Pullout resistance of horizontal plate anchors was first investigated by Balla (1961). Turner (1962), Bakar and Kondar (1966), Matsuo ((1967) conducted scale model experiments to understand dimensional analysis to derive ultimate uplift load (Qu) for circular plate anchors. The large number of experimental investigations were carried out by Bemben & Kupferman (1975), Das and Seeley (1975), Das (1978), Rowe and Davis (1982), Clemence (1983), Datta and Sing (1984) Das et.al. (1985), Chattopadhyay and Pise (1986), Barua & Chattopadhyay (1989), Ghaly et al (1991), Ghaly & Hanna (1994), Rao & Kumar (1994), Sharma & Pise (1994) Handojo & Chang (1997), Shankar et al (2007), Kumar and Kouzer (2008).
Many analytical and experimental studies have been accomplished in this area notably by Mors, H. (1959), Mayerholf & Adams (1968), Vesic (1971), Clemence & Veesaert (1977), Saeedy (1987), Das (2007), Deshmukh & Chaudhary (2010), Das & Shukla (2013).
The installation of anchor plates depends on the direction of load applied. Anchor plates may be horizontal to resist vertically-directed uplifting load, inclined to resist axial pullout load, or vertical to resist horizontally-directed pullout load. The process of installing an anchor plate is tedious and not an easy task compared to helical but still has wide applications in geotechnical engineering. During the installation process, the soil should be excavated to the required depth and then backfilled with good soil after placing the anchor plate.
Anchors can be installed by excavating the ground or by drilling/driving to the required depth and then backfilling and compacting with good quality soil this type is referred to as backfilled plate anchors. In many cases, plate anchors may be installed in excavated trenches. These anchors are then attached to tie rods which may either be driven or placed through augured holes, anchors placed in this way are referred to as direct bearing plate anchors.
Anchor plates are categorized based on two aspect:
I. According to shape
II. According to application.
1. According to shape
Soil anchors are installed in different shape like circular (axisymmetric plates), square & rectangular. The shape is determined based on bearing capacity of anchor plates and the inflicted tension against the soil in which it is located. These anchors are then attached to tie rods which may either be driven or placed through augured holes in to the ground.
2. According to Application
Anchor plate may be horizontal to resist vertically-directed uplifting load, inclined to resist axial pullout load, or vertical to resist horizontally-directed pullout load, as shown in Figure
A. Balla’s Theory
Based on some early theories with subsequent variations, Balla (1961) suggested for shallow circular anchors, that the failure surface in soil will be as shown in Fig. 2.4. Where aa’ and bb’ are the arc of the slip surface. The radius (r) of this arc is equal to,
r =\(\frac{H}{\text{sin}(45+\frac{\varPhi }{2})}\)
The angle α is equal to (45 – Φ/2).
Balla proposed the net ultimate uplift capacity of the anchor is the sum of two components: (a) weight of the soil in the failure zone and (b) the shearing resistance developed along the failure surface.
Qu =\(\gamma {H}^{3}\left[{F}_{1}\left(\varPhi ,\frac{H}{D}\right)+{F}_{3}\left(\varPhi ,\frac{H}{D}\right)\right]\),
Where, the sum of the function F1 and F3 are obtained by figure given below
The breakout factor Nq is defined as,
Nq =\(\frac{{Q}_{u}}{\gamma A H}\)
Where,
A = Area of the plate anchor.
The breakout factor increases with H/D ratio up to Nq* at H/D(cr). Based on Balla’s method, the shallow anchor plates are defined at H/D ≤ H/D(cr) and deep anchor plates at H/D ≥ H/D(cr).
B. Saeedy's Theory
An ultimate holding capacity theory for circular plate anchors embedded in sand was proposed by Saaedy (1987) in which the trace of the failure surface was assumed to be an arc of a logarithmic spiral.
According to Saeedy (1987), during the anchor pull out the soil located above the anchor gradually becomes compacted, in turn increasing the shear strength of the soil and, hence, the net ultimate uplift capacity. For that reason, he introduced an empirical compaction factor which is given in the form.
$${\mu }=1.044{D}_{r}+0.44$$
Where,
\({D}_{r}\) = relative density of compaction
µ = compaction factor
Thus, the actual net ultimate capacity can be expressed as
\(\) \({Q}_{u\left(actual\right)}=\left({F}_{q}\gamma AH\right){\mu }\)
C. Meyerhof and Adam’s Theory
Meyerhof and Adams (1968) proposed a semi theoretical relationship for estimation of the ultimate uplift capacity of strip, rectangular and circular anchors. It needs to be pointed out that this is the only theory presently available for estimation of Q for rectangular or square anchors. The principles of this theory can be explained by considering a shallow strip anchor embedded in sand as shown in Fig.
The angle α depends on several factors such as the relative density of compaction and the angle of friction of the soil, and it varies between (90° - Φ/3) to (90° − 2Φ/3).
