sandstone landforms shaped by negative feedback …...colorado plateau (usa) 7 alcoves (shelters)...

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NGEO2209

NATURE GEOSCIENCE | www.nature.com/naturegeoscience 1

1

Sandstone landforms shaped by negative feedback between stress and erosion Jiri Bruthans1, Jan Soukup1, Jana Vaculikova1, Michal Filippi2, Jana Schweigstillova3, Alan L. Mayo4, David Masin1, Gunther Kletetschka1,2, Jaroslav Rihosek1 1 Faculty of Science, Charles University in Prague, Albertov 6, 128 43 Prague 2, Czech Republic 2 Institute of Geology, AS CR, v. v. i., Rozvojova 269, 165 00 Prague 6, Czech Republic 3 Institute of Rock Structure and Mechanics, AS CR, v. v. i., V Holesovickach 41, 182 09 Prague 8, Czech Republic 4 Brigham Young University, Department of Geosciences, Provo UT 84602, USA

Corresponding author

Jiri Bruthans

e-mail: [email protected]

Supplementary Information List of Abbreviations Abbreviation Explanation SLS Strelec Locked Sand F Overburden load Ssat Cross-section area of landform TS Tensile strength of surface TSa TS measured on sandstone exposures under ambient humidity TSa(DR) TSa derived from drilling resistance measurements TSd TS measured at unconfined SLS cubes, which were oven-dried TSs TS measured at unconfined SLS cubes, which were fully immersed by water in normal atmospheric

pressure TSsV TS measured at unconfined SLS cubes, which were fully immersed by water in reduced pressure (2 kPa) TSsL TS measured at uniaxially loaded SLS cubes, which were fully immersed by water in normal atmospheric

pressure W/E Weathering/Erosion

Sandstone landforms shaped by negative feedback between stress and erosion

© 2014 Macmillan Publishers Limited. All rights reserved.

http://dx.doi.org/10.1038/ngeo2209

2

Supplementary Information Table of Contents

1. Supplementary introduction ................................................................................................................ 3

a. Evolution of ideas on sandstone landforms origin .................................................................... 3

b. Previous studies on the effect of stress field on landform evolution ......................................... 4

c. Basic characteristics of fabric interlocked materials ................................................................. 6

d. Fabric interlocking, stability and dry masonry as a simplified model of fabric-locked structure7

2. Experimental investigation of the sandstone mechanical behaviour ................................................ 8

a. Material used in the study.......................................................................................................... 9

b. Material characterization ......................................................................................................... 12

c. Compression experiments with SLS at higher stress levels .................................................... 12

d. Compression experiments with SLS under extremely low stress levels ................................. 13

e. Tensile strength and cohesion mechanisms of SLS ................................................................. 15

f. Mechanical behaviour of cemented sandstone......................................................................... 17

3. Continuum mechanics interpretation of the SLS mechanical behaviour ....................................... 19

4. Disintegration mechanisms ............................................................................................................... 20

a. Slaking ..................................................................................................................................... 20

b. Raindrop impact and flowing water ........................................................................................ 21

c. Disintegration of cemented sandstones by salt and frost weathering ...................................... 22

5. Physical and numerical modelling of landform evolution ............................................................... 24

a. Physical modelling .................................................................................................................. 25

b. Numerical modelling ............................................................................................................... 30

6. Supplementary discussion and conclusions ..................................................................................... 32

a. Evolution of landforms in fabric interlocked materials ........................................................... 32

b. Importance of discontinuities and examples from cemented sandstones and other materials 33

c. Concluding remarks and implication ....................................................................................... 37

Supplementary References:................................................................................................................... 38


3

1. Supplementary introduction

a. Evolution of ideas on sandstone landforms origin

On sandstone landscapes the tafoni are the most common small-scale weathering form13

. On

larger scale weathering results in shapes that constitute of arches, alcoves (rock shelters), pedestal

rocks, and towers and cliffs2. Arches and natural bridges occur in many sandstone areas. There are

about 400 arches1 longer than 50 m in the world. Despite their unusual and aesthetic appeal, natural

arches and bridges are among the least studied of sandstone landforms31

. Some of arches, alcoves and

pillars should have been around for long periods of time given the degree of denudation in their

immediate surroundings. Examples are Delicate Arch and Rainbow Bridge at Colorado Plateau

(USA), sandstone structures that are freestanding above the eroded surroundings (Fig. 1a main paper).

Smaller sandstone landforms have substantial strength and persistence against weathering (narrow

arches in rock cities, pillars used by climbers for anchoring, etc.).

Sandstone landforms have been studied for more than 150 years2. Despite the long-term research

there are many contrasting ideas for origin of these landforms (Suppl. Table 1). Ideas on landform

evolution are commonly unsupported by evidence other than observation of forms in nature,

morphometric analysis and the material observations under scanning electron microscopy (SEM) and

examination of chemical and mineralogical composition of sandstone and commonly present salts

(Suppl. Table 1). Presence of salt and/or occurrence of freezing water and/or similar potential

weathering/erosion (W/E) processes at site are commonly considered as sufficient evidence to claim

such process responsible for origin of these landforms. In most of cases authors do consider solely

W/E process (e.g. salt crystallization) being responsible for the shape of the landforms (Suppl. Table 1

and references therein). Rarely clear distinction is made between weathering and shape forming

process: “Even if salt weathering can be proved to be the cause of rock disintegration, how cavernous

form develops through this process is still unclear2 and “Sophisticated geometry of honeycomb

surfaces suggests that besides processes forming the pits some construction plan has to be involved20

.

Already Yatsu32

considered that “the principal role of geomorphology is, of course, in studying

the evolution of landforms”. However, he was quite sceptical concerning achievements in this field. In

the last decade increasing pessimism arises: “Geomorphologists and scientists in cognate disciplines

struggle to explain the genesis of weathering features3 “Answers to questions associated with how

sandstone landscapes evolve or how decaying architecture may be conserved will hopefully emerge2.

Sandstone physical properties are called enigmatic due its unpredictable response to weathering8.

Research explaining the weathering features and processes is considered increasingly reductionistic2.

Supplementary Table 1

Ideas on evolution of selected sandstone landforms. CR – Czech Republic; SEM – Scanning electron microscopy.

Form Processes assumed to be

responsible

Based on Location (country) Reference

alcoves (shelters) plunge-pool erosion or

sapping

field observations,

morphometric

analysis

Colorado Plateau (USA) 68

alcoves (shelters) solution, spring sapping field observations Golden gate Highlands (South

Africa)

31

alcoves (shelters) exfoliation field observations Saxon-Bohemian Switzerland

(Germany, CR)

69

alcoves (shelters) etching, scarp-foot

weathering

field observations Uluru and Kata Tjuta (Central

Australia)

70

alcoves (shelters) sapping (calcite

crystallization, frost

weathering)

field observations,

SEM, morphometric

analysis


alcoves (shelters) salt weathering chemical analysis,

erosion

measurements

Gosford (NSW Australia) 71

alcoves (shelters) rockfall due to undermining

by sapping erosion (salt-

weathering, freeze-thaw,

field observations,

review



4

cement dissolution,

weathering the shale),

backwasting along sheeting

fractures

alcoves (shelters) moisture flux field observations,

SEM

Wollongolong, (NSW Australia) 1

alcoves (shelters) salt weathering field observations,

SEM

Sydney region (Australia) 72

alcoves (shelters) salt weathering, case

hardening

field observations,

SEM

Al- Quawayra (Jordan) 73

alcoves (shelters) break down due to stress

exceeding tensile strength

field observations,

stress modelling

various areas 4,5

alcoves (shelters) failure due to pore water

pressure, swelling clays or

leaching the cement; lateral

stresses

field observations,

SEM

various areas 1

arches arcuate exfoliation field observations Saxon-Bohemian Switzerland

(CR)

74

arches exfoliation field observations Saxon-Bohemian Switzerland

(Germany, CR)

69

arches cement dissolution influenced

by pattern of horizontal and

vertical fracturing

field observations Colorado Plateau (USA) 75

arches preexisting fractures field observations Colorado Plateau (USA) 10

arches undercutting field observations Colorado Plateau (USA) 63

arches undercutting, failure along

principal stress surfaces

stress modelling,

field observations


arches partial destruction of

exfoliation plates, sapping,

stream erosion, granular

disintegration


arches weathering along parallel

joints

field observations Golden gate Highlands (South

Africa)

31

pedestal rocks fast weathering of weak rock

under resistant cap rock

field observations Lookout Mt. (USA) 77

pedestal rocks soil moisture weathering field observations various areas 78

pedestal rocks etching, differential rate of

weathering and erosion

field observations Golden gate Highlands (South

Africa)

31

pedestal rocks to exploitation of localized

intense fracturing by

weathering and erosion


pillars in caves finger flow lithification SEM, schmidt

hammer, field

observations

Tepuis (Venezuela) 44, 45, 66,

67

pillars in caves stream erosion field observations Tepuis (Venezuela) 52

b. Previous studies on the effect of stress field on landform evolution

It was suggested1

that “sandstone landforms can be resolved into regularly recognizable

architectural structures such as rock walls, domes, arches, buttresses and beams”. They also pointed

that the interaction of the surface forms with variable stresses operating must be also assessed. But in

their opinion it is precisely on this issue that most studies of landforms are weakest. Similarly the

greatest majority of geomorphological textbooks do not even mention the geometry of stress patterns.

In addition, widespread neglect of the implications for sandstone geomorphology of findings from

rock mechanics and engineering geology is disappointing1. However, authors were concerned mainly

with question how landforms sustain the loads imposed in them.

Generally the rock stress is considered to increase the weathering rate4, 5, 33, 34, 35, 36

. Stress-induced

features were defined4 as those created solely by the mechanical action of some stress field. Such

features are characterized by fracture pattern4. It was claimed

4, 5 that natural walls, bastions and towers

are not purely erosional forms but are primarily conditioned by prevailing stresses caused by gravity

of its own mass. They also claimed that stress field may significantly contribute to decay of rock


5

masses (weathering) and may affect the erosion rate. It was argued that rock walls break down at base

of cliffs due to stress concentration4, 5

.

Arcuate plan form of sandstone amphitheatres (embayments) was compared to an arch lying on

its side so that lateral stresses tend to hold individual blocks on the curved face in place1. This

knowledge corresponds to experiments and field practice showing such landform will be more stable

than a straight rock wall17, 37

. It was demonstrated that radius-to-height ratios of amphitheatres are far

from random1.

Origin of arches is explained by development of fissures in ceiling of undercut blocks followed

by failures along arcuate shape based on modelling18

and observation in coal mines38

. This results in

arched roofs. Similarly based on observation of arches at Colorado Plateau (USA) and analytical

models showing the principal stress in beam and plate with semicircular hole it is expected that arches

are evolving upward into undercut block in response to stresses from gravity loading19

. Arch was

developed by failure of rock along arcuate surfaces. Some natural arches can be compared to dry

masonry arches in terms of shapes and presence of blocks stabilized by compression1. They

demonstrated that spectacular natural arches indeed have the optimal shape in terms of stability.

Many especially smaller arches do not show such fracture surfaces (Suppl. Fig. 1) and the

processes responsible for their development remain unclear. The above mentioned observations and

experiments do not explain why many arches are freestanding from otherwise denudated surfaces.

