEC input command file used to simulate the north-south profile of Allende.

(36)

Chapter 8 8.1 8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

8.10 8.11 8.12

8.13

8.14

8.15

UDEC input command file used to simulate the north-south profile of AL9.

UDEC input command file used to simulate the east-west profile of AL9.

UDEC input command file used to simulate the north-south profile of AL 12.

UDEC input command file used to simulate the east-west profile of AL 12.

UDEC input command file used to simulate the north-south profile of AL 10.

UDEC input command file used to simulate the north-south profile of AL

11.

(37)

(38)

I

ISand dune migratior:l

~

Rock

Mass Geotechnits

~ (th1s research)

oo

Rock mass strength studies

/Analysis of rock

geomechanicC!I behaviour Karst mor,phometr.y

Materials

Figure 2.1: Process-Form-Material interacti6"ri triangle (after Allison,

1996).

The triangle

shows where researc.h methodologies lay in relation process, materials anp form. An adequate understanding of geomorphological evolution of landforms can only, be gained if'

reference is· made to ,material properties, the shape of the landform and' the· processes responsible for the evolution of the landform. The current research is embedded in the centre of ~his relationship utilising geotechnical information, morphometric data anp process rates in understanding landform evolutior:~.

(39)

C) c:: :2

en

rn Q) :;, CI)C::: c::::o:: 0 c::

- o

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-t>

Q)Q) CD rn ""0 .... Q)~

3:

·=

C) c:: c.. c.. ~

(40)

Hypothetical scales

(used for theoretical modelling)

..

c

CD

~

!

:::::s

-

·-J!

...

0

Q) .~ t/) C)

c::

·-

t/)

ca

e

(.) Q)

I

C

1000

m

Scales in the natural environment

Mt. Thor, Baffin Island. Note

the steeply dipping bedding out of the free-face.

Porru Bolu, Picos de Europa is formed from a large truncated pillar.

Great Close Scar, Yorkshire Dales, UK. Small cliff in limestone with block detachment.

Troll Wall, Norway. The face was formed by a post-glacial rock avalanche. Sandstone Wadi Rum, Vertical joints failure. inselberg, Jordan. control

lngleborough summit cliffs in Yoredale mudstone, Yorkshire Dales.

Figure 4.1: Hypothetical slope scales and examples of natural slopes at these scales.

The scale boundaries used are a hierarchical framework, with a continuum of slope scales between the boundaries defined here.

(41)

"'

b

Figure 4.2: Stress boundary conditions imposed on each model. Arrows represent

stress boundaries, while the cirCles I squares indicate a velocity boundary used to fix

(42)

rn-ll.. ~

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~ 'lii (.) ·;:: 0 (ij ·s; Cll Cl

m-e... ~

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% lateral strain % axial strain

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rn-

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0.10 \

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~

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I Granite 0 -0.00001 -0.000005 0 0.000005 0.00001 0.000015 0.00002 0.000025 0.00003

% lateral strain % axial strain

~igu~rs

4.3:

Stress-strain response of unjointed 1 m rock masses to simulate the behaviour of intact material.

(43)

0.16 0.16 0.16 0.14 \ 0.14·

'

0.14

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\

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~ 0.12 \ ~ 0.12

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ro 0.12

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% lateral strain % Axial strain % lateral strain % Axial strain % lateral strain % Axial strain

0.16, 0.16 1.0 0.14i

-

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(44)

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.

_0.14

.

0.14

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0.12

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0.1

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% Axial strain % Lateral strain % Axial strain % Lateral strain % Axial strain

0.16 0.16-0.16 0.14. ~ 0.14 _0.14

'

\ _\

ro-

0.12

_'

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% Lateral strain % Axial strain % Lateral strain

(45)

0.16' 0.16 . 0.16 0.141

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...

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~ 0.12

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w

N -0.6 -0.4 -0.2 0 0.2 0.4 0.6 _-0.6 _-0.4 _-0.2 ₀ _0.2 _0.4 _0.6 _-0.0005 _0.0000 _0.0005 _0.0010 0

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0.16 0.16 0.16

0.14 0.14

.

0.14

\

'

\

ro-

0.12 \

ro-

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a.. _\ a.. _\ a.. _\

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(46)

0.16-.---~--- -

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iii

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1m Limestone

1- o.osm 0.1 m - 0 . 2 m - o.3 m - 0.4 m - o.s ml 0.5 1.5 2 % Axial strain

1m Sandstone

O.OSm 0.1 m 0.2 m 0.3 m 0.4 m O.Sm

I

0.5 1.5 2 2.5 3 3.5 % Axial strain - - - · -

-1m Granite

1- o.osm 0.1 m -o.2m -o.3m - 0.4m - o.sm

I

2.5

4

0 0.0005 0.001 0.0015 0.002 0.0025 0.003

% Axial strain

Figure 4.7: Comparative axial strain curves for 1 m rock masses composed of