Fracture stresses at shallow depths during burial

Tectonoph_vsics, 169 (1989) 59-65 Elsevier Science Publishers

59

B.V., Amsterdam

- Printed

in The Netherlands

Fracture stresses at shallow depths during burial D. BAHAT Department of Geology and Mineralogy, Ben Gurion Uniuersity of the Negeu, Beer Sherla (Israel) (Received

February

11.1987;

revised version

accepted

February

9, 1989)

Abstract Bahat,

D., 1989. Fracture

Single-layer to folding

joints

and uplift.

morphology

formed

0, = 1.0 MPa, Subsequently, at a burial continued

stresses

at about

of about further

occurred stress

during

when

pore pressure

I?~= 1.0 MPa, a dihedral

150 m, where

P = 2.0 MPa,

to depths

of perhaps

and

extensional

P = 1.5 MPa,

horizontal

at shallow

joints

ir, = -0.5

200-400

MPa,

depths

during

marked

by circular

horizontal

maximum

minimum

angle of 35 o and were marked

effective

stress

by axial horizontal

sr = 1.0 MPa, and

burial

prior

fracture-surface effective

stress

0, = -0.5

MPa.

plumes

lormed

_ = 1.8 MPa. Fracturing

m.

1987a), short (length generally < 1 m), characterized by low spacing (commonly 15-25 cm)

Introduction

and often have fracture

Voight and St. Pierre (1974) Price (1974) Magara (1981) Narr and Currie (1982) and Engelder

burial,

siderations to depths (1981) drew attention

but restricted

their con-

greater than 1 km. Sibson to the feasibility of near-

surface hydrofracturing at low differential stresses. Jointing at shallow depths during burial and diagenesis is the subject matter of the present paper. Lower Eocene chalk layers with alternating beds of chert nodules (known as the Mor Formation) occur in the Beer Sheva and Shephela synclines near Beer Sheva. They are slightly folded and intensively fractured by several distinct groups of systematic single-layer joints and multi-layer joints (Bahat, 1988). The single-layer joints are confined to individual chert-free chalk layers. These joints are closed (with “hair-line” contacts, Bahat, 0040-1951/89/$03.50

% 1989 Elsevier Science Publishers

on their surfaces.

(several meters), commonly contain veins several centimeters wide and do not show distinct fracture-surface morphologies. Single-layer joints are considerably more abundant than multi-layer ones.

ments due to uplift. Price (1974), Watts (1983) and Engelder (1985) also analysed the tectonophysics during

markings

The multi-layer joints are long (tens of meters) and cut many chalk layers. They are widely spaced

(1985) among others, have evaluated quantitatively the conditions that promote fracture in sedi-

of jointing

Tectonoph_vsics, 169: 59-65.

near Beer Sheva, Israel, developed

that produced

burial

burial.

in two stages. Initially,

100 m depth

effective

hybrid joints depth

depths

in Lower Eocene chalks Fracturing

vertical

during

at shallow

B.V.

The multi-layer joints postdate the single-layer joints; they are subparallel to the ore-existing single-layer joints, but they involve much larger extensile strains, as shown by the extension veins, the fracturing of some of the chert nodules, and the development of new narrowly sp,iced joints. These multi-layer joints resulted frcm tension, possibly due to Neogene uplift (Voight and St. Pierre, 1974; Gvirtzman, 1979). The cross-fold single-layer joints (those fractures which are oriented subnormal to the fold axes) are divided into three sets. One set trending 328” (N32” W) is characterized by the circular -annular fracture markings (Fig. la) and the two

Fig. 1. Fracture circular

markings

undulations

on surfaces

on a 32g” joint diameters).

on single-layer

joints

in Lower

on the right, and radial b. Straight

horizontal

plumes

Eocene

plume on joints

sets trending 309 o and 344” show plumes (Fig. la, b) (Bahat, 1987a). The strike single-layer joints in the area (those fractures that parallel to fold axes) differ in certain characteristics from the cross-fold joints (Bahat, 1988) and are not included in the present investigation. The combined thickness of the Lower and Middle Eocene formations in the Beer Sheva area is

chalks

around

on a 342” joint oriented

345’

Beer Sheva. a. Two adjacent

on the left (both

have approximately

markings, 35 cm

(note meter scale).

about 200 m (Braun et al., 1977). In the Shephela syncline the two formations probably never exceeded 150 m each (Gvirtzman and Buchbinder, pers. commun., 1986). Partial erosion of this sequence may have occurred during the Late Middle Eocene uplift of the region (Gvirtzman, 1979). This period was followed by deposition of 100-150 m of Upper Eocene - Oligocene sediments (The