What makes the arch to be less erodible than its surroundings? What are the factors which model the

arch from undercut slab of sandstone?

It was observed that some honeycombs have axis parallel with curve of the arch vault and

assumed that stress is one of the factors controlling the morphology of honeycomb surfaces20

, but

except morphology description author did not study the relationship between stress and forms20

. It was

assumed, based on shape of sandstone tower that erosion slowed down in most loaded parts of tower39

.

Some sandstone landforms are markedly similar to load-bearing elements used in medieval times39

.

Most papers concerning sandstone landscapes, however, do not consider the stress at all (Suppl.

Table 1). Viles3 in her discussion of scale issues in weathering process did not mention rock stress as a

factor in her abundant list of factors controlling weathering, with exception of “pressure release”. With

one exception20

none of the vast number of papers considered the possible stabilizing effect of stress

on weathering and erosion. Stress is thus so far viewed as either destructive factor or factor which may

stabilize the loose blocks from falling if geometry of fractures is favourable.


6

Supplementary Figure 1

Examples of small-scale arches, pillars and alcoves from different localities. a) SLS in Strelec quarry; b), c) Jizera formation

sandstone, Bohemian Switzerland; d) Teplice formation sandstone, Adrspach (a-d) Czech Republic); e) Navajo sandstone,

Zion National Park, USA; f) Sandstone in Kayenta formation, Glen Canyon, USA.

c. Basic characteristics of fabric interlocked materials

Locked sand is material which cohesion is result of interpenetrative fabric of quartz grains23

. In

this study, we adopted one particular material from Strelec Quarry, Czech Republic referred to as SLS

(see Sec. 2a). This material is a typical example of locked sand, so we adopt it to demonstrate the

locked sand properties:

The relative density of SLS is 120 %, which means that SLS porosity is less that can be attained

by the American Society for Testing Materials or comparable tests for achieving minimum porosity 23

.

This indicates diagenetic consolidation.

Based on saturated uniaxial compressive strength the SLS can be classified as weak

sandstone24

. However, the SLS properties fully correspond to locked sand, which is group of materials

with peculiar properties23, 28, 26

(Suppl. Table 2). Similar to other locked sands, SLS has high strength,

high friction angle and high residual friction angle, it has brittle behaviour. It is uncemented and so

friable that it can be disaggregated by brushing the surface with paintbrush and disintegrates fully

when immersed in water. Its porosity is less than the minimum attainable in laboratory; it has a highly

quartzose mineralogy, and considerable geological age (Suppl. Table 2). Locked sand samples became

less stable with diminishing size40

. Explosives are needed to separate material in quarry (scale tens of

meters), but cube of the same material with edge length of 3 cm is so fragile that it cannot be lifted by

fingers. While some researchers state that for locked sand steeply curved failure envelopes23

are

typical, others demonstrated that in many cases the failure envelopes are in fact linear41

.

Many types of sandstone previously referred as soft-sandstone or friable sandstone are probably

locked sands23

. Behaviour of these materials is similar to SLS. For instance St. Peter sandstone

(labelled as locked sand23

) disintegrates readily when placed unsupported in water, but it is strong in

its contact state under some confining stress23

. Similar example is sandstone in eastern and southern

parts of Bungle Bungle massif – Kimberly (Australia), formed by essentially cohesionless grains1, 42

,

very poorly cemented Precipice sandstone in Queensland, Australia43

and unlithified layers of arenites


7

inside “quartzite” sequence in Tepuis (Venezuela), which can be classified as itacolumite, the flexible

sandstone44, 45

(Suppl. Fig. 2). Peak strength of locked sand is strongly influenced by intensity of

interlocking41

. Diagenetic processes reduce the porosity of sand leaving essentially uncemented sand

with an interlocked fabric46

. In case of shallow burial the considerable time span is needed to produce

the locked sand. Therefore all locked sands are older than quaternary23

.

Locked sands show solution-recrystallization texture with crystal overgrows - pyramidal

truncations23

. Pyramidal truncations and crystal faces usually form at surface areas of grains not in

contact with other grains. However, in some cases these structures can form right at this contact and

push grains appart23

. Itacolumite is considered end member of diagenetic process in quartzose

sandstones with nearly stylolitic grain contact but without creation of the true intergranular

cementation23

. Origin of locked sands is attributed to a pressure solution from detrital quartz

grains41

. An interlocked fabric in sands cannot be produced artificially40

.


Polished sections of three different fabric interlocked materials. a) Strelec Locked Sand with high porosity and interlocking

only at small percentage of subangular grain boundaries; b) Navaho sandstone (JN sample, – Suppl. Table 3) composed of

perfectly rounded sand grains cemented by carbonate. Sandstone is weathered into interlocked array of angular flakes; c)

quartzite from table mountains in Venezuela (VE sample, Chimanta, Churi Tepui – Suppl. Table 3). The pore space was lost

by compaction and resulting dissolution of grains and re-precipitation as cement. The missing cement between grains (white

narrow areas lining the grains) makes the material, where the grains are perfectly interlocking but in the same time the

cementation cohesion is missing.


Comparison of Strelec Locked Sand (SLS) properties with other locked sands. Locked sands properties were obtained from28,

40, 41, 46, 80, 81, 82, 83. UCS –uniaxial compressive strength.

Parameter SLS Other locked sands

porosity (%) 22 23-42

relative density (%) > 121 125-140

matrix content (≤25 um) (%) 1.4 0-10

tangential index (%) - 18-26

UCS dry (MPa) 2.7-3.2 0.1-3.0

UCS saturated (MPa) 3.0 -

peak friction angle (o) 74 36-70

peak cohesion (kPa) 6 5-360

d. Fabric interlocking, stability and dry masonry as a simplified model of fabric-locked structure

Cohesion is defined as shear strength at zero normal stress. Out of four cohesion types listed in

the main text the capillary cohesion, electrochemical and cementation cohesions are well known47

.

Fabric interlocking on the other hand deserves more attention. Fabric interlocking is rising from the

material structure, which enables effective interlocking of otherwise loose grains (or any elements in


8

general). The ability of interlocking to produce tensile and compressive strength has been

recognized48

. Fully developed interlocking quartz grains will produce sandstone46

. Based on field

observations, it was hypothesized that compressive stress may hold the weak sandstone together:

“Entire sandstone was thoroughly etched and left as a mass of essentially cohesionless grains held

together mainly by the compressive stress generated by their own weight42

.

If stress is mentioned in geomorphological literature it is mostly discussed in connection of rock

strength. Strength is defined as applied shear stress at which given rock fails49

. However, different

kind of failure may also occur which is not associated with brittle and dilatant deformation, but rather

with disintegration of fabric into individual grains. These two processes are principally different

phenomena, although both are related to stress in some way. As the fabric stability is the critical issue

to explain the experiments mentioned further, we will shortly introduce this field.

It was clearly demonstrated that critical height of slopes of unweathered rock is determined by the

mechanical defects of the rock such as joints and faults (rock mass strength) and not by strength of the

rock itself (intrinsic rock strength)37, 41

. Joints subdivide the rock into individual blocks, which almost

fit each other, and the cohesive bond across the joints is equal to zero50

. If the continuous joints form a

three-dimensional network they transform the rock into cohesion-less aggregate of blocks comparable

to dry masonry50

. Importantly, even cohesion-less aggregate of blocks, where blocks fit each-other can

form vertical slope if orientation of join pattern with reference to the slope is optimal50

.

When speaking about the dry masonry itself, the actual values of compressive stresses are usually

very low; they are seldom more than hundredth part of the crushing strength of the stone51

. Failure of

masonry thus happens due to lack of stability and not due to lack of strength. To stabilize the vertical

pillars carrying the arches of medieval churches the weight was added at the top of the wall to keep

thrust line in the pillar. “Contrary to what one might suppose, weight at the top is likely to make a wall

more and not less, stable51

.

A very important property of dry masonry is that force necessary to release the element from

masonry is proportional to the vertical stress within the masonry. Static friction between bricks in dry

brick wall increases with load and thus it is easier to release (pull out) brick from the top part of the

wall than from the bottom. As a force of pulling out the element rises with stress, there is a potential

for indirect relationship between the stress and intensity of disintegration process if material has

dominantly the fabric interlocking (i.e. interlocked material which behaviour is very similar to that of

dry masonry). A negative feedback is theoretically possible: As the landform (e.g. pedestal rock) is

undermined from its sides the stress in remaining part of the landform rises, which decreases the

effectiveness of disintegration process.

2. Experimental investigation of the sandstone mechanical behaviour

To interpret the development of landforms within a rational manner, we first investigate the

mechanical behaviour of sandstone on the element level (such that the stress state within the specimen

can be considered as homogeneous). As we will discuss further, we consider that most sandstones and

other granular materials forming landforms have some degree of fabric interlocking. We thus study

primarily the behaviour of uncemented saturated locked sand, where this effect is not hindered by the

other cohesion types. However, to demonstrate generality of our conclusions, we later discuss also the

behaviour of partially saturated and cemented materials.


9


Landforms in SLS documented in the Strelec quarry. All forms are developed at SLS exposures excavated several weeks to a

maximum of 6 years ago and are thus with no doubt less than 6 years old. Slaking is probably the main process entraining the

grains of SLS into flowing or standing water (Sec. 4a). a) Fast flowing stream rich with sand in suspension with arch

resisting to flow (bottom left part of photo); b)The arch from previous figure one day later; c) Arch excavated by flood-

flow; d) Arch resisting to water from waterfall for at least several weeks; e) Cavities expanding from vertical

fractures; f) Small-scale alcoves created by seeping groundwater; g) Similar alcoves like in the previous figure but created by

immersion in artificial lake; h) Cave pillar in subsurface stream; h), i), j), k) Inclined pillars/alcoves/arches with visible lines

of stress. Black scale bar in all figures represents 10 cm.

a. Material used in the study

Two types of sediments were sampled for the study: i) Locked sand with no cementation

cohesion and dominating fabric interlocking, i.e. locked sand (referred to as SLS) and ii) Sandstones

(and other sediments) with dominating cementation cohesion, i.e cemented sandstone.

The SLS material was sampled in the Strelec Quarry, Czech Republic, where so called Hruba

Skala sandstone, Cretaceous marine quartz sandstone with a kaolinite matrix is being mined. The

collected SLS corresponds to erodible sandstone29

. The SLS in quarry is weak enough to be eroded by

running water and rain and was mined for decades by spraying a jet of pressurized water. The same

material, however, has to be mined by explosives when dry, and it has formed stable (up to 40 m high)

vertical mining faces prior to recent safety regulations in the quarry. The SLS forms in the quarry and

natural exposures a wide variety of natural landforms (columns, arches, rock shelters) with size

ranging from centimetres to tens of meters (Suppl. Figs 3, 4).

Samples of SLS were taken at quarry faces up to several months old in the area situated 50 m

below the original ground surface and 20 m below the original water table. Samples of SLS were cut

from various sandstone blocks by hand saw according to method40

. Only such material that has solely

fabric interlocking (when immersed) was collected. To select the proper material, several couples of

cubes from each sandstone block were cut. The first cube from couple was unconfined; the top of the

other cube was covered by plate with the same area as the cube side and loaded by 6 kg (Suppl. Fig.

