2. Burmister’s Two-Layered
System Theory
• Donald M. Burmister developed the two layer
theory in 1943.
• As known the flexible pavement sections are
composed of layers.
• The effect of layers above subgrade is to
reduce the stress and deflections in the
subgrade.
• And elastic modulus of the top layer is the
highest.
3. • He considered the pavement as an elastic
layer resting on a semi-infinite elastic
subgrade.
• If layers of soil subgrade, sub-base course and
base course are assign elastic modulii of Es, Esb
,Eb. It is considered in this theory Eb < Esb < Es
• Vertical stress depends on the modular ratio
(i.e., E 1 / E2 ).
• Vertical stress decreases considerably with
increase in modular ratio.
4. • For example, for a/h1=1 and E1 / E2 = 1, σz at
interface = 65% of contact pressure for a/h1=1
and E1 / E2 = 100, σz at interface = 8% of
contact pressure.
5.
6. Assumptions made in
Burmister's two-layered system
• The soils of each of two layers are
homogeneous, isotropic, and linearly elastic.
• The upper layer (layer l) is weightless and is of
infinite extent in the horizontal direction, but
of finite thickness. The lower layer (subgrade)
is infinite in extent both horizontally and
vertically downward.
7. • Boundary conditions
(a) the surface of the upper layer is free of normal
and shearing stress outside the limit of the loading
area.
(b) at infinite depth the stresses and displacements in
the subgrade are equal to zero.
• The solution of the two-layer problem satisfies the
continuity condition of stress and displacement across
the interface between the upper and lower layers, i.e.
at the interface, the normal and shearing stresses and
the vertical and horizontal displacements are equal in
the two layers.
• The value of the Poisson's ratio is 0.5.
8. Vertical Surface Deflection
in a Two layer System
• Burmister (1958) developed a chart for
computing vertical surface deflection in a two-
layer system.
• The deflection factor, F2, is obtained from the
chart based on the values of a/ h 1 and E 1 /
E2 .
• Then the deflection is computed from the
following equations: –
Deflection under a flexible Plate =
9. • Deflection under a rigid Plate =
• Where E2 is the modulus of lower layer
(subgrade) and F2 is called the deflection factor
which is dimensionless and is a function of both
ratio of the modulus of elasticity of the subgrade
to that of the pavement and the depth to bearing
radius ratio.
• Below chart shows values of F for various depth
ratios and modulii of elasticity.
• The deflection factor F2 is introduced in two
layered system which is dependent on h/a and
Es/ Ep.
12. • It is observed from figure that the vertical
stress on the subgrade is reduced from 70 to
30 percent by introducing a pavement layer of
thickness equal to radius of the load or h = a,
having elastic modulus 10 times higher than
the elastic modulus of subgrade soil i.e., for
Ep/ Es = 10.
• Burmister approach therefore utilises the
reinforcing action of the pavement layer.
