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II. Types of Deformation Produced by Plants

II. Types of Deformation Produced by Plants

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to allow a root or shoot to grow. Differences in scale are also important:

the engineer deals with stresses acting over areas of square meters and

can employ a statistical concept of stress; in plant studies we are concerned with areas of the order of one square millimeter, and the plant

organ is often commensurate in size with the structural or mechanical

elements of the soil.



One manifestation of tensile failure is the rupturing of soil crusts by

emerging shoots. An appropriate measure of the strength of crust materials being deformed in this way is the modulus of rupture (Carnes,

1934). The force required to rupture the crust depends on the dimensions

of the ruptured plates, and emergence should be related to this force

rather than to the modulus itself. Arndt (1965) points out that rupture

of the surface crust can be followed by jamming of the broken plates of

soil (Fig. l a ) , This increases the force required for emergence.

FIG. 1. ( a ) Examples of soil deformation by emerging seedlings. The surface

seal has cracked naturally, or been ruptured by the plant, with the plates subse(a' + z')"'. ( b ) Shear failure

quently jamming. Jamming occurs when a + dl d'

in the form of an inverted cone. (From Arndt, 1965.)

+ <

Roots can also rupture soils by tensile failure. Barley et al. (1965)

observed that radicles of peas, Pisum sutivum L., 2 mm. in diameter,

were able to split cores of compact loam (Fig. 2 ) . In contrast, the thinner

(0.3 mm. diameter) radicles of wheat, Triticurn aestivurn L., formed

channels in cores of compact loam, but the bursting force was not great

enough to rupture the cores.

Rupturing may involve either general or local tensile failure. When





5 cm.

FIG.2 . Tensile failures produced in a core of compact loam by pea radicles.

(From Barley et al., 1985.)

a failure is general, by definition, it spreads to a soil boundary; in local

failure the tension cracks do not extend to the boundary but are accommodated by compression of the soil.



Besides failing under tension, soils also fail under shearing stresses

imposed by plant organs. Terzaghi (1943, p.119) describes general

shear failure in soils under shallow foundations. In Terzaghi’s model the

soil compresses little with increasing application of the load until a

critical load is reached, when the soiI fails completely. Failure takes

place on a sliding surface described by a plane and a logarithmic spiral.

The load that the soil will support depends on the strength parameters,


apparent cohesion, c, and the angle of internal friction,


The kind of failure described by Terzaghi has been observed when

roots first penetrate saturated clay (Cockroft, unpublished data). An

example of general shear failure caused by seedling emergence has been

given by Arndt (1965) (Fig. l b ) ; the soil fails along the surface of an

inverted cone having its apex at the top of the seedling,




In unsaturated compressible soil much of the volume increase of the

growing plant organ may be accommodated by compression, and the



zone of shear failure in which the stresses are in “plastic equilibrium”

(Terzaghi, 1943, p.23) may frequently fail to spread to a soil boundary.

When this is so we speak of “local shear failure.” Examples of local shear

failure with compression caused by growing roots have been given by

Barley (1954, 1963). Roots were shown to have compacted coarse textured media for a radial distance of several millimeters around the root.

The volume of the cores in which the roots were grown remained constant. Shear, together with compression, is probably the most common

way in which growing plant organs deform ordinary, unsaturated soils.

In saturated clay plant organs may form channels by consolidation

together with shear failure. If the volume of the root is accommodated

without displacing the boundaries of the clay, as water and clay are

only slightly compressible, water must be either absorbed by the penetrating root or drained through an outer boundary of the clay. This

process, by definition, involves consolidation ( Terzaghi, 1943, p.265) ,

but, as a hole is being formed, shear failure must also occur.

The process described above differs from one-dimensional consolidation as met in engineering practice. In one-dimensional consolidation the

consolidating axial stress, ul,and the resulting radial stress, us,are not

in plastic equilibrium but are related by the expression u3 = K,u,, where

KO is the coefficient of earth pressure at rest. For medium-textured soils

with 9 = 40°,K Oz 0.5, and for clays with lower values of 9, K O varies

from 0.6 to 1.0. When consolidation is accompanied by shear failure the

two stresses are related by the coefficient of active earth pressure, K ,

(Terzaghi, 1943, p.50); K , is as low as 0.2 for coarse-textured soils but

can approach 1.0 for clays.


Forces Required to Deform Soils


1. Tensile Failure

General tensile failure of surface crusts is commonly treated in terms

of elasticity theory. In the modulus of rupture test the force, F , required

to rupture a slab of length a, width b, and thickness z, for single-center

point loading is given by

and for two-point loading at a / 3 and 2 a/3 by



where up is the tensile strength of the soil. Analyses of tensile failure for

more complicated configurations are available in the theory of elasticity

( Timoshenko and Goodier, 1951) .

The tensile rupture of bulky structures can also be described theoretically. Applying a spherical model, the zone of plastic equilibrium around

the base or point of a probe can be treated as a pressure bulb of radius R

(see Section 111, A, 3 ) . The radial pressure at R, u ~will


burst a soil clod

if the cross-sectional area of the structural element is such that tensile

resistance is less than the force developed over the cross section of the

pressure bulb. Whether a clod will fail in tension depends then on the

magnitude of uR,the tensile strength of the soil uT,and on the size of the

clod. If rupture occurs during radial enlargement rather than during

penetration a cylindrical model should be used.

Local radial cracks may develop either around individual roots or between adjacent root channels (Fig. 2 ) . Using either a spherical or cylindrical model, the tangential stress U t , which reaches a maximum at R,

closely approaches the tensile strength of the soil. Where the plastic zones

of adjacent roots overlap v(Tt is increased, and local rupture is likely to


2. Shear Failure without Compression

The conventional description of forces acting on the base of a pile

or probe (Terzaghi, 1943) shows that the bearing capacity qp of a

shallow ( z = d ) foundation, of depth z and width d, failing in general

shear, is given by

qp = cNc

+ P Z N ,+ pdN,


where c = apparent cohesion, p = bulk density, and N,, N,, Np =

bearing capacity factors.

The values of the bearing capacity factors depend only on the angle

of internal friction, When saturated clays are distorted with negligible

drainage, the strength of the clay is not altered by an applied load since

the load is carried by the pore water (see Section 111, C, 1). Shear

strength is then determined solely by c, and the soil is called a frictionless or = 0 soil. For circular shallow footings in saturated undrained

clay qpz 7.5 c. According to Terzaghi’s model qp increases continuously

with x. This relation applies to rough probes entering saturated “undrained” clays, the requirement of the “undrained condition being met

either because the clay is so impermeable that it fails to consolidate, or

because the rate of loading or penetration is so high that there is time

for only a negligible amount of consolidation.



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