5a). Both cubes were immersed in water for at least 5 minutes. In the case when only unconfined

cubes from the pairs disintegrated, the material was specified as SLS and used for experiments.


10

Samples of SLS were transported firmly wrapped to plastic foil, fixed and stored in firm box to

prevent mechanical damage.

Cemented sandstone samples were collected from Colorado Plateau (USA), Bohemian

Cretaceous Basin (Czech Republic) and Tepui Churi (Venezuela) (Suppl. Table 3). Blocks of

cemented sandstones were collected from natural outcrops to obtain material, which was exposed to

W/E processes. The cemented sandstone samples were cut by diamond saw cooled by water onto

cubes with edge lengths of 4±0.1 cm.


Natural landforms in Hruba Skala sandstone (Teplice formation) in Bohemian Paradise, Czech Republic. a) the Duhova

Arch; b) the Branzezska Arch; c) Alcove in Apolena; d) Arches in Apolena of different scales with pillars; e) Sintrova Cave

with vaulted roof; f) Freestanding pillar in Apolena; g) Pillars with varying widths developing along the vertical fractures;

Photos a) and b) by J. Adamovic.


11


Principal types of uniaxial loading cubes. a) SLS cube loaded by lead weight (6 kg); b) SLS cube compressed by torque

screwdriver; c) Cemented sandstone cube compressed by torque screwdriver


List and characterization of materials used in the study. Abbreviation: c-coarse grained, f-fine grained, ch-case hardening.

Type: fi - fabric interlocked material, ct - cemented material. Formation/member: ss.-sandstone. Lithology/cement: kaol. -

kaolinite, Fe ox. - ferric oxides. Environment: M - marine, F - fluvial, A - aeolian. Age: Prot. - Proterozoic; Jur. - Jurasic;

Cret. - Cretaceous; Olig. - Oligocene.

Abbre

viation

Type* Location Country Longitude;

latitude

Formation

/member

Lithology

/cement

Environment Age

SLS fi Strelec Czech Rep. N50.4936,

E15.2460

Hruba Skala

ss., Teplice

FM

quartz ss. /kaol. M53 Cret. 53

H

(Hc

Hf

Hch)

ct Valdstejn Czech Rep. N50.5617,

E15.1664

Hruba Skala

ss., Teplice

FM

quartz ss. /kaol. M53 Cret. 53

K ct Kyjov Czech Rep. N50.9115,

E14.4506

ss., Jizera FM quartz ss. /kaol. M53 Cret. 53

P ct Plzen Czech Rep. N49.7578,

E13.3401

ss.,Kladno FM arcose ss. /Fe ox. F Carb. 53

T ct Teplice-

Adrspach

Czech Rep. N50.5877,

E16.1386

ss.,Teplice FM quartz ss. /kaol. M53 Cret. 53

V ct Vsemily Czech Rep. N50.8402,

E14.3543

ss., Jizera FM quartz ss. /kaol. M53 Cret. 53

UP ct Glen Canyon USA N37.4605,

W110.5317

Navaho ss. quartz ss. A54 Jur. 54

UT ct Crystal Peak USA N38.7943,

W113.5956

Tunnel Spring

Tuff

rhyolite/ clay

calcite

- Olig. 84

H3H4 ct Helper USA N39.7277,

W110.8678

Star Point ss. quartz ss./

dolomite,

calcite, clay

F, M54 Cret. 54

Gin1 ct Ute-Mt. USA N37.3130,

W108.6623

Dakota ss. quartz ss./kaol. M54 Cret. 54

Gin2 ct Ute-Mt. USA N37.3335,

W108.8528

ss., Morrison

FM

quartz ss./calcite F54 Cret. 54

VE ct Tepui Churi Venezuela N5.2725,

W62.0130

Roraima

Supergroup

quartzite and ss. F, A, M44 Prot. 44

JN ct Professor

valley

USA N38.8005,

W109.3118

Navaho ss. quartz ss. A54 Jur. 54

JES ct Profesor

valley

USA N38.7919,

W109.2724

Entrada

(slickrock) ss.

quartz ss. A54 Jur. 54

JW ct Profesor

valley

USA N38.8047,

W109.2869

Wingate ss. quartz ss./clay A54 Jur. 54


12

b. Material characterization

The SLS revealed to be a key material for our experiments; therefore, its properties are presented

here in detail. The SLS contains only 1.6 wt.% of fraction <25 μm based on wet sieving analysis.

According to XRF and semi-quantitative XRD analysis the fraction <25 μm is composed of well-

ordered kaolinite (75%), quartz (24%) and illite (1%) with SiO2 and Al2O3 content 99.1%29

. The

remaining 0.9% is composed mainly of K2O, TiO2 and Fe2O3. Neither silica nor calcite and iron oxide

cement were identified in any sample of SLS based on SEM/EDS (Simon-Neuser HC2-LM) and

cathodoluminescence inspection (Quanta 450). Opal was not detected by FTIR (Nicolet 6700) in silt

and clay fraction separates from SLS. Kaolinite was identified as the only mineral binding agent in

erodible sandstone by SEM/EDS and FTIR.

Cemented sandstone samples selected for study can be split into three general categories (Suppl.

Table 3): i) Quartz sandstones with a negligible portion of non-quartz grains and low content of clay

(H, K, T, V); ii) arkoses (P) and iii) quartz sandstone cemented by carbonate (UP, JN, Gin2). As all

these materials pose cementation cohesion, they represent ideal material to test the effect of stress on

salt and frost weathering of the cemented sandstones. Sediments from Bohemian Cretaceous Basin

were never buried deeper than few hundred meters below ground surface, while sediments at Colorado

plateau and Venezuela were buried to depth of several kilometers52, 53, 54

.

c. Compression experiments with SLS at higher stress levels

First, the „conventional“ mechanical behaviour was studied using materials where the stress state

is high enough to ensure the locked fabric does not disintegrate into individual grains (see further).

Uniaxial compressive strength was measured on SLS specimens equilibrated with 35 % and 90 %

relative air humidity and on fully saturated SLS specimens. The uniaxial compressive strengths were

carried out using 74 mm length by 38 mm diameter cylinders and 50 mm cubes. The strain rates were

0.45 and 0.004 mm per minute. In order to determine peak and critical strength characteristics and to

inspect Mohr's failure envelope of SLS, standard consolidated drained triaxial tests were conducted.

Cylindrical samples (height 74 mm, diameter 38 mm) were prepared with regard to high brittleness

and friability of material to avoid damage of internal structure. All samples were gathered from single

block of SLS. Triaxial tests were performed on VJT TriScan100 testing machine for confining

pressures of 50, 100, 150, 200, 250 and 300 kPa.

Mohr-Coulomb failure envelop of SLS is nearly linear based on triaxial measurements. Angle

of internal friction is 72° for peak state. Uniaxial compressive strength of SLS is 2.5 and 3.0 MPa for

samples equilibrated with 35% and 90% relative humidity, respectively. Uniaxial compressive

strength is 3.0 MPa for saturated sample. Failure during tests usually occurred between 1.1-1.5%

strain. Results of triaxial and unconfined compression tests, together with the failure envelope, are

shown in Suppl. Fig. 6. SLS showed highly dilatant behaviour expressed by large difference between

peak and critical state strength in axial strain-stress diagram and by negative volumetric strains in axial

strain-volumetric strain diagram. Similar behaviour of locked sands at higher stress levels has already

been observed previously by other researchers26, 28, 55

.


13


Results of triaxial and unconfined compression tests on saturated samples of SLS, together with failure envelope based on the

triaxial tests. p’ is the effective mean stress defined for triaxial conditions as p’=(σ’a+2σ’r)/3, q is deviatoric stress defined as

q=σ’a-σ’r, σ’a is effective axial stress, σ’r is effective radial stress, friction angle can be calculated from the slope Mp of the

failure envelope within the p’ vs. q diagram from sinφ=3Mp/(6+Mp).

d. Compression experiments with SLS under extremely low stress levels

The second set of uniaxial compression experiments was performed under extremely low stress

levels (less than 10 kPa). It was observed that within this stress range, which is often overlooked by

the geomechanical community, but which is crucial for the interpretation of the W/E processes, the

SLS shows unusual behaviour.

The SLS specimens, stabilised by the natural state of partial saturation and by clay bridges

between the particles, were formatted by gently cutting by hand saw. Cubes with edge length of

10±0.5 cm were prepared for the uniaxial compression experiments at low stress levels and also for

measurements of tensile strength (Sec. 2e).

When SLS cubes are completely immersed in water without axial load they quickly disintegrate.

This disintegration is attributed to the decrease of the electrochemical cohesion accompanied by

surface slaking (entrapped air in the pores compressed by surface tension forces of entering water

exerts pressure to pore sides sufficient to break loose the material, see Sec. 4a for detailed discussion).

When a cube of SLS is subjected to constant vertical pressure and immersed in water disintegration of

the vertical sides proceeds until a stable hour glass shape forms (Fig. 2a main paper). In Figure 2a,

cross-section area of the form is marked as Ssat and overburden load as F. Initially the vertical stress

(F/Ssat) is relatively small because the overburden load is distributed over a large area. Hour glass

shaped thinning of the cube reduces the cross-sectional area (Figure 2a main paper) with a net effect of

increasing the stress. When the stress becomes high enough to stabilize the locked fabric (critical

stress) the form becomes stable. The critical stress is thus a minimum stress needed to stabilise the

locked fabric.

The relationships between critical stress and Ssat to landform stabilization were evaluated in

experiments on 16 immersed 10 cm SLS cubes in water (Fig. 2b main paper). An initial vertical force

of 10 N was applied to each cube. After immersion initial form stabilization was achieved. The applied


14

force was then decreased in steps and the Ssat and applied force were measured after form

stabilization was achieved at each step. Plotted in the Fig. 2b (main paper) are the Ssat and the

calculated critical stress associated with each stabilized form. Critical stress remains relatively

constant (0.5 – 2.6 kPa) until the Ssat decreased below about 20 % of the original size. As the pillar

becomes thinner (Ssat 20 % of original Ssat) the critical stress increases rapidly (up to 8 kPa, Fig.

2b main paper). When Ssat is < 20 % of the original Ssat the elliptical cross-section of pillars

progressively alter to a rib structure and lines that parallels the principal stress directions (Fig. 2a main

paper). Similar features are visible at surface of some natural landforms (Suppl. Fig. 8).


Relationship between load and TS in shallow subsurface zone of Strelec locked sand (SLS) cubes. Thick black lines represent

average values of TS. TSd measured at unconfined SLS cubes, which were oven-dried; TSs measured at unconfined SLS

cubes, which were fully immersed by water in normal atmospheric pressure; TSsV measured at unconfined SLS cubes, which

were fully immersed by water in reduced pressure (2 kPa); TSsL measured at uniaxially loaded SLS cubes, which were fully

immersed by water in normal atmospheric pressure


15


Stress lines visible at various landforms in Strelec Quarry (a to c), d) Cave on Quirl table mountain, Saxon Switzerland; e)

Tri Musketyru Cave, Adrspach-Teplice area.

e. Tensile strength and cohesion mechanisms of SLS

Tensile strengths of surfaces (TS) of SLS cubes were measured under several different conditions

to estimate the contribution of individual types of cohesion on the total cohesion: 1) At unconfined

oven-dried cubes (105 oC) (TSd); 2) At unconfined cubes fully immersed by water under atmospheric

pressure (TSs); 3) At cubes fully immersed by water under atmospheric pressure with certain uniaxial

load (TSsL); and 4) At unconfined cubes fully immersed by water under reduced air pressure (2 kPa)

(TSsV). TS were measured according to29

: T profile aluminium (surface area 2 by 2 cm; weight 3 g)

was glued by epoxy to SLS surfaces. After hardening a tensile force was gradually increased

perpendicular to sandstone surface by increasing the volume of water in a plastic bag attached to the

aluminum plate by a string and small pulley until the SLS beneath the epoxy failed. TS was obtained

as ratio of maximum (pull off) force and contact area (kPa).

