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Strengthening the Soil Engineering Characteristics by Using Anchors During an Earthquake Impact
B.Sc., M.Sc., Ph.D., F.G.S., Lecturer, Laboratory of Soil Mechanics and Foundation Engineering, Geotechnical Engineering Division, Department of Civil Engineering, Aristotle University of Thessaloniki, Thesssaloniki, Greece |
ABSTRACT
The varied topographic features of the earth's surface are possible only because the shear strength of the soil or rock exceeds shearing stresses imposed by gravity or other loading. Factors leading to instability can generally be classified as (1) those causing increased stress and (2) those causing a reduction in strength. Factors causing increased stress include increased unit weight of soil by wetting, added external loads such as buildings, steepened slopes either by natural erosion or by excavation and applied shock loads such as seismic forces. Loss of strength may occur by adsorption of water, increased pore pressures, shock (due to earthquake) or cyclic loads, freezing and thawing action, loss of cementing materials, weathering processes and strength loss with excessive strain in sensitive clays.
Confronted with these slope stability problems, a suitable ground improvement method is needed. Anchorage is one of the alternatives. The soil strength can be improved by introducing locally separated reinforcing elements such as anchors. The soil reinforcement implies ground anchors which are used in all types of rock and soil, strengthening their engineering characteristics.
For these reasons slope stability was analyzed, with plane or circular failure during an earthquake impact (shock load) with and without application of anchoring force.
KEYWORDS: slope stability, improvement, anchors, seismic stress, strength.
INTRODUCTION
The rate of slide movement in a slope failure may vary from a few millimeters per hour to very rapid slides in which large movements take place in a few seconds. Slow slides occur in soils having plastic stress-strain characteristics where there is no loss of strength with increasing strain. Rapid slides occur in situations where there is an abrupt loss of strength, as in liquefaction of fine sand or a sensitive clay. Many slopes exhibit creep movements (a few millimeters per year) on a more or less continuous basis as a result of seasonal changes in moisture and temperature. Such movements are not to be confused with a shear failure.
Examples include slopes of complex geology or badly weathered slopes where the varied materials and their strength cannot be readily identified.
Slopes involving heavily overconsolidated clays and shales (recoverable strain energy) of stiff fissured clays (i.e. Oxford clay) are difficult to be analyzed (Beene, 1967).
Conclusively the difficulty of slope's analysis increased as:
(1) the complexity of slope's geomorphology is increased
(2) the homogeneity of slope's material (rock or soil) is decreased
(3) the number of micro or macro-fractures of rock or soil mass is increased.
Slopes that may be analyzed include natural slopes, slopes formed by excavation through natural materials, and artificial embankments.
The most common methods of slope-stability analysis are based on limit equilibrium. In this type of analysis the factor of safety with regard to the slope's stability is estimated by examining the conditions of equilibrium when incipient failure is postulated along a predefined failure plane, and then comparing the strength necessary to maintain equilibrium with the available strength of the soil. All limit equilibrium problems are statically indeterminate and, since the stress-strain relationship along the assumed failure surface is not known, it is necessary to make enough assumptions so that a solution using only the equations of equilibrium is possible. The number of type of assumptions that are made leads to the major difference in the various limit equilibrium methods of analysis (Dunn et al, 1980).
The prestressed anchors create forces of known direction and magnitude involved with the above mentioned stability conditions. These forces contribute to the stability of the superficial structure and tie together the entire complex consisting of the structure and the co-operating rock-soil medium. Anchorage, as a means of locking together the structure with the ground mass, makes it possible to choose with comparative ease on the basis of the static analysis, the magnitude, direction and load centre of the anchoring forces. These forces, incorporated into the entire system of forces acting on the structure, ensure the stability of the latter with the highest economy and efficiency. Anchorage applied in this way secures the structure against vertical displacement due to uplift, against turning over, tangential displacement along the foot, shear failure along the critical surface within the underlying strata and in move recent constructions, against seismic effect (Hobst and Zajic, 1983).