FRACTURE

STRESSES

DEPTHS

DURING

61

BURIAI

of these

England

started

are rare in the Beer Sheva area, prob-

densities

of 2.38-2.40

Beith-Guvrin sediments

AT SHALLOW

Formation),

ably because

another

but outcrops

period

of uplift

tion

in the area

occurred

in the

in the Late

50 m thick

Ziqlag

Thus, the area offers the opportunity fracturing

at shallow

depths

and jointing,

400 m), i.e. at low effective Diagenetic

processes

low overburden pore

pressure,

fracturing.

pressures which

Miocene,

pressure. at

of several hundred

pore

fluid

ing a pore fluid pressure

an important

role in

of diagenesis),

chalk

of northwest

that

fracture

Europe,

pressure

more than sufficient

Thermal

effects

(Voight

Fracturing

history,

perhaps

with an overburden

Formation of single-layer dence process

of only

could

reach

in 4.5

(assum-

to cause tensile

in chalk at these depths.

by Ginsburg (1957) and Murray (1961) and his own observations, Dravis (1979) suggested that

burial

Follow-

ratio X = 0.6 at that stage

are omitted in the present depths involved.

vanced stages of diagenesis have been identified in these rocks. The diagenesis started early in the

meters.

at 300 m overburden

compaction and water loss took place at a depth of about 0.5 m. On the basis of previous studies

relatively little overburden ever existed over the Cretaceous Austin Chalk in South Texas: yet ad-

increased

the first stage of deformation

in high

At the

g cm- 3 the rate

(1977) limits his analysis

calculations,

MPa during

migration.

was considerably

and may result

et al. (1974) observed

in the Maastrichtian

Guildford,

occur

diagenesis.

fluid pore pressure

were 2.4-2.6

Mimran

to overburdens

the rock reached

the CaCO,

migration

ing Mimran’s

(less than

overburden

plays

Hakansson

of CaCO,

by these factors.

for studying

of compaction

enabled

stage when densities

Formation.

of burial

when

g cmm3 during

At this stage the two factors,

and erosion

occurred during the Early to Middle Miocene (Gvirtzman, 1979). The last period of sedimentaresulting

to occur

and study

joints

St. Pierre.

1974)

due to the low

during

the subsi-

There are observations suggesting that the single-layer joints in the Lower Eocene chalks formed earlier than those in the Midcle Eocene

a few feet. Mimran (1977) suggested that substantial removal of CaCO, from chalks in southern

30 rd

=

ZO-

Y

lo-

b

e

a-

a

100 270

:

‘,

290

Fig. 2. Histograms

of joint

Shephela

(b) Lower Eocene,

syncline;

azimuth

azimuths

310

330

350 AZIMUTH

measured

in Lower

Eocene

Beer Sheva syncline;

of the axes of the Shephela

N

010

030

and Middle

(c) combined

Eocene

050

rocks around

(a) and (b); (d) Middle

and Beer Sheva synclines

070

090

Beer Sheva. (a) Lower Eocene,

Eocene.

Beer Sheva syncline.

are 028 o and 050 O. respectively.

The

chalks.

Fracture

in the

before the younger

older

chalks

developed

rocks were sufficiently

TENSILE

lithified

-l.O-o5

for fracturing: (1) Study of regional indicates

are characterized (2) There both

joints

around

that the Lower and Middle by distinct Eocene

in the Middle single-layer

Eocene

chalks

sets developed

I.0 15 29

25

Beer Sheva sets (Fig. 2).

indications

that,

(Bahat,

1988) and

chalks

cl.5

Eocene chalks

fracture

are independent

the Lower

C~JMPRESSIVE 0

(Bahat,

1987b),

in recurring

in the

stress epi-

sodes. (3) Cross-fold

joints

in the Lower Eocene chalks

are cut by normal faults which were formed during the Lower Eocene (Bahat, 1985). Therefore, these

joints

associated

are

considered

here

with the subsidence

in the Middle

Eocene

to have

process.

chalks were fractured

faulting in the rocks (Bahat, 1987b). (4) Single-layer jointing in the Lower chalks

seems

compression single-layer

to have developed

been

The joints

Eocene

due to regional

from 328” (Bahat, 1987a), whereas jointing in the Middle Eocene chalks

appears to be the consequence of stresses associated with local block tectonics (Bahat, 1986). Hence, jointing of Lower Eocene chalks could have than Eocene burden.

t

after

Fig. 3. Diagram are

the

two

respectively, respective

of changes horizontal

in stress with depth. and

vertical

P is the pore pressure, effective

stresses.

increase jointing

to certain (modified

in magnitudes

prior ta jointing peaks.

e,. e,, and 0;

principal

stresses,

and Cx, SY and 0, are the

Reductions

tive stresses occur periodically pressures

the

The

of effec-

each time pore

reverse

occurs

on

after Price, 1974; fig. 7).