The following reasoning was employed in selecting the different measurement states. Capillary

cohesion caused by interstitial liquid bridges22

is negligible in both saturated and oven dry samples47

(Suppl. Table 4). Electrochemical cohesion in clay bridges between sandstone grains will be highest in

oven-dry samples and it will drop strongly in sample saturated by water (or other solvents with high

dielectric constant56

) (Suppl. Table 4). With increasing dielectric constant of pore fluid the repulsive

force between adjacent clay particles will increase, thus decreasing the cohesion56

. Cementation

cohesion is independent of moisture content and applied load21

(Suppl. Table 4). TSsV is thus

reflecting dominantly cementing cohesion, since under full saturation the tensile strength generated by

capillary, electrochemical and fabric interlocking will be negligible. Difference between TSsL and

TSsV is reflecting contribution of fabric interlocking as capillary and electrochemical cohesions will be

negligible. TSd reflects sum of cementation and electrochemical cohesions (fabric interlocking and

capillary cohesions will be negligible). By combining the TSd, TSsV and TSsL one can roughly

quantify contribution of all individual cohesions and fabric interlocking except the capillary cohesion.

SLS has TSsV 0.2 – 0.7 kPa and its cementation cohesion is thus negligible. This confirms the

observation on SEM/EDS that the SLS is not bound by silica, carbonate or iron-oxide cement29

. SLS

has TSs 0 – 0.5 kPa which reflects partial disintegration of SLS material by slaking (sec. 4a).


16

TSsL up to 20 kPa (average 4 kPa) reflects tensile strength due to fabric interlocking in shallow

subsurface of SLS cubes. The relationship between stress and TSs at cube surfaces (Suppl. Fig. 7) is

rather scattered. TSs values considerably vary at the same level of stress (Suppl. Fig. 7) probably

because of the hidden discontinuities and damaged zones in surface zone of cubes. TSd 3 – 19 kPa

reflects electrochemical cohesion of dry SLS. Electrochemical cohesion is caused by kaolinite clay

bridges between quartz grains based on SEM. To examine into what degree the electrochemical

cohesion participates on stabilization of saturated SLS material the 5 cm oven-dried (105 oC)

unconfined cubes were immersed in various solvents (Suppl. Table 5). Cubes disintegrated fast and

completely in solvents with high dielectric constant. On the other hand, the cubes did not disintegrated

in solvents with low dielectric constants. Cubes disintegrate in various bromoform-ethanol mixtures

but they were stable in pure bromoform. As density of the used bromoform (2.83 g/cm3) exceeds the

density of quartz (2.65 g/cm3) the intact SLS cube was floating in bromoform.

When SLS cubes are immersed in solvents with high dielectric constant (e.g. water) the

electrochemical cohesion becomes very low due to rise of repulsive forces57

. Strongly reduced

electrochemical cohesion cannot withstand pressures developed by destructive process and SLS cube

disintegrates unless sufficient strength due to fabric interlocking is generated by stress. On the other

hand if cubes are immersed in solvents with low dielectric constant (e.g. toluene) the electrochemical

cohesion decreases only slightly compared to the case of high dielectric constant, it exceeds the

destructive force and cubes remain stable. Grain aggregates left after fast disintegration of cubes (Sec.

4a) are bound by kaolinite based on SEM. This indicates that kaolinite does not disintegrate

spontaneously when saturated and is thus not dispersed in water. Rather, it is just weakened compared

to the dry state, but it is still slightly cohesive. Above-mentioned observations indicate that even SLS

saturated by water has some electrochemical cohesion. TSa measured under ambient humidity at

exposures of SLS in the quarry vary between 2 – 13 kPa29

. TSa includes various combinations of the

capillary and electrochemical cohesion and fabric interlocking.


Dependence of cohesion type and fabric interlocking on degree of saturation and loading. * reduction depends on wetting the

clay particles in pores space and dielectric constant of solvent.

TS notation TSd TSsv TSsL

Sample treatment (moisture content) oven dry immersed in reduced

pressure (2 kPa)

immersed

Uniaxial load unconfined unconfined uniaxially loaded

Capillary cohesion negligible negligible negligible

Electrochemical cohesion maximum strongly reduced* strongly reduced*

Cementation cohesion maximum maximum maximum

Fabric interlocking negligible negligible maximum


Disintegration of Strelec locked sand (SLS) cubes in various solvents as a function of dielectric constant of solution.

Solvent Solvent group Dielectric

constant of

solvent

Disintegration of SLS

cube after total

immersion

Turbidity (ejected into

solvent during

disintegration)

water polar protic 80 fully turbid for hours

acetonitrile polar aprotic 37.5 fully turbid for minutes

ethylene glycol polar protic 35.6 fully turbid for hours

anhydrous ethanol

(99.9 %)

polar protic 24.6 fully turbid for hours

acetone polar aprotic 21 partly turbid for minutes

ethyl acetate polar aprotic 6 partly turbid for minutes

bromoform non polar 4.4 no solvent transparent

toluene non polar 2.38 no solvent transparent

petrol non polar ~2 no solvent transparent

air - 1 no -


17

f. Mechanical behaviour of cemented sandstone

Additional set of measurements has been performed on cemented sandstone samples.

We aimed to demonstrate that the cementing agent is prone to disintegration and the final stability

of the landform is facilitated by fabric interlocking, as in the uncemented locked sand materials. TSa

of the cemented sandstone was directly measured29

. Metal plates (5 cm in diameter) were glued by

epoxy to cemented sandstone surfaces). After hardening a tensile force was gradually increased

perpendicular to sandstone surface until the sandstone beneath the epoxy failed. The maximum (pull

off) force was measured by tensiometer, contact area was measured and TS was obtained as ratio of

both parameters (kPa).

Beside direct measurements of TSa the drilling resistance technique was used to estimate TSa

values29

. Drilling resistance estimates the strength of material based on depth of drill hole drilled under

constant pressure and constant number of rotations29

. Drilling resistance, which is easily and quickly

measurable parameter, enabled us to estimate the TSa from up to hundreds of places at single type of

sandstone, which strongly increases the chance that extreme values of TSa from field will be included

in the set of measurements. Typically hundreds of drilling resistance measurements were done on

particular types of cemented sandstones. TSa and drilling resistance measurements were aimed to

cover both extremes: the unweathered and the most weathered material at natural exposures.

A total of 182 pairs of drilling resistance and TSa measurements were obtained from exposures

and blocks of Hruba Skala sandstone and cemented sandstones in Bohemian Cretaceous Basin and

Colorado Plateau (Suppl. Fig. 9). TSa has relatively tight relationship (r2=0.75) with drilling

resistance. Based on this relationship the drilling resistance readings were recalculated to TSa (labelled

in text as TSaDR to distinguish them from direct TSa measurements) (Suppl. Table 6).

The decrease of TS from fresh to weathered parts of cemented sandstone was quantified. Direct

measurements of TSa and TSs of some sandstone types are listed in Suppl. Table 7. TSa of Navajo

sandstone was up to 1400 kPa in case of least weathered surfaces but just 6 kPa of intensively

weathered portions of exposures. TSs of Navajo sandstone was only 0.2 – 4 kPa in case of intensively

weathered portions of exposures. Even more remarkable contrast has been observed in the case of

Helper site where fresh sandstone has TSa up to 5100 kPa but strongly weathered parts just 3 kPa.

Data in Suppl. Tables 6 and 7 clearly demonstrates that intensively weathered exposures of cemented

sandstone have TSa 2 to 3 orders of magnitude lower than the original fresh sandstone. TSa of such

portions of exposures are comparable to TSa of SLS and thus existence of fabric interlocking zones at

surface zone of cemented sandstones is likely. These results are in accord with58, 59

who emphasized

highly weathered nature of many of the sandstone surfaces at Colorado Plateau.


18


Relationship between drilling resistance measurements (DR) and TSa at sandstone exposures measured in Bohemian

Cretaceous Basin and Colorado Plateau (182 couples of measurements). Measurements were done on Navajo, Wingate, Star

Point, Kayenta and Hruba Skala sandstones and Crystal Peak Tuff.


TSaDR (kPa) derived from DR measurements on cemented sandstone exposures on Colorado Plateau and Tunel Spring Tuff.

n – number of measurements.

Formation/

locality

Hruba Skala

ss./Bohemian

Paradise

Teplice ss./

Adrspach-

Teplice

Kladno Fm./

Plzen

Navaho ss.

/Glen

Canyon

Star Point

ss./ Helper

Tunel Spring

Tuff/ Crystal

Peak

n 221 249 11 436 275 269

mean 30 59 17 55 208 88

maximum 550 980 550 2600 6800 2600

minimum 5 6 6 6 17 23

max/min 110 163 91 433 400 113


TSa and TSs measured at exposures and blocks of cemented sandstones on Colorado Plateau and Tunel Spring Tuff. *only

weathered parts

Formation/locality max TSa

(kPa)

min TSa

(kPa)

max/min

TSa

number of TSa

measurements

min TSs

(kPa)

number of TSs

measurements*

maxTSa/mi

nTSs

Wingate ss./Glen

canyon

1860 25 74 23 7 3 266

Navaho ss./Glen

canyon

1380 6 230 56 0.2 16 6900

Star Point ss./ Helper 5100 3 1700 25 3 6 1700

Tunel Spring

Tuff/Crystal Peak

1470 7 210 30 - -


19

3. Continuum mechanics interpretation of the SLS mechanical behaviour

In the Sect. 2c-e, results of different laboratory experiments on SLS have been summarized and

conceptual micromechanical models for its behaviour have been put forward. In order to perform

numerical simulations of landform evolution using numerical methods, however, the mechanical

behaviour must be described using a continuum mechanics-based constitutive model. Such a model is

a topic of this section.

Let us first summarise the SLS (and other locked sand) mechanical behaviour as measured in the

experiments described in this paper and in the previous studies by different authors. As described in

Sec. 2e, different sources of cohesion exist within the SLS, most importantly the fabric interlocking,

cohesion due to capillary water effects in partially saturated medium and electrochemical cohesion due

to clay bridges between the individual sand particles. All the cohesion sources but the fabric

interlocking are significantly reduced by immersion in water, either thanks to the disappearance of the

capillary menisci or by electro-chemical interaction of water with the cohesion-creating material. The

disaggregating may be facilitated by pore fluid pressures generated by slaking (described in detail in

Sec. 4a), or by mechanical impact of rain drops (Sec. 4b). It turns out that the saturated case is the

most critical for evaluation of the landform stability, as the saturated material has the lowest cohesion

and is thus the most prone to disintegration. At the same time, any landform material, even in

relatively arid areas, is expected to periodically undergo a state of water saturation, at least in the

surface layers which are the most critical for erosion. For this reason, we focus here on the modelling

of saturated material. Here follows a summary of the saturated SLS mechanical response.