Anchoring in rock or soil is a constructive process in which prestressed components (termed anchors in this case) are embedded in the ground. The main idea is that when sliding starts to occur in the soil, the anchored metallic strips will provide complementary shear strength and therefore will stop further deformation. The anchors are inserted into boreholes drilled in advance, and are fixed at the distal end. After fixing, the anchors are usually prestressed and their exposed upper ends are fixed to heads. The structure to which the anchor heads are attached, is either one which is dependent for its stability on the anchors, or it is merely a plate, slab, bar, grid or any other structured element which distributes the stress induced by the anchor heads onto the wider surface of the rock or soil. Anchoring in the ground fulfils three basic functions:
- It establishes forces which act on the structure in a direction towards the point of contact with the rock or soil (i.e. anchoring a dam or retaining wall) (Brandl, 1985).
- It establishes stress acting on the ground (if prestressed anchorage is used) or at least a reinforcement of the rock or soil (if non-prestressed anchorage is used) through which a grid of anchors is applied.
- It establishes prestressing of the anchored structure itself.
From this point of view slope stability analysis in present work involved plane and circular failure surfaces, (usually internal strength of material and stress conditions of ground mass influence the shape of failure surface), as follows:
(a) Analysis of a general slope stability involving, lateral stresses, hydrostatic pressure, cohesion, angle of friction and weight of unstable mass.
(b) Analysis of shearing stress contributed to instability and calculation of anchoring force (prestressed).
(c) Analysis of slope stability involving the weight of unstable mass, seismic force, angle of friction and anchoring force (prestressed).
(d) Analysis of slope stability with circular plane of failure involving the weight of unstable mass, seismic force, angle of friction, cohesion with and without anchoring force (prestressed).
The final conclusion derived was that for a value of angle of slope and friction there will be a definite value of â for which the shearing stress of disturbance and anchoring force will be the maximum.
SLOPES OF FINITE HEIGHT AND PLANE FAILURE SURFACES
Plane failure surfaces often occur when a soil deposit or embankment has a specific plane of weakness. Oxford clay is an example of stiff-fissured overconsolidated clay in South of Scarborough, North-East Yorkshire area of England (Stavridakis, 1977). The movements of the slide masses in Oxford clay were translational and relatively shallow (Parry, 1988).
Also excavations into stratified deposits where the strata are dipping toward the excavation may fail along a plane parallel to the strata.
Many earth dams have sloping cores of relatively weak material compared to the shell of the dam, and a possible failure along a plane through the core should be investigated.
Methods of analysis that consider blocks or wedges sliding along plane surfaces have been developed to analyze cases where there is a specific plane of weakness, (Seed and Sultan, 1967).
Therefore 
.
Figure 1. Influence of lateral load, cohesion, friction, hydrostatic pressure on slope stability
Figure 2. Diagram of a ground slope with a hypothetical shear plane at which appears the maximum force r
 | (1) |
where g = unit weight.
For this reason (cotâ - cotá)[sin2â - sinâ · cosâ · tanÖ] 
constant
cotâ · sin2â - cotâ · sinâ · cosâ · tanÖ - cotá · sin2â + cotá · sinâ · cosâ · tanÖ = constant
therefore
or
or 
or 
or (tanÖ - 2) cotâ - cotá · (tanÖ + 2) sinâ · cosâ = 0
or 
or 
or
 | (2) |
If values of slope angle á, range between 0o and 90o and the á increases then cotá → minimum and 
increases therefore sinâ or angle â of shear stress plane
(failure plane) increases (Barron et al., 1970).
By substitution of Ö and á values to equation (2) the angle â of failure plane would be found for maximum r shear stress which contributes to instability. Finally by substitution of Ö, á and â values to equation (1) the maximum r value of shear stress would be calculated.
From the equation 
the anchoring force P can be determined for safety factor K (i.e. 1.5) of the slope of total height H, shearing force r at angle âof shearing plane.
The afore-mentioned is proved as follows:
K = factor of safety = 
where P = anchoring force and r · l = shear force per unit width for l length of shear plane.
Therefore P = K · r · l and 
or 
and 
.
INFLUENCE OF EARTHQUAKE ON SLOPE STABILITY
O = centroid of the soil block
E = seismic force, is applied through the centroid O
G = weight of the soil block
E', E" = parallel and vertical to failure plane components of E respectively
G', G" = parallel and vertical to failure plane components of G respectively
Z = anchoring force (prestressed)
á = angle of slope
â = angle of failure plane
Ö = angle of friction
Figure 3. Slope analysis assuming the application of an anchoring and seismic force.
The destructive effect of an earthquake depends on the distance from its epicentre and on the degree of acceleration of the local ground mass either in the vertical or the horizontal direction. For this reason it is necessary to know in which direction the structure is susceptible to deformation.