started during burial at depths shallower 150 m, before sedimentation of Middle chalks could have contributed to overThis fracturing possibly continued to 200

m and perhaps Paleostresses

down to 400 m depths.

and fracture

at 100 m depth

1977). The tensile strength 7; is taken to be 0.5 MPa. This is because the chalk at this stage is already

consolidated,

but at the initial

few hundred

meter depths it is still partly soaked with water and considered to be weak, and 0.5 MPa is the lowest result of Brazilian tests obtained for chalks

The circular-annular fracture markings that characterize surfaces of set 328” suggest that these joints developed normal to the minimum horizontal principal stress, a,, when the effective maximum horizontal stress, EY, equalled the effective

in the investigated area (Koifman and Flexer, 1975, p. 64). It may be argued that the q value was lower than 0.5. On the other hand, Coulon

vertical stress, & (Bahat, 1987a). On the basis of the above assumed fracture constraints (depths shallower than 150 m) fracture is here calculated for the depth (h) of 100 m when lines cJ and & cross each other (Fig. 3). Watts (1983) found an analogous line crossing in chalks of the North Sea at depths shallower than 550 m. The gradient of overburden pressure a, of 25 MPa km-’ is adopted irom Voight and St. Pierre (1974). A chalk density of 2.5 g cm-3 seems to be reasonable (Mimran,

and Frizon de Lamotte (1988) attribute to Upper Cretaceous chalks in the Paris Basin T. values that ranged from 0.6 to 0.8 MPa during their fracture in the Tertiary. Hayati’s (1975, p. 94) work on water-saturated Israeli chalks indicates a Poisson ratio u = 0.29. X is considered to be 0.6 (Mimran, 1977). Coulon and Frizon de Lamotte (1988) suggest h = 0.5 for hygroscopic chalks whose suffering from diagenesis has been comparatively limited. The relationship between tensile strength T, effec-

FRACTURt

STRESSES

tive principal

AT SHALLOW

DEPTHS

DURING

stress a,, and pore pressure

63

BCRIAL

P (Jaeger

and Cook 1979, p. 225) is: a, = u y-P=

-q

(1)

6: is given by ~(1 -

X), where X is the ratio of

to a,, and an additional and

y strains;

6, = U,V/(l

Jaeger and Cook,

1979, p. 372) is:

that

being

is completely

of the surrounding

y strains subject

restricted

rock (Magara,

is based

context.

Johnson

to a,, lateral by the pressure

1981). Consider-

(1970,

tot01 stresses

effective stresses

on

ing the low stresses and low stress duration involved, this assumption is quite reasonable in the present

I5-

(2)

of zero x and

the assumption

P

(for zero x

- V)

The premise expansion

basic equation

p. 213) applies

:;:I:;::-1 0

-0.5

350

c

0.5

IO

15

20

%

ox

25

3.3

3.5 MPa

@z

a2

Fig. 4. Mohr diagram showing the relationshlps between 0, and 5: on~ointmg and between effective and total stresses.

eqn (2) for general plain strain conditions. Accordingly, a, = -0.5 MPa; P = 2.5 x 0.4 + 0.5 = 1.5 MPa, and S_ = 5, = 2.5 (1 - 1.5/2.5) = 1.0 MPa.

Hence,

u,, - u1 = 2.5 - 1.0 = 1.5 = 5, - 5, =

(3) Lines

CT, and

3) they both

1.0 + 0.5 = 1.5 = 31).

are approximated Paleostresses,

fracture

and plume development

u, have the same slope (Fig.

follow eqn (2). Lines to have constant

1979, fig. 12.5; Watts,

u,, u,. and

uZ

slopes (Means.

1983. fig. 8).

The zigzag construction

(modified

after

Price.

The axial horizontal plumes which characterize the surfaces of sets 309” and 344” suggest that these joints developed normal to ur when a, > u,

1974, fig. 7) of lines a,, ?i: and P between h = 100 m and h = 200 m is based on the car sideration that individual plume markings confined between

(Gramberg, 1965) at depths greater than 100 m (Fig. 3). For further calculations the following assump-

the layer boundaries imply slow fractu-e propagtion (Bahat, 1987a) due to episodic pore pressure.

tions are made:

The pore pressure alternately increases. transmits stresses through the rock and causes cracking. and