1. The SLS material has a considerable uniaxial compression strength reaching about 3 MPa

(Sec. 2c). Similar results have been reported in26

, who studied uncemented locked sand from

Northern Alberta (uniaxial strength of 2 MPa).

2. Peak friction angles measured in axisymmetric compression with different non-zero radial

stresses (so-called triaxial tests in soil mechanics terminology) are exceptionally high,

reaching 72° (Sec. 2c). Similar high peak friction angles were observed on different locked

sand materials by other authors. For example St. Peter sandstone, φp=57-63° 55

and

uncemented locked Reigate silver sand, φp=49 – 62° 28

.

3. Laterally loaded SLS material has low, but non-negligible TS. Measurements reported in Sec.

2e (Suppl. Fig. 9) provided values mostly falling within the range of 1 to 10 kPa. The TS was

practically independent of the lateral stress. Similar response (i.e. high friction angles and low

TS) was reported on San Francisco weakly cemented sand27

.

4. The above three observations are relevant to describe the global stability of the fabric

interlocked material. Substantially different response is, however, observed when the stress

levels fall below a critical threshold needed for the locked fabric stability. In particular, the

studied SLS material has practically negligible (<0.5 kPa) TS in uniaxial extension, Sec. 2e.

5. Possibly the most unusual is the behaviour revealed in the experiments on uniaxially loaded

saturated SLS cube samples (Sec. 2d, Fig. 2b main paper). The samples were stable under

vertical stresses higher then approx. 1 – 8 kPa. Under lower vertical stresses, they quickly

disintegrated into individual grains.

A model for fabric interlocked material considering all the above mentioned properties is

proposed in Fig. 3 in the main paper. Properties Nos. 1 to 3, relevant to the material with locked fabric,

may be described by means of conventional theory of plasticity (though with unusually high friction

angle). In agreement with the plasticity theory, material fails once the Mohr circle touches the failure

envelope. This envelope is denoted as “strength envelope of fabric interlocked material” in Fig. 3 in

the main paper. For SLS, it is characterised by high friction angle of 72° (properties Nos. 1 and 2) and

non-negligible TS of 1 to 10 kPa (property No. 3). The fact that the TSsV does not depend on the

lateral stress (unless it is zero) suggests that the failure envelope is very steep initially, probably

converging towards the theoretical limit of 90°. Similar strength envelope was suggested for San

Francisco weakly cemented sand27

. Authors of27

supported it, in addition to the tests described while


20

discussing properties Nos. 1 – 3, by the so-called FSP stress path tests (axisymmetric experiment with

constant axial stress and reduction of lateral stress27

).

Conceptually completely different behaviour is identified at very low stress levels. The material

does not fail in a brittle and highly dilatant manner, as typical for sheared fabric-interlocked materials,

but instead the fabric degrades completely and the material disintegrates into individual grains. To

describe this observation within the continuum mechanics model, so-called “locus of fabric

instability” is proposed in Fig. 3 in the main paper. The fabric disintegrates once the complete Mohr

circle falls within this locus. The lower and upper stress boundaries of the locus of fabric instability

are represented by properties Nos. 4 and 5 respectively discussed above. Namely, the lower stress

boundary corresponds to the uniaxial extension strength (-0.5 to 0 kPa in the case of SLS) and the

upper stress boundary to the critical minimum stress for fabric stability observed in uniaxial

compression tests (1 to 8 kPa in the case of SLS). Note that unlike the global failure envelope, the

locus of fabric instability is not a pure material property, but it also reflects the actual disintegration

process. More specifically, the increase of disintegration process energy increases the size of the locus

of fabric instability. To the knowledge of the authors, the locus of fabric instability or its equivalent

has not been described as yet in the literature. This is probably the reason, why the stabilising effect of

stress on landform development has been overlooked so far.

4. Disintegration mechanisms

While the stress has in the previous sections been identified as the main stabilizing agent of the

SLS fabric, a mechanical input is needed to disintegrate the material once the stress falls to the critical

level. In this Section, we summarise and investigate the main mechanisms causing fabric

disintegration.

a. Slaking

Slaking is caused by excess air pressure in capillaries that is generated by surface tension forces

of water, which is entering the pores previously occupied by air. The entrapped air in the pores exerts

pressure to pore sides sufficient to break loose the material60

.

To assess possible effect of air in the disintegration process some immersion experiment were

done in reduced air pressure. SLS cubes were placed to glass desiccator and “vacuum” was applied

(air pressure of 2 kPa). Then vacuum pump was stopped and water but not air was allowed to flow into

the glass desiccator. After filling the glass desiccator by water the desiccator was immersed and

opened within a water tank, so that the stability the of cube immersed in vacuum could be inspected

visually. Water was then drained and the cube was left to dry up for at least 24 hours. After that, cube

was immersed again, this time under normal atmospheric conditions.

While the unconfined SLS cubes always disintegrated when immersed in atmospheric pressure,

the unconfined cubes immersed in vacuum did not disintegrate, but instead they kept vertical sides.

These cubes all disintegrated when immersed again in atmospheric pressure, however. Similarly, the

confined cubes immersed in atmospheric pressure always disintegrated when confinement was

released unlike those immersed in vacuum. Disintegration mechanism is thus not operating in the case

of saturation under reduced air pressure.

Other observations suggest that slaking is an important destructive process: If an unconfined cube

of SLS is immersed slowly by rising water (≤ 1 mm/minute) it disintegrates immediately to individual

sand grains. Turbidity and air bubbles are released during disintegration. If rise of water table is faster

the disintegration is delayed up to several tens of seconds after the immersion of the external face of

sandstone. If the cube is kept loaded during immersion it does not disintegrate. However if load is

removed the immersed cube immediately starts to disintegrate very rapidly and it does disintegrate not

to grains but to grain aggregates made of several to several tens of grains. Air bubbles are released

during the disintegration process. The destructive process thus acts differently under slow immersion

compare to abrupt release of the load previously applied to immersed specimens. Release of the air

bubbles and different disintegration pattern can be explained by slaking.


21

Disintegration of SLS in water is accompanied by ejection of cloud of fine particles, which may

potentially indicate dispersion of kaolinite. To clarify this phenomenon, the grain size distribution of

the ejected particles in water (fraction <25 um) was studied by laser granulometry (17 % of particles

<2 um, 33 % of particles 2 – 5 um, 50 % particles 5 – 25 um). As kaolinite accounts for 75 % of

fraction <25 um in SLS, only 23 % of kaolinite particles has size which correspond to potentially

dispersed state (particles <2 um). Based on sodium absorption ratio (0.1 – 0.4) the kaolinite in SLS is

not dispersive29

. Also the fact that grain aggregates left after fast disintegration of cubes are bound by

kaolinite rules out the dispersion of the kaolinite. Kaolinite is thus ejected into water mechanically

during violent air pressure release when pores are disrupted by slaking. Turbidity formed during

slaking thus at first glance mimics the turbidity released by dispersive clays. Similar disintegration

pattern and turbidity release caused by slaking was observed61

in case of cylinders made of non-

dispersive Ca-kaolinite.


Results of erosion of SLS cubes by in rain simulator. *only partial erosion

SLS subsample No. Uniaxial load (kPa) Time of rain shower until

disintegration (minutes)

Remaining mass of cube (dry wt.

% of initial mass)

24 0 5.3 -

24 0.5 >65* 75 %

24 0.6 >65* 68 %

24 1.0 53 -

27 0 5.5 -

27 0 6.5 -

27 0 7 -

27 0 6.4 -

27 0 55 -

27 0 6 -

27 0.5 >70* 63 %

27 760 >180* 67 %

27 760 >180* 77 %

27 760 >960* 53 %

27 760 >190* 66 %

b. Raindrop impact and flowing water

Impact of raindrops is important process, which erodes the SLS material. To study this process,

SLS cubes were exposed to simulated rain. The rainfall simulator (Eijkelkamp version 09.06) was

used (rain intensity 6 mm/min, diameter of drops 6 mm and kinetic energy of rain 4 J/m2/mm) on pairs

of SLS cubes. In each pair one cube was unconfined and the other was uniaxially compressed. Torque

screwdriver was used to reach the given load (precision ±6 %) (Suppl. Fig. 5b), which correspond

roughly to stress 760 kPa based on calibration with tensiometer.

Unconfined cubes were completely eroded in a 5 – 7 minutes with one exception, whereas the

compressed cubes survived for >65 minutes with less than 30 % of cube material eroded (Suppl. Table

8). Erosion ceased on uniaxially loaded cubes after 60 minutes and only minor additional erosion was

observed on a cube subjected to artificial rain for 960 minutes. In case of SLS cube exposed to

artificial rain the stress 0.5 kPa was capable to stabilize the experimental landform (Suppl. Table 8).

Note that the slaking mechanism described in Suppl. Sec. 4a is active also during raindrop impact

and, in fact, our experiments do not allow us to distinguish which mechanism is the dominant source

of fabric disintegration in rain simulator.


22

c. Disintegration of cemented sandstones by salt and frost weathering

Effect of stress on rate of salt and frost weathering was studied by means of various cemented

sandstones and other rocks (Suppl. Table 3). Three pairs of cubes were used for each rock type to test

if stress is capable to decrease the disintegration rate in case of salt and frost weathering. In each pair

one cube was unconfined and the other was uniaxially loaded. Unconfined cube was left bare,

touching the base by its lower side. Other cube was compressed by placing the stiff steel square plates

of the same size as the cube sides to the opposite sides of the cube. (Suppl. Fig. 5c). Plates were

compressed against the cube sides by tightening the nuts on steel casing constructed around the cube.

Nuts were tighten by torque screwdriver to 0.75 Nm, which correspond to confinement of 1.2 MPa

based on the calibration with tensiometer. As the cubes were uniaxially loaded without knowledge of

their original orientation the confinement direction was random and the results were not limited to

specific direction in respect to stratification.

Susceptibility to salt weathering was studied by repeated 24-hours cycles consisting of

submerging of the cemented sandstone cubes to 16 % NaSO4 solution at room temperature for 2 hours;

followed by drying in oven for 20 hours and 2 hours of cooling. During drying, the temperature was

gradually increased from 25 °C to 105 °C in the first 7 hours to avoid salt crystallization inside the

cubes. This method follows the procedure of EN1237062

, but higher concentration of NaSO4 was used

to speed-up the disintegration. Cubes were weighed in each cycle. To compare the rate of

disintegration of uniaxially loaded and unconfined cubes the number of cycles needed to reduce the

weight of cubes to 20 % of original weight was selected. Smaller percentage cannot be used since

some pillars formed from uniaxially loaded cubes failed when residual weight of cube decreased

below 20 % and confinement was lost. The number of cycles was averaged separately for uniaxially

loaded and unconfined cubes, the standard deviation was calculated and results were plotted to the

graph.