The use of anchoring forces in earthquake zones helps to bring about a reduction in the additional load of the surcharge induced by acceleration, since these forces, in contradiction to those associated with the mass of the structure, do not change under the influence of movement. With increasing distance of the structure from the epicentre, the horizontal component of any acceleration becomes increasingly predominant; it brings about changes in horizontal loading forces, and at the same time acts on the mass of the structure through the effect of inertia, thus producing and additional horizontal force proportional to the mass of the structure. Therefore horizontal acceleration is a greater threat to vertical structures, even though there is on lateral loading (Hobst and Zajic, 1983; Kumar, 2001; Choudhury, 2002; Choudhury and Rao Subba, 2003).
In case of a seismic activity, horizontal seismic forces are activated, in the centroids of each element i and generate instability phenomena (Figure 3).
The afore-mentioned is expressed by the following equation:
Ei = å · Giwhere Gi = weight of element and å = seismic coefficient but 
where g = acceleration of gravity and ã= acceleration of the seismic wave through the soil therefore a
general equation is formed E = å · G.
- Forces contribute to instability (sliding) are the following:
G' + E' = T where G' and E' parallel components, to failure plane, of G and E
but 
and 
or by substitution
T = Gsinâ + Åcosâ (resultant T contributes to sliding).
- Forces contribute to stability are the following:
G" - E" = T1' where G" and E" vertical components, to failure plane of G and E
but 
and 
or by substitution
- Another parameter contributes to stability is friction and especially the angle of friction.
The component T1' = OÃ = G" - E" is analyzed on AB; the triangle 
contributes to
stability as follows: 
or B'Ã = tanÖ(Gcosâ - Esinâ) or T1 = tanÖ(Gcosâ - Åsinâ) (resultant T1 contributes to stability).
Where Z is the direction and anchoring force.
If Z force will be analyzed in parallel and vertical direction to AB (failure-sliding surface)
then in triangle 
or ÄÆ = Æsinä (parallel component) or T2 = Zsinä
(resultant T2 contributes to stability).
Also the vertical component of anchoring force contributes to stability 
or T3' = cosä · Æ.
In triangle 
(Ö-angle of internal friction) 
ÇÄ = ÐÄ · tanÖ or
T3 = T3' tanÖ, T3 = Zcosä · tanÖ (resultant T3 contributes to stability).
Forces components contribute to stability | Force component contributes to instability |
T1 = tanÖ(Gcosâ - Åsinâ) T2 = Zsinä T3 = Zcosä · tanÖ | Ô = Gsinâ + Ecosâ |
Then the safety factor V is (Figure 3)
V(G·sinâ + Å·cosâ) = tanÖ·(G·cosâ - Å·sinâ) + Æ(sinä + tanÖ·cosä) but 
V(G·sinâ + E·cosâ) = tanÖ·(G·cosâ - Å·sinâ) + Æ[sin(90-Ö) + tanÖ·cos(90-Ö)]
V(G·sinâ + Å·cosâ) = tanÖ·(G·cosâ - Å·sinâ) + Æ(cosâ + tanÖ·sinÖ)
V·G·sinâ + V·E·cosâ = tanÖ·G·cosâ - tanÖ ·E·sinâ + ÆcosÖ + ÆtanÖ ·sinÖ
but E = å · G so V·G·sinâ + V·å·G·cosâ = tanÖ·G·cosâ - tanÖ·å·G·sinâ + ÆcosÖ + ÆtanÖ·sinÖ
| G[V(sinâ + åcosâ) - tanÖ(cosâ - å·sinâ)] = ÆcosÖ(1+tan2Ö) | (3) |
the triangle 
is the sliding block so F = F1 - F2 or
 | (5) |
where Z is anchoring force.
The value of anchoring force Z = max can easily be determined by differentiating the following equation for r with respect to â
where ã, Ç, Ö are constant.
V·cotâ·sinâ - V·cotâ·sinâ + V·å·cotâ·cosâ - V·å·cotá·cotâ - tanÖ·cotâ·cosâ + tanÖ·cosâ·cotá +
V·cosâ - V·cotá·sinâ + V·å·cotâ·cosâ - V·å·cotá·cosâ - tanÖ·cotâ·cosâ + tanÖ·cosâ·cotá +
+ tanÖ·å·cosâ - tanÖ·å·sinâ·cotá = D = constant
by differentiating the previous equation 
Finally
(6)
The value of â (angle of failure plane) for maximum anchorage force could be calculated by the substitution of å, Ö, V and á values to equation (6).