(1) The Mohr diagram shows that if the angular difference of 3.5o (344’-309”) represents a

then subsides (Secor, P gradually increases

dihedral

manifested

angle,

(Y, of conjugate

hybrid

sets (which

1969). Therefore, In general. with depth, but this trend is

by a zigzag

plumes

The

real depths

(--a,) of - 57; during fracture (Fig. 4). In this analysis the application of the Griffith’s parabolic envelope (Secor, 1965) at the left side of Fig. 4 for

pths can be elucidated by following the dashed lines of 0,. S_ and P in Fig. 3. Fractures in sets 309 and 344 develop when (a)

the 35” dihedral angle is justified, as it represents the average homogeneous field of major tension

a, = - 0.5 MPa These conditions

and minor shear affecting the joint reasonably well, although it is appreciated that, in detail, jointing occurs under conditions of stress gradients (Bahat, 1987a). Here the angle of internal friction is rather large 55”. (2) If, at h = 0, T, = 0 (initially the rock has no strength), eqn (1) would require cX = 0 at that depth.

depth (Fig. 3), even though a, is still a I!ttle higher than -0.5 MPa. A small allowance for jointing at @, > 0.5 MPa is reasonable if it is considered to be a fatigue process at which fracture generally occurs under reduced tensile stress conditions (Atkinson. 1982). Other conditions of fracture at 150 m are u, = 1.5 MPa. a. = 3.8 MPa. P = 2.0 MPa. 5, = -0.5 MPa and O_= 1.8 MPa.

periodic

are not known. fracture

conditions

and (b) S_ - ??, = 57; would be approximated

but

at

which

approximate

develop

line.

produce 01 that ranges from 10” to 50”; Hancock, 1985) it would imply effective stress difference

their

and de-

(Fig. 4). at 150 m

Following fracture at 150 m, P is reduced to a, (approximate hydrostatic conditions) and a, becomes 0. Then, P gradually increases again (Secor, 1969) and when the conditions at 175 m depth approach Z’ = -0.5 MPa, and ir, - cX= 51; fracture is repeated (Fig. 4). This cyclic process repeats itself at increasing frequency with depth. However, beyond a certain fracture intensity in the rock P does not increase any more; it maintains reduced levels and fracture stops (this is schematically shown at 200 m depth in Fig. 3). The values of uv and c, are known where u,, = crZ(Fig. 3). This occurs at the depth where circular fracture markings develop at h = 100 m. The line crossing of uv and a, implies for uy conditions of superposed gravitational and horizontal tectonic stresses (Means, 1979, fig. 12.5). The magnitude of the horizontal tectonic stress uv at 0 m depth is practically determined in Fig. 3 by the above assumption (3) that uy - u, = constant.

Discussion

The present results demonstrate how jointing may occur at low differential stresses (in support of Sibson’s suggestion, 1981). The possibility that fracture may have initiated at depths shallower than 100 m should not be ruled out. This could occur under conditions of water overpressure when the tensile strength of the chalks under watersaturated conditions should have been further reduced. Hayati (1975, p. 39) observed a considerable reduction in chalk strength under the latter conditions. Fraissinet et al. (1988) estimate that fracture of chalks in the Paris Basin occurred at paleodepths of about 60 m when 6x ranged between - 0.3 and about - 0.9 MPa. The early development in Lower Eocene chalks of circular fracture markings at shallow depths by extension, which was followed by fracture of hybrid joints marked by plume morphology due to combined extension with minor shear (Leon, 1934; Muehlberger, 1961) at greater depths suggested here, coincides with rock mechanic considerations which require the increase of the dihedral angle of conjugate sets with confining pressure (and effective mean stress).

Whereas horizontal axial plumes are common on surfaces of single-layer joints in Middle Eocene chalks, circular fracture markings which require a,. = 3: are absent (Bahat, 1987a). It is therefore argued that single-layer jointing in Middle Eocene chalks occurred only under conditions of ZZ# 6,. Line a,. has a zigzag shape at the compressive side of the diagram (Fig. 3). This suggests that fracture normal to cry would not occur under the given pore pressure conditions as long as horizontal tectonic compression u, was operative. i.e., Us# a,. The implication is that single-layer joints subparallel to the fold axis (normal to a,.) could be developed only during relaxation episodes of uy. Only then would increase of pore pressure cause tensile ay. This suggestion seems to coincide with a similar conclusion by Coulon and Frizon de Lamotte (1988). They investigated hydraulic breccias which are associated with joints and concluded that “ hydrofracturing can only occur under extensional regimes”. Finally, the present study is related to weak rocks, and small differences in estimates of the tensile strength or other mechanical properties of the investigated material are, percentage-wise, quite significant. This, of course, is a shortcoming of the entire analysis. A comparison of independent estimates from different fracture provinces is therefore valuable in assessing the results. Acknowledgments

A personal communication with B. Buchbinder and G. Gvirtzman, and a review of an early version of the manuscript by Y. Mimr&n, N.J. Price and an anonymous referee, are gratefully acknowledged. A field trip with Michel Coulon to see chalk outcrops in France has contributed greatly to this study. This work was supported by the Ministry of Energy and Infrastructure Earth Science Research Administration. References Atkinson, B.K., 1982. Subcritical crack propagation in rocks: theory, experimental

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