Unconfined cubes exposed to salt weathering disintegrated faster than the compressed cubes for

most of tested cemented sandstones (Fig. 2d main paper). The largest difference in disintegration rate

between uniaxially loaded and unconfined cubes were observed in case of H and JN sandstones. In

these cases the weight of unconfined cubes was reduced to 20% of the original weight on average 3.4

– 4.6 and 2.9 faster than uniaxially loaded cubes (Fig. 2d main paper). In case of other cemented

sandstones the unconfined cubes reached the 20 % of original weight on average 1.5 – 2.4 faster than

the uniaxially loaded cubes. Only in the case of samples V, GIN2 and JES the disintegration rates of

unconfined and uniaxially loaded samples were very similar. Such results clearly demonstrate that

confinement reduces the disintegration rate by factor of 1.5 to 4.6 in the case of most of cemented

sandstones. Relatively small difference in disintegration rate between unconfined and uniaxially

loaded cubes of V and JES samples may be explained by observed preferential disintegration along

hidden weak zones (ferric iron-rich zones in the case of V cubes).

Results indicated that uniaxially loaded cubes of quartz sandstones are more durable (H, K, T, V

and GIN1) than cubes cut from other sandstone types. Interestingly some of the most durable

sandstones (H) are mechanically weak in terms of drilling resistance. On the contrary, materials with

higher content of feldspars and other minerals and/or cemented by larger amount of calcium carbonate

disintegrated much faster by salt weathering (P, UP, UT, JN, JES).

Cube surfaces disintegrated to single grains and small chips few mm thick after the cubes were

immersed to salt solution. During the drying part of each cycle the disintegration did not occur. Salt

crystallization disrupts the material but in the same time it cements the loose grains and chips. Once

the salt is dissolved during immersion to salt solution these grains and chips are released. The time of

disintegration is thus not connected to time of disruption of the material structure. Only in case of

strong heterogeneity inside the cubes (pronounced layering, weak zones; sample UP) the structural

features controlled the shape of the weathered material. Uniaxially loaded cubes disintegrated into

pillars, in many cases quite narrow (Suppl. Fig. 10). It is important to stress here that the confinement

of cubes is more or less randomly oriented with respect to sandstone layering in the case of massive

sandstones. Only in the case of visible bedding, the cubes were uniaxially loaded in direction

perpendicular to bedding. The results suggest that pillars will develop along the axis of confinement


23

and may have various orientations with respect to bedding. This is also the case for natural small scale

pillars (Suppl. Fig. 1).

Susceptibility to frost weathering was measured by repeated cycles consisting of submerging the

cemented sandstone cubes to water ( +20 oC) for ≥8 hours followed by removing the cubes from

water and placing them in a freezer ( -20 oC) for ≥8 hours. To remove the loose grains, the cubes

were turned upside down each 10th

cycle for 10 seconds and submerged to water. Three pairs of cubes

were used for each rock type (Suppl. Table 3). Cubes were weighted in each cycle.

In the case of the H sandstone the unconfined cubes subjected to frost weathering disintegrated

completely within 51 – 89 cycles. Uniaxially loaded cubes on the other hand still kept 54 – 82% of the

initial weight at 90 cycle (Suppl. Fig. 11). Unconfined cubes made of coarse sandstone were much less

durable compared to the fine-grained sandstone (Suppl. Fig. 11). Samples K, P, T and V were

subjected to 135 cycles of frost weathering. Uniaxially loaded cubes lost less than 5% of the initial

weight, while unconfined cubes K, P, T and V lost 59-100% of its initial weight (Suppl. Table 9).


Examples of narrow pillars developed from uniaxially loaded cubes of cemented sandstones by means of salt weathering. a),

b) T sandstone (44 cycles); c), d) Gin2 sandstone (44 and 64 cycles respectively); e), f) Gin1 sandstone (63 cycles); g) h)

H3H4 sandstone (44 cycles). Height of all pillars is 4 cm.

Disintegration occurred after submerging the frozen cubes in water, during the freezing part of

cycle the disintegration did not occur. Freezing water disrupts the material but in the same time the ice

cements the loose grains and chips. Once the ice melts after immersion to water these grains and chips

are released. The time of disintegration is thus not connected to time of disruption of the material

structure. Uniaxially loaded and unconfined cubes disintegrated by peeling off single grains and small

chips few mm thick. In the case of uniaxially loaded cubes the pillars were formed in the confinement

direction, while the unconfined cubes often disintegrated into spheroids.


24


Weight loss of cemented sandstone cubes subjected to freeze/thaw cycles. L-uniaxially loaded, U-unconfined. H##-type of

sandstone and cube number, c-coarse, f-fine.


Average decrease of weight in 135 frost weathering cycles in unconfined and uniaxially loaded cubes of cemented

sandstones.

Sample Cubes Average decrease of weight in 135

frost weathering cycles

K unconfined 74 %

K uniaxially loaded 5 %

P unconfined 80 %

P uniaxially loaded 0 %

T unconfined 100 %

T uniaxially loaded 5 %

V unconfined 59 %

V uniaxially loaded 4 %

5. Physical and numerical modelling of landform evolution

Typical landforms in sandstone landscapes are arches, alcoves, pedestal rocks and pillars. All

these shapes were successfully reproduced in laboratory simply by repeated immersion the SLS blocks

in standing water. Numerical modelling was then used to visualize the principal stress direction and

magnitude inside the experimental landforms. As natural arches and alcoves are commonly developed

above subhorizontal discontinuities10

(field observations on Colorado Plateau and the Czech

Republic), the effect of discontinuities was studied by physical and numerical modelling.


25

a. Physical modelling

To document the necessary conditions for development of common landform shapes in sediments

with fabric interlocking, we used SLS material under conditions of partial immersion in laboratory and

in one case under natural rain action (Suppl. Fig. 12).

Laboratory experiments were done with two different initial shapes:

1) Rectangular blocks or cubes of SLS with edges 10 – 40 cm long, with all sides unconfined and

top unloaded or loaded (Suppl. Figs 12, 13). To simulate the effect of fractures and other

discontinuities on the final shape, few millimetres wide notches were cut into some blocks.

2) Cylinders of SLS with diameters 10 – 15 cm, confined tightly by wrapping foil. Before

modelling the cylinder was cut perpendicularly to its axis into slices 3 – 5 cm thick. Slices were hung

so that all weight was carried by wrapping foil (Suppl. Fig. 14, 16). Therefore the whole circular

perimeter of the cylinder, except of topmost part was loaded by its own weight. Vertical sides were

left unconfined. Cylinders were cut by horizontal and sloping notches to simulate discontinuities.

Blocks and cylinders were partly or totally immersed in water to remove the material from all areas

where the stress was sub-critical.

Arches were produced in the cases where the SLS blocks were prior immersion cut through in the

central part or where the SLS block base was unsupported in the middle (Suppl. Figs 12, 15, 16, 17).

Suppl. Fig. 12 shows originally rectangular block reshaped to arch within 450 days of exposure to

natural rain action.

Alcoves were successfully created by immersion of SLS cylinders hanging in plastic foil, which

were partly cut by horizontal notch (Suppl. Fig. 14). Horizontal notch represents subhorizontal

fracture, bedding plane or shallow notch eroded by sapping (Fig. 4 main paper). Notch does not

transmit the stress. As a consequence the material above and below the notch is unprotected by stress

and it is removed by slaking, creating thus the alcove.

Experimental landforms resembling pedestal rocks or cave pillars were repeatedly produced in

experiments by partial immersion of rectangular blocks of SLS (Suppl. Fig. 13, 17). Immersed SLS

material was retreating and cross-section area of experimental landforms was decreasing until the

stress reached the critical stress. After that the disintegration ceased and landforms were stable.


26


Evolution of an arch from rectangular block of SLS with base supported only on sides solely by natural rain action. Rain

erosion has been gradually exposing the high stress arch. Low stress areas (lower part of block in the middle and upper

corners were eroded as predicted by numerical modelling (Suppl. Fig. 18). a) After emplacement; b) 109 days of exposure; c)

223 days of exposure; d) 455 days of exposure; e) Numerical model of stress in SLS block on figure a; f) Numerical model of

stress in SLS block on figure d. The length of red lines indicates the principal stress magnitude.


27


Experimental pedestal rock developed by repeated partial immersion of rectangular SLS block. Pillar thickness decreased as

the load was decreased. The blue line represents the maximum level of immersion in each step. a) Initial shape of

experimental landform with load 18 kg before (a) and after first immersion (b); c) landform with load 6 kg after second

immersion to the same level; d) landform during third immersion loaded only by SLS material above water table); e), f)

different views of the stable final shape (pedestal rock) after third immersion.


What are necessary and sufficient conditions to create an alcove? Result of the laboratory modelling of alcove produced by

cutting the narrow horizontal notch into SLS self-confined cylinder and immersing it.


28


Experimental arch created by repeated partial immersion of loaded block with rectangular opening. As the load was

decreasing the mass of the arch decreased as well. The blue line represents the maximum level of immersion in each step. a)

Initial shape of experimental landform. Rectangular opening was created to ensure that loose sand will be transported out of

the opening; b) After first flooding; c) Experimental arch after second immersion, loaded by 1.4 kg; d) Stable final shape

after removal of loose sand covering the base of landform and third immersion (load 0.7 kg); e) Detail of right part of arch

with well-developed stress lines (c.f. Suppl. Fig. 8)


29


Experimental arch created by repeated partial immersion of self-confined cylinder of SLS. Outher boundary is lined by

plastic foil, all other boundaries are bare. a) Notches cut through the whole cylinder; b) Disintegration of cylinder during

immersion; c) Stable shape, red lines indicate newly cut notches; d) Stable shape after immersion; e) Another extension of

notches; f) Final seemingly fragile but stable shape.


Experimental cave pillars developed by repeated partial immersion of SLS block with artificially thinned central part (blind

drill-hole). Pillar thickness decreased as the load was decreased. The blue line represents the maximum level of immersion.

a) Experimental landform with drill-hole and load 6 kg after first immersion (subhorizontal fracture was formed during

drilling); b) Expanding central opening after third immersion in landform loaded by 1.4 kg; c) Two separated pillars after

forth immersion (load decreased to 0.3 kg; d), e) Different views of the stable final shape after fifth immersion and removal

of loose sand covering the base of landform (load 0.3 kg). Note that subhorizontal fracture developed before immersion was

stabilized by load in both pillars.


30

b. Numerical modelling

Stress field in sandstone landforms was modelled by PLAXIS program PX201030

using the

parameters obtained from triaxial measurements (Suppl. Table 2). The objective of the modelling was

to visualize the principal stress directions in the natural landforms and to test whether the stress

distribution near the landform surface corresponds to results of laboratory modelling. As we were

interested in the stress field description of otherwise stable landform, the fabric disintegration

characterized by the locus of fabric instability has not been considered in the model. Modelling was

done in 2D, so arches were modelled as tunnels with constant cross-section, columns were modelled

as axially symmetrical (along vertical axis) and alcoves were modelled as openings within the massif.

The material behaviour was described by a standard Mohr-Coulomb material model.

Numerical modelling with parameters derived from triaxial tests indicated that the SLS material

can form up to 35 m high vertical cliffs. This is in accord with real height of natural cliffs of SLS29

. In

modelling of the studied landforms, we searched for answers to the following two main questions:

1) What is the distribution of stress in the studied landforms (freestanding arches/alcoves,

pedestal rocks and pillars) at the onset of modelling (rectangular blocks and in evolved landforms?

2) Why are the walls of sandstone landforms usually smooth without larger horizontal

protrusions?

