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II. Types of Deformation Produced by Plants
MECHANICAL RESISTANCE OF SOIL
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
K. P. BARLEY AND E. L. GREACEN
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
MECHANICAL RESISTANCE OF SOIL
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
K. P. BARLEY AND E. L. GREACEN
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.