Finally by the substitution of å, Ö, V, á and â values to equation (5) the maximum value of anchoring force Z was computed.
SLOPES WITH CIRCULAR FAILURE PLANE
A) Slope sliding affected by an earthquake impact and no application of anchoring force:
- Equilibrium equation is revealed as follows:
(7)
where F = factor of safety
Gi = weight of a slice on a slope selection with circular failure plane
âi = angle of failure plane of a slice
Ei = seismic force of a slice
Ö = angle of friction
c = cohesion
li = length of shear plane of a slice
B) Slope sliding affected by an earthquake impact and application of anchoring force.
- Equilibrium equation of this slope stability problem is shown below:
(8)
to find the anchoring force 
(9)
where äi = angle of anchor's deflection from the normal to the slide surface in each slice.
The importance of the inclination (äi) of prestressed anchors and the coefficient of friction (tanÖ) along the shear surface, for the degree of prestressing needed to stabilize a slope is apparent. The effect of inclining anchors is more pronounced when the friction at the slide surface is low. However, as the angle between the prestressed anchors and the normal to the shear surface increases, the effect diminishes (Figure 4 and 5) (Subba and Kumar, 1994).
There are the following three distinct positions to be analyzed in these stability conditions (Figure 4):
Therefore equation (9) will be transformed as follows:
Figure 4. Effect of prestressed anchors on the sliding of a slope with circular failure plane.
where Z = anchoring force ZV = vertical to failure plane component of Z Zh = parallel to failure plane component of Z äi = angle of deflection of the anchoring force from the normal to the slide surface |
|
Figure 5. Distribution of anchor prestress, vectors direction of Zh components of the anchoring force and variation of angle äion a slide surface, (after Hobst and Zajic, 1983).
in equilibrium conditions
| Z = (E1- G1tanÖ) – c·l1 | (10) |
Conclusively in (1) position, cohesion c and seismic force play a vital role to slope stability condition and especially to the necessity of anchoring force.
where Ei = seismic force Gi' = Gi·sinâi Gi" = Gi·cosâi ZV= vertical component of anchoring force äi = 0 |
| where (I) = (Gisinâi + Ei·cosâi) - Zhi - cli where Zhi = 0 in slice (2) of figures 4 and 5 |
→ maximum while the parallel component Zh → 0 (Figure 4, 5 and 6).
Therefore equation (b2) will be transformed as follows:
 | (11) |
The Z maximum value can be determined by differentiating this equation for Z with respect to
Z·tanÖ + cl2= F·G2·sinâ2+ F·E2·cosâ2- G2·cosâ2·tanÖ + Å2 ·sinâ2·tanÖ
F·G2·sinâ2 + F·E2·cosâ2 - G2·cosâ2·tanÖ + E2·sinâ2·tanÖ = constant
by differentiation
F·G2·cosâ2+ F·E2·(-sinâ2) - G2(-sinâ2)·tanÖ + E2·cosâ2·tanÖ = 0
and finally
or
for equilibrium conditions
(-G2·sinâ2- Å2·cosâ2)tanÖ = G2·cosâ2 - Å2·sinâ2
(-G2·tanâ2 - E2)tanÖ = G2 - E2tanâ2
-G2·tanâ2·tanÖ - E2·tanÖ= G2 - E2tanâ2
-G2·tanâ2·tanÖ - E2·tanâ2= -G2 - E2tanÖ
 |
(12) |
By substitution of G2 (weight of slice), E2(seismic force of slice), Ö(angle of friction) to equation (12) the angle 
would be determined for Z = maximum (anchoring force). By the substitution of G2, E2, c, l2, Ö, â2 and F = (1.5-2.5) to equation (11) the maximum anchoring force could be calculated.
→ maximum.
Therefore equation (b2) will be transformed as follows:
.
The angle ä of the upper side of anchor is negative (Figure 5).
Finally 
in equilibrium conditions
Z = -G3 - E3tanÖ + cl3 or
| Z = cl3 - (E3tanÖ + G3) | (13) |
DISCUSSION AND CONCLUSION
Slope stability problems are stated below:
(1) The presence and direction of fissures (non-systematic joints), (Terzaghi, 1936).