The both questions were answered satisfactorily. In general, our models clearly demonstrate that

the major principal stress in the intact sandstone block is oriented vertically and increases downwards.

However, if subhorizontal discontinuity is present in the block the stress flow around the discontinuity

is forming the areas of low stress adjoining the discontinuity (stress shadow). (Suppl. Fig. 18). As a

consequence, the material in low stress areas is expected to retreat until the stress at landform surface

will reach the critical value.

The stress is very low in any modelled horizontal protrusions, which induces their easy

erodability and lack in natural sandstone exposures. This issue was investigated in more detail. Suppl.

Fig. 19a shows a model of a pillar with protrusion. The model has been created at the laboratory scale

and loaded at the top surface by an additional vertical load of 2 kPa. Suppl. Fig. 19b distinguishes two

areas, one with major principal stress higher than 8kPa (red zone), and one with major principal stress

lower than 8kPa (blue zone). It is clear that most part of the protrusion falls with the blue zone, thus

inside the locus of fabric instability. The fabric of the material forming protrusion is thus unstable and

it is susceptible to erosion. Suppl. Fig. 19d shows Mohr stress circles obtained from different points

within the model (location of the points is indicated in Fig. 19c). Stress state of the points within the

protrusion (E, F) falls within the locus of fabric instability, while stress state of the points within the

main load-bearing structure of the pillar (A to D) fall within the stress region protected from erosion

by fabric interlocking.


31


a) Stress field around the discontinuity. Highest principal stress magnitude (the longer the red lines the higher the stress

magnitude) is directly above the opening, which in fabric interlocked material result in higher stability of the surface above

the opening and thus lower erosion rate of surface compare to wider surroundings. Delicate arch is one of examples of such

effect Highest principal stress magnitude is in thinnest parts and on the top of the arch, which will stabilize the arch compare

to surrounding area; b) Stress field in initial and final shape of arch (Suppl. Fig. 15); c) Stress field in initial and final shape

of cave pillars (Suppl. Fig. 17); d) Stress field in initial and final shape of pedestal rock (Suppl. Fig. 13); f) Stress field in the

pillar. Note that principal stresses are aligned parallel with pillar surface; on the right: The same pillar with protrusion. Note

that in the outer side of protrusion the stress magnitude is minimal and it is low in central part of protrusion. Material in

protrusion will be thus not stabilized by stress.


32


a) Principal stresses within the model of a pillar (160 mm total height) loaded on the top surface by an additional vertical

load of 2 kPa. b) Areas with the major principal stress higher than 8 kPa (shown in red) and below 8 kPa (shown in blue). c)

Location of selected stress points. d) Mohr circles for stress points from c). Mohr circles for stress points within the

protrusion (E, F) fall within the locus of fabric instability, while Mohr circles for stress points within the main load-bearing

structure of the pillar (A to D) fall within the stress region protected from erosion by fabric interlocking.

6. Supplementary discussion and conclusions

a. Evolution of landforms in fabric interlocked materials

Based on laboratory experiments, numerical modelling and field observations, the mechanism of

evolution of a) arches, b) alcoves, c) pedestal rocks, and d) pillars in cavities in fabric interlocked

sandstones is proposed (Fig. 4 main paper):

a) Above any subhorizontal discontinuity such as tectonic fracture, bedding plane, shallow

incipient horizon (few centimetres high horizon conducting water and quickly eroded, e.g. by frost

weathering), the zone of high stress is formed resembling by shape the arch (Suppl. Figs 12, 18). In

other words, the incipient arch structure is present in any undercut block far before the W/E processes

starts to carve the block. Once the high stress zone is exposed at retreating surface, the denudation rate

will decrease or even cease in high stress zone (Fig. 4 main paper). However the denudation in

surroundings of high stress zone will proceed at original rate. This will virtually excavate the arch out


33

of the ground. After excavation the arch will still be protected from denudation while the surface in its

surroundings will keep denudating. Numerical modelling thus explains why Delicate Arch, Rainbow

Bridge and many other arches are freestanding and sandstone in their surrounding was long ago

eroded away.

b) Alcoves and shallow cavities develop by the same principle. They form if vertical wall is

partly undercut by subhorizontal discontinuity. Such discontinuity forces the principal stresses to run

around it, forming zone of low stress (Fig. 4 main paper). Fast erosion of material from the low stress

zone will result in reshaping the original horizontal discontinuity into alcove.

c) The thin rock segments carrying pedestal rocks are created by the erosion process, whose rate

is controlled by stress. Negative feedback between stress and surface retreat ensures that form will be

undercut from all sides and yet the center of gravity will not be undermined: The deeper the erosion

undercuts the higher is the stress at eroding surface and the slower the erosion is. In the case of slaking

the erosion stops, leaving incredibly thin stem, yet the whole pedestal rock structure is perfectly

balanced (Suppl. Fig. 13).

d) The hour glass pillars in caves and cavities are created by erosion starting along (sub)vertical

fractures or other (sub)vertical discontinuities. As the area of horizontal section of the pillars decreases

the stress in sandstone pillars increases and their erosion rate decreases until it finally may cease

(Suppl. Fig. 17, Figs. 1d and 4 main paper).

Freestanding sandstone pillars up to several tens of meters high occurs in areas with dense

subvertical fracturing1 (Suppl. Fig. 4c). The main part of these landforms is stabilized by stress. The

top of the pillar has to be protected either by resistant material or by case hardening. With raising

height and decreasing cross-sectional area of the pillar the stress and thus resistance against the W/E

processes increases in the lower part of the pillar. While the base of pillar is protected from W/E

processes by high stress the talus and flat sandstone exposures in surroundings of the pillar are left

unprotected. If erosion is concentrated to ground surface, the surroundings of pillars will retreat while

pillar base will be protected by stress. This will excavate the pillar more and more out of the ground.

b. Importance of discontinuities and examples from cemented sandstones and other materials

As described in detail in the above paragraph, arches, alcoves and hour glass pillars are caused by

planar discontinuities, which force the stress vectors to run around them forming 3D stress arrays

inside the sandstone. As the planar discontinuities are common in sandstone landscapes it is not

surprising that landforms listed above are relatively common.

It was demonstrated that effective horizontal partings (sometimes only few centimetres thick clay,

shale or highly fractured sandstone, weak or easily weathered), in the otherwise uniform sandstone of

the Colorado Plateau play a critical role in slope segmentation and thus strongly affect the erosion

rate63

. Based on the observation at Colorado Plateau, we believe that effective horizontal partings are

unaffected or only poorly affected by stress stabilization (fabric interlocking is not operating there due

to different composition of these materials). As a consequence, the retreat along these horizons will

not stop. The complexity of the most sandstone landscapes arises from presence of two different

materials: i) fabric interlocked materials whose retreat rate diminishes with rising stress and ii) other

materials, which are eroded irrespectively on stress or even proportionally with stress. If the material

in an incipient horizon is continually eroded the alcove will grow in length until the ceiling will fail

and then a new alcove will be gradually formed. Negative feedback between stress and surface retreat

in the case of such alcove may operate in the whole rock mass except thin effective horizontal partings

(Fig. 4 main paper). Clay and shale horizons are therefore strongly affecting the sandstone landscapes1,

63, 64, 65.


34


Pedestal rocks in cemented materials showing traces of negative feedback between stress and W/E. Dashed lines approximate

original size of boulders. Arrows represent place where stress is transmitted to underlying rocks. a) Boulder inside the talus

accumulation below temporary waterfall. Since the formation of talus accumulation the boulder surface retreated except

places, which are protected from erosion by high stress as they transmit the stress to the other boulders (Adrspach-Teplice

rock city, Czech Republic). b) Granite pedestal rock, Girraween National park, Queensland, Australia. Note the narrow stem

supporting the whole block. Over time the block disintegrated into an ellipsoidal shape except for the basal part, which

apparently experienced no retreat because of stress stabilization.

The landforms in fabric interlocked materials occur all around the globe. In fact, we strongly

believe that most sandstone landforms are, at least to some extent, formed by negative feedback

between stress and W/E processes. The best-developed forms can be expected in materials, where

fabric interlocking is dominating. Such materials typically have high uniaxial compressive strength but

low TSs. Examples are uncemented or weakly cemented quartz sandstones (locked sands) in Central

Europe and elsewhere (Sec. 1c). Evidence of negative feedback between stress and surface retreat

exists from Adrspach area, Czech Republic in a talus accumulation subjected to intense periodic water

flows. The original surfaces of some boulders in the talus accumulation are eroded away except those

parts, which are stabilized by stress transmitted from one boulder to another (Suppl. Fig. 18a). As a

result the boulders end up sitting on pillars. Great examples of stress-induced landforms are pillars in

the largest quartzite caves in the World in Venezuela (Fig. 1d main paper). The cave spaces are often

supported by pillars, which are seemingly made of more resistant material than their eroded

surroundings44, 45, 66, 67

. However, once a sandstone pillar is disconnected, stress is lost, the rest of pillar

becomes soft, and the pillar quickly erodes away (Suppl. Fig. 19). Strong arguments why these pillars

cannot be created by finger-flow were listed52

. In our opinion the negative feedback between stress

and surface retreat is the only process, which is capable to explain the evolution and consequent

stabilization of these pillars.


35


Interrupted pillar in Colibri Cave, Chimanta, Churi Tepui, Venezuela. At the top of the pillar remnant, the erosion traces are

visible. Photo Martin Sluka. Compare to undisturbed pillars (Fig1d in the main text), which resist the flood flow.

Sandstone grains are definitely not the only elements with fabric interlocking. Weathered granite

with loose quartz and feldspar crystals perfectly packed together fulfils these conditions as well. This

might be, why granitic terrains often have similar assemblages of weathering forms as do sandstones31,

36 (Suppl. Fig. 20b). Fabric interlocking seems to be responsible for stabilization of otherwise loose

fragments of brecciated carbonate, forming alcoves in Pilot Valley, Utah (Suppl. Fig. 22). Similar

examples can be found in many other places (alcoves in various rocks disintegrating into loose

fragments). Similarly, rock mass fractured into interlocked blocks should behave as a fabric

interlocked material17

. In large arches, bridges and alcoves across Colorado Plateau, the individual

elements might be in many cases the sandstone blocks (exfoliation sandstone slabs), rather than

individual quartz grains (Suppl. Fig. 23). Therefore the concept of fabric interlocked landforms seems

to be widely applicable for geological settings on scale of millimetres to hundreds of meters.


36


Cavernous weathering and alcove in carbonate breccia in Pilot Valley, Utah, USA. a) Smaller caverns; b) Alcove, note thick

accumulation of sharp edged talus; c) Disintegration of the carbonate and; d) Detail of the alcove overhanging wall. It is

obvious that material disintegrates into loose rock fragments, which have only fabric interlocking in alcove ceiling.


