## Rat

Side resistance

Uplift uCk

Figure 7.14. Basement subject to uplift forces

Permanent wGk t 7m

In this example, the resistance from friction on the basement walls is significant. Since it is a stabilizing action, this resistance should be an 'inferior' value, which may, counter-intuitively, come from 'superior' values of soil strength. The example also considers the use of tension piles to increase the stabilizing forces. The design of the individual piles should follow the methods described in Chapter 13.

### Notes on Example 7.4

O Although a variable component of loading is identified, it is a stabilizing force and will not be used when verifying the relevant ultimate limit state. The subscript 'sup' refers to superstructure and the subscript 'sub' refers to substructure.

© There are no variable destabilizing actions, so only the 1.1 factor is used on the permanent component. The variable component of the stabilizing force is not included.

© The value of pk (= 0.113) is the product of the characteristic earth pressure coefficient Kak (= 0.238) and the characteristic coefficient of interface friction tan 5k (with 5k = 25.3°). Both Ka and 5 depend on 9.

© When tan 9 is divided by the partial factor y9, the design angle of shearing resistance becomes = 32°. This increases the value of Ka to 0.307 but decreases the value of 5k to 21.3°, resulting in a larger value of p (= 0.12). This is a less severe condition than for characteristic conditions (see ©).

© This value of p is calculated from the superior value of 9ksup (= 45°), divided by a superior partial factor Y9,sup (= 0.8), producing 9d = 51.3°. This decreases the value of Ka to 0.123 but increases the value of 5k to 34.2°, resulting in a smaller value of p (= 0.084). This is more severe than for © and © and hence will be used for design.

© The design resistance for the one-storey basement is verified. The traditional global factor of safety is 1.22.

© The design resistance for the two-storey basement is not verified. The traditional global factor of safety is 0.83.

© Additional resistance may be provided by piles. The horizontal effective stress o'h acting on the piles is calculated from o'h = Kso'v , where o'v is the vertical effective stress along the pile. For simplicity, we have assumed Ks is independent of material properties.

© The value of design resistance for the UPL limit state is calculated by applying a material factor (y9 = 1.25) to the tangent of the characteristic angle of interface friction between the soil and the pile 5k. In this instance, 5k should be an inferior value (since this minimizes the pile resistance). It could be argued that the design resistance should be treated as a stabilizing action, in which case the characteristic resistance would be multiplied by YG,stb = 0.9. If this approach was adopted, it would be less conservative than the approach we have adopted in these calculations.

® With the addition of piles, the design resistance of the two-storey basement is now verified. The traditional global factor of safety is 1.29.

Example 7.4 Basement subject to uplift Verification of stability against uplift (UPL)

One-storey basement

### Design situation

Consider a three-storey building which applies a self-weight loading at foundation level estimated to be wGk = 30kPa (permanent) and carries imposed loads on its floors and roof amounting to qQk = 15kPa (variable). The building is to be supported by a one-storey basement of width B = 18m and depth D = 4.5m. The basement walls are tw = 400mm thick, its floors tf = 250mm thick, and its base slab tb = 500mm thick. The characteristic kN

weight density of reinforced concrete is yck = 25-, as per EN 1991-1-1.

The ground profile comprises 20m of dense sand and groundwater levels are kN

close to ground level. The sand's characteristic weight density is yk = 19-, m its angle of shearing resistance ^ = 38°, and its 'superior' angle of shearing resistance ^ sup = 45°.The weight density of water should be taken as kN

Actions

The characteristic water pressure acting on the underside of the basement is Yw uk = Ywx D = 44.1 kPa, giving a resultant destabilizing action underneath the kN

basement of UGk = ukx B = 795-. Characteristic actions from the kN

super-structure are WGk sup = wGk x B = 540-(permanent) and m kN

Characteristic self-weight of the sub-structure (basement) is:

m kN

from the floors W^ f = tf x ( B - 2tf) x yck = 109.4-

from the base slab W^ b = tb x ( B - 2tf) x Yck = 218.8-

m kN

total weight %k,sub = WGk,w + WGk,f + WGk,b = 418~°

Total self-weight of the building is W^k = W^k sup + W^k sub = 958-.

Effects of actions

Partial factors on destabilizing permanent and variable actions are YG dst = 1.1 and yq dst = 1.5 and on stabilizing permanent actions

Yg stb = 0.9 . Thus the destabilizing vertical action is kN

Vd dst = YGdst x ^Gk = 874.1-and the stabilizing vertical action m kN

Vd,stb = YG,stbx WGk = 862 [email protected] Material properties

The sand's characteristic angle of shearing resistance is fk = 38°, giving an

active earth pressure coefficient Kak ---,—r = 0.238 and a

wall friction 5k = — fk = 25.3°. Thus Pk = Ka ktan(ôk) = 0.113 ©.

The partial factor on the coefficient of shearing resistance Ym = 1-25 gives a design angle of shearing resistance fd = tan f

active earth pressure coefficient increases to Kaj =--,—r = 0.307

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