Undrained strength (short term stability) of stiff-fissured London clay might be reduced as much as 30% by the presence of fissures.
Tests on joint surfaces (in London clay) indicate that the fracture which produced the joint virtually destroyed the cohesion of the clay and reduced the value of Ö by only 1.5o(Stavridakis, 1977).
For this reason laboratory testing for long-term stability in fissured, cohesive and overconsolidated clay, in terms of residual strength parameters will give better information than the peak values.
(2) Orientation of the failure plane, in relation to the applied forces.
(3) The development of shears in clays is accompanied by particle orientation which depends on the amount and the nature of the clay minerals present (Skempton and Petley, 1967). Studies of natural clay have shown that the principal slip “surface" consists of a band, 10-50 microns wide in which the particles are oriented with the direction of movement (Stavridakis, 1977).
Consequently, a flattened principal slip surface, where the particles have the maximum degree of orientation possesses the minimum resistance to shear, while simultaneously exhibit “residual" strength.
(4) An overconsolidated clay has been subjected to a great weight such of ice during the glacial period.
This means the presence of stored energy and the development of horizontal stresses, which may exceed the overburden pressure by 50% even more in some cases.
A detailed study of Skempton and Brown (1961) of the variation of horizontal stress with depth in London clay at Bradwell, showed that the ratio horizontal to vertical effective stress increased toward the surface from a value about 1.5 at a depth of 100ft to 2.5 at 10ft. So in shallow regions the horizontal stresses could cause failure of the clay. Bjerrum (1967) hypothesized that in plastic clays diagenetic bonds may form which inhibit the development of high lateral pressures during unloading, resulting in stored strain energy. This energy could subsequently be released if the bonds were destroyed as a result of weathering (recoverable strain energy) (Johnston and Chiu, 1984).
The above mentioned tendency for lateral expansion and a low value of residual strength, compared to the peak where they have been considered, lead to a progressive failure. In conclusion slopes involving overconsolidated clays are difficult to be analyzed especially if an earthquake impact is considered. In particular seismic stresses in overconsolidated clays release high lateral pressures resulting in a catastrophic effect.
From this point of view, slopes should always be stabilized by using prestressed anchors. Where there is any danger, for whatever reason, and the slope is locked to the ground with non-prestressed anchors, it is to be expected that prior to activation of the anchorage a partial displacement of the slope along the slip surface will occur. As a consequence of this the shear resistance of the ground is reduced, because the cohesion factor, c, is lost, and the angle of static friction is replaced by the angle of kinetic friction, Ör (gradation of residual angle of friction), which can be as much as 30% lower.
In an earthquake, the stress pattern in the rock or soil may change and this can result in an expansion of the failure zone into the surroundings of the anchor, and a reduction in the fixing strength of the latter.
In present work, analysis of slope stability with plane and circular failure surface was made with or without the application of an anchoring force. The ordinary method of slices for slip circle analysis was used. It was assumed that the resultant forces acting upon the sides of any slice is parallel to the failure surface. Also this method of slope-stability analysis based on limit equilibrium in terms of total stress. This method was extended to frictional cohesive soils with the assumption that they are homogeneous.
It was found that the angle 
of failure plane is a basic parameter of slope stability and defines the following:
a) the magnitude and direction of the shearing stress and anchoring force which contribute to instability and stability respectively.
Also the angle 
influences the inclination of ground anchors in relation to critical slip surface at different heights on the slope which governs the mobilization of shearing resistance provided by ground anchors.
b) the maximum anchoring force (prestressed) and maximum shearing stress of disturbance.
It was concluded that seismic stresses and stress conditions of an unstable mass define the stress application conditions of an anchor (prestressed or non-prestressed).
Also ground anchors located at the lower half of a slope are more critical and more effective in contributing to stability of the slope than those located at the upper half of the slope. Ground anchors located at lower part of the slope tend to develop more tensile forces than those located at upper part of the slope (Figure 5).
In relation to the above, it was assumed that improvement by using ground anchors is applicable to all types of rock and soil, improves the strength and increases the friction of the ground.
A final conclusion is that anchorage is an economic and effective ground improvement method of increasing the resistance to shear failure during earthquakes in the structures supporting vertical and horizontal loads. It increases the safety of the structure against overturning, too. Therefore anchored structures are safer from the effects of earthquakes than are unanchored structures.
REFERENCES
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