Here, following forces are the reason for ultimate uplift capacity,
a) The weight of the soil, W = Ƴ * 1 * B * H (for unit length), and
b) The passive force Pp' per unit length along the faces ab and cd. The force Pp' is inclined at an angle α to the horizontal. For an average value of α = 90 - Φ/2, the magnitude of δ is about (2/3) Φ.
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For strip anchors, the area A per unit length is equal to 1 x B = B. So (from Das and Seeley, 1975),
Qu =\(W+{K}_{u}\gamma {H}^{2}\text{tan}\varPhi\)
Where,
Ku = Nominal uplift coefficient (Ku tan Φ = Kph tan δ)
Kph = Horizontal component of the passive earth pressure (Pp’)
The variation of the nominal uplift coefficient Ku with the soil friction angle Φ is shown in Fig. 8
Qu =\(W+\frac{\pi }{2}{S}_{F}\gamma D{H}^{2}{K}_{u}\text{tan}\varPhi\)
Where,
SF =\(1+m\frac{H}{D}\)
m = Coefficient which is a function of the soil friction angle Φ shown in Fig.
The breakout factor Nq can be derived from following Equation,
Nq =\(\frac{{Q}_{u}}{\gamma A H}\)
So, Nq =\(1+2\left[1+m\left(\frac{H}{D}\right)\right]\left(\frac{H}{D}\right){K}_{u}\text{tan}\varPhi\)
Qu =\(W+\gamma {H}^{2}\left(2{S}_{F}B+L-B\right){K}_{u}\text{tan}\varPhi\)
Nq =\(1+\left\{\left[1+2m\left(\frac{H}{B}\right)\right]\left(\frac{B}{L}\right)+1\right\}\left(\frac{H}{B}\right){K}_{u}\text{tan}\varPhi\)
Experimental observations of Meyerhof and Adams on circular anchors showed that the magnitude of SF * Ku = [1 + m (H/h)] * Ku for a given friction angle Φ increases with H/B to a maximum value at H/B = (H/B)cr and remains constant thereafter. This means that, beyond (H/B)cr, the anchor behaves as a deep anchor. These (H/B)cr values for square and circular anchors are given in Fig. 10
D. Veesaert and Clemence's Theory
Based on laboratory model tests results, Veesaert and Clemence (1977) suggested that for shallow circular anchors the failure surface at ultimate load may be approximated as a truncated cone with an apex angle as shown in Fig. 11. With this type of failure surface, the net ultimate uplift capacity can be given as under
$${Q}_{u}= \pi \gamma {K}_{0}\left(tan\varphi \right)\left({cos}^{2}\frac{\varphi }{2}\right)[\frac{{H}^{3}\text{tan}\left(\frac{\varphi }{2}\right)}{3}+\frac{h{H}^{2}}{2}]$$
Where,
V = volume of the truncated cone above the anchor
\({K}_{0}\) = coefficient of lateral earth pressure
$$\text{V}= \frac{\pi \text{{\rm H}}}{3}\left[{h}^{2}+{\left(h+2Htan\frac{\varphi }{2}\right)}^{2}+\left(h\right)\left(h+2Htan\frac{\varphi }{2 }\right)\right]$$
$${F}_{q}=\left\{4{K}_{0}\left(tan\varphi \right){(cos}^{2}\frac{\varphi }{2}\right){\left(\frac{H}{h}\right)}^{2}\left[\frac{0.5}{\frac{H}{h}}+ \frac{tan\frac{\varphi }{2}}{3}\right]\}$$
+\([4+8\left(\frac{H}{h}\right)tan\frac{\varphi }{2}+5.333{\left(\frac{H}{h}\right)}^{2}{tan}^{2}\frac{\varphi }{2}\)] --Eq. (1)
\({F}_{q}=\frac{{Q}_{u}}{\gamma AH}\) --Eq. (2)
Veesaert and Clemence (1977) suggested that the magnitude of K may vary as 0.6 to 1.5 with an average value of about 1.
Figure shows the plot of \({F}_{q} vs \frac{H}{h}\) with\({K}_{0}=1\). In this plot it is assumed that (\({H/h)}_{cr}\) is the same as that given by Meyerhof and Adams (1968).
E. Mor’s Theory (Soil Cone Method)
Some research to determine uplift capacity of anchor plate Qu has been done only on shallow circular plate anchor in earlier cases by Mors (1959), Downs & Cheiurzzi (1966) and other researchers. Mors (1959) proposed that the failure surface in soil at ultimate load may be approximated as a truncated cone having an apex angle of θ = 90° + Φ/2 shown in Fig. 2.1. Later, Downs & Cheiurzzi suggested that the apex angle θ may be equal to 60° shown in Fig. 2.2.
The net ultimate uplift capacity can be considered equal to the weight of the soil located inside the failure surface. So,
Qu = Ƴ * V
Where,
Ƴ = Unit weight of soil
V = Volume of soil in truncated cone,
h = Diameter of anchor plate
For Downs & Chieurzzi theory,
V =\(\frac{\pi }{3}{H}^{3}\left\{{h}^{2}+{\left[h+2H\text{cot}60\right]}^{2}+h\left(h+2H\text{cot}60\right)\right\}\)