37


Large-scale features clearly affected by stress in Navajo sandstones at Powel Lake, Utah, USA. “A” places represent alcove

and “B” places buttress, blue line represent arch-like structure. a), b), c) Alcoves formed due to failure of exfoliation plates in

places such as “A” but protected by increased stress at B. It seems that alcoves are product of segmentation: At the same time

that incipient alcoves starts to evolve and undermine the vertical wall, the increasing stress in alcove surroundings starts to

protect the exfoliating plates from failure, to form buttress. As a result the alcoves alternate with buttresses in a periodical

manner. d) Theatre-headed valley. Extremely smooth circular shape demonstrates that retreat in the whole huge form (150 m

in height and width) is orchestrated by a single stress field.

c. Concluding remarks and implication

Previously published ideas on origin of arches, alcoves, pedestal rocks and pillars were often

vague and mostly unsupported by other evidence than observation of forms in nature, morphometric,

petrological and mineralogical analysis of sandstone and/or salts. Presence of salt/occurrence of

freezing water and/or presence of other potential W/E processes were misleadingly considered as the

critical condition for the origin of landforms.

To our knowledge this is the first time when the above mentioned landforms were reproduced by

laboratory experiments from the same material in which they occurs in nature. It was shown that the

landform stability is caused especially by fabric interlocking, and landform evolution is enabled by the

disintegration processes (slaking, salt and frost weathering). We believe that ability to create the

landforms under controlled laboratory conditions in accord with numerical modelling of stress and

interpretation of the locked sand mechanical behaviour within the framework of continuum mechanics

introduces solid evidence that stress field is the critical factor controlling the shape of such landforms.

Here we show that disintegration processes are mere tools, which are orchestrated by stress field to

carve the spectacular landforms. While some disintegration process is always available, it is the stress

field which is the critical factor.

Contrary to the usual impression, the stress is not only destructive but sometimes it serves as a

critical stabilizing factor. Common thinking in the engineering-geology community about stress as the


38

limiting factor of stability (from the upper side) may explain why the stabilizing effect of stress was so

long overlooked. In fact, the concept of locus of fabric instability has not been known within the field

of geomechanics till now. The evolution of many sandstone landforms is an issue of stability of huge

array of interlocked grains of blocks with minimum tensile strength rather than issue of rock strength.

Similarly to masonry the adding weight to the right place will stabilize the whole structure.

Supplementary References:

31. Grab S. W., Goudie, A.S., Viles, H.A. & Webb, N. Sandstone geomorphology of the Golden Gate Highlands National

Park, South Africa in a global context, Koedoe 53, 1-14 (2011).

32. Yatsu, E. Rock Control in Geomorphology (Sozosha, Tokyo, 1966).

33. Vidal-Romaní, J.R. Geomorphología granítica en Galicia (NW España). Cuad. Lab. Xeol. Laxe 13, 89-163 (1989).

34. Vidal-Romaní, J.R. & Twidale, C.R. Sheet fractures, other stress forms and some engineering implications.

Geomorphology 31, 13-27 (1999).

35. Vidal-Romaní, J. R. Forms and structural fabric in granite rocks. Cad. Lab. Xeol. Laxe 33, 175-198 (2008).

36. Twidale, C.R. & Vidal-Romaní, J. R. Landforms and geology of granite terrains (Balkema, Laiden, 2005).

37. Hoek, E. & Bray, J. Rock Slope Engineering (Institute of Mining and Metallurgy, London, 1991).

38. Herget, G. Stresses in Rock (Balkema Rotterdam, 1988).

39. Mikuláš, R. Poznámky ke vzniku některých prvků mikroreliéfu pískovcových skal. Ochrana přírody 56, 19-21 (2001b).

In Czech.

40. Cresswell, A. W. Block sampling and test sample preparation of locked sands. Geotechnique 51, 567-570 (2001).

41. Richards, N.P. & Barton, M.E. The Folkestone Bed sands: microfabric and strength. Q. J. Eng. Geol. 32, 21-44 (1999).

42. Young, R.W. in Geomorphological landscapes of the World (ed. Migoń, P.) 333-340 (Springer, London, 2010).

43. Wray, R. A. L. Phreatic drainage conduits within quartz sandstone: Evidence from the Jurassic Precipice Sandstone,

Carnarvon Range, Queensland, Australia. Geomorphology 110, 203-211 (2009).

44. Aubrecht, R. et al. Sandstone caves on Venezuelan tepuis: return to pseudokarst. Geomorphology 132, 351-365 (2011).

45. Aubrecht, R. et al. Venezuelan tepuis-their caves and biota. AGEOS - Monograph, (Comenius University, Bratislava,

2012.

46. Barton, M.E. in Geotechnical engineering of hard soils-soft rocks (eds Anagnostopoulos, A. et al.) 367-374 (Balkema,

Rotterdam, 1993).

47. Atkinson, J. The mechanics of soils and foundation (Taylor and Francis. New York, 2007).

48. Sitar, N. in Special Publication on Geological Environment and Soil Properties (ed. Yong, R.N.) 82-98 (ASCE., 1983).

49. McNally, G. H. & McQueen, L. in Sandstone City: Sydney’s Dimension Stone and Other Sandstone Geomaterials (eds

Nally, G. H. & Franklin, B. J.) 178-196 (EEHSG of the Geological Society of Australia, Sydney, 2000).

50. Terzaghi, K. Stability of steep slopes on hard unweathered rock. Geotechnique 12, 251-270 (1962).

51. Gordon, J. E. Structures – Or Why Things Dont Fall Down (Pelican, Harmondsworth, 1978).

52. Sauro, F., Piccini, L., Mecchia, M. & De Waele, J. (2012): Comment on “sandstone caves on Venezuelan tepuis: Return

to pseudokarst? by Aubrecht, R. et al., Geomorphology 132, 351-365 (2011). Geomorphology 197, 190-196 (2013).

53. Uličný, D. Depositional systems and sequence stratigraphy of coarse-grained deltas in a shallow-marine, strike-slip

setting: the Bohemian Cretaceous Basin, Czech Republic. Sedimentology 48, 599-628 (2001).

54. Hintze, L.F. Geologic History of Utah (ed. B. J. Kowallis, Brigham Young University Geology Studies Special

Publication 7. 1993).

55. Dittes, M. & Labuz, J. Field and laboratory testing of St. Peter Sandstone. J. Geotech. Geoenviron. Eng. 128, 72-380

(2002).

56. Mitchell, J.K. & Soga, K. Fundamentals of soil behaviour (Wiley, Hoboken, 2005).

57. Spagnoli, G., Stanjek, H. & Sridharan, A. Influence of ethanol/water mixture on undrained shear strength of pure clays.

Bull. Eng. Geol. Environ. 71, 389-398 (2012).

58. Gregory, H.E. Geology of the Navajo Country; a reconnaissance of parts of Arizona, New Mexico, and Utah. USGS

Professional Paper 93 (U.S. Government Printing Office, Washington, 1917).

59. Gregory, H. E. The San Juan Country a geographic and geologic reconnaissance of southeastern Utah. USGS

Profesional Paper 188 (U.S. Government Printing Office, Washington, 1938).

60. Arulanandan, K. & Heinzen, R.T. in Erosion and Solid Matter Transport in Inland Waters (eds IAHS-AISH, UNESCO)

Vol. 122 75-81 (Adlard & Son Ltd, Dorking, 1977).

61. Moriwaki, Y. & Mitchell, J. K. in Dispersive Clays, Related Piping and Erosion in Geotechnical Project (eds Sherard, J.

L. & Decker, R. S.) STP 623 287-302 (ASTM, Philadelphia, 1977).

62. EN 12370 Natural stone test methods – Determination of resistence to salt crystallisation, European standard EN

12370:1999. European comitte for standardization (1999).

63. Oberlander, T. M. in Geomorphology in Arid Regions (ed. Doehring, D.O.) 79-114 (Allen & Unwin, Boston, 1980).

64. Howard, A. D. & Kochel, R. C. in Sapping Features of the Colorado Plateau (eds Howard, A. D., Kochel R. C. & Holt,

H. E.) 6-56 (STIO & NASA, Washington, 1988).

65. Holland, W. M. Slot valleys. Austr. Geogr. 13, 338-339 (1977).

66. Aubrecht, R. et al. Venezuelan sandstone caves: a new view on their genesis, hydrogeology and speleothems. Geol.

Croat. 61, 345-362 (2008).

67. Aubrecht, R. et al. Reply to the Comment on “Sandstone caves on Venezuelan tepuis: Return to pseudokarst?.

Geomorphology 197, 197-203 (2013).


39

68 Lamb, M.P., Howard, A.D., Johnson, J.R., Whipple, K.X., Dietrich, W.E. & Perron, J.T. Can springs cut canyon into

rock? J. Geophys. Res. 111, 1-18 (2006).

69. Cílek V. in Geomorphological landscapes of the World (ed. Migoń, P.) 201-209 (Springer, London, 2010).

70. Twidale, C. R. in Geomorphological landscapes of the World (ed. Migoń, P.) 321-332 (Springer, London, 2010).

71. Lambert, D. The influence of ground water salts in the formation of sandstone shelters near Gosford, NSW. Institute for

Conservation of Cultural materials Bulletin 6, 29-34 (1980).

72. Young, A. R. M. Salt as a agent in the development of cavernous weathering. Geology 15, 962-966 (1987).

73. Goudie, A.S., Migon, P., Allison, R.J. & Rosser, N. Sandstone geomorphology of the Al-Quwayra area of south Jordan.

Z. Geomorphol. 46, 365-390 (2002).

74. Vařilová, Z., Přikryl, R. & Cílek, V. Pravčice Rock Arch (Bohemian Switzerland National Park, Czech Republic)

deterioration due to natural and anthropogenic weathering. Environ. Earth Sci. 63, 1861-1878 (2011).

75. Dixon, J. C. in Geomorphological landscapes of the World (ed. Migoń, P.) 39-47 (Springer, London, 2010).

76. Bradley, W.A. Large-scale exfoliation in massive sandstones of the colorado plateau. Geol. Soc. Am. Bull. 75, 519-528

(1963).

77. Froede, C.R. & Akridge, A.J. Isolated areas of pulpit rocks on the Lookout Mountain synclinal ridge: possible origin and

development. Southeast. Geol. 41, 225-228 (2003).

78. Twidale, C. R. & Campbell, E. M. On the origin of pedestal rocks. Z. Geomorphol. 36, 1-13 (1992).

79. Nicholas, R. M. & Dixon, J. C. Sandstone scarp form and retreat in the Land of Standing rocks, canyonlands national

park, Utah. Z. Geomorphol. 30, 167-187 (1986).

80. Cresswell, A., Barton, M.E. & Brown, R. Determining the maximum density of sands by pluviation. Geotech. Test. J. 22,

324-328 (1999).

81. Cresswell, A. & Barton, M.E. Direct shear tests on an uncemented, and a very slightly cemented, locked sand. Q. J. Eng.

Geol. Hydrogeol. 36, 119-132 (2003).

82. Barnes, D.J. & Dusseault, M.B. The influence of diagenetic microfabric on oil sands behaviour. Can. J. Earth. Sci. 19,

804-818 (1982).

83. Mesri, G., Feng, T.W. & Benak, J. M. Postdensification penetration resistance of clean sands. J. Geotech. Engrg. 116,

1095-1115 (1990).

84. McBride, E.F. & Picard, M.D. Origin and development of tafoni in Tunnel Spring Tuff, Crystal Peak, Utah, USA. Earth

Surf. Process. Landf. 25, 869-879 (2000).


http://link.springer.com/journal/12665

sandstone landforms shaped by negative feedback …...colorado plateau (usa) 7 alcoves (shelters)...

Documents