UkM rw h d yw d j

d, since this is a permanent dest d,dst = Yg,dstYw (y + dj = Yg,dstYw (( + 1)d and, since this is a permanent destabilizing action, its design value is:

The characteristic vertical total stress acting on the same plane is:

,stb = Ykd and, since this is a permanent stabilizing action, its design value is:

Substituting these expressions into ud dst < od stb and simplifying produces:

Yg s

Yg d

1. For this situation, we conclude that the partial factors specified for limit state HYD are equivalent to a global factor of 3.0 on the critical hydraulic gradient icrit. Thus for the same situation, the verification based on pore pressure and total stress is more onerous than the one based on seepage force and submerged weight.7

The total stress approach gives a traditional factor of safety of 3, which is within the range of values (1.5-4.0) suggested in the literature, whereas the seepage force approach gives a safety factor of 1.5, which is at the lower limit of the traditionally recommended values. (Note that, to avoid piping, the characteristic hydraulic gradient should be even smaller than calculated here — see Section 7.5.3.) This demonstrates the problem that, when net forces or pressures are used (as in the seepage force approach), an unintended reduction in reliability can result. We recommend using gross forces and pressures (as in the total stress approach) wherever possible.

7.5.2 Internal erosion

Internal erosion — within a soil stratum, at the interface between strata, or at the soil-structure interface — occurs when large hydraulic gradients carry particles away. If the erosion continues, collapse of the structure follows.

Filter protection at the ground's free surface and suitable filter criteria must be used to prevent internal erosion and to minimize material transport. Non-cohesive soils that satisfy the filter criteria should be used and, in some cases, in multiple layers that ensure a stepwise change in particle size distribution. EN 1997-1 does not provide detailed rules for filter design, for which the reader should refer to any well-established text on the subject.8

If the filter criteria are not satisfied, Eurocode 7 requires verification that the design value of the hydraulic gradient id is 'well below' the critical hydraulic gradient, taking account of the direction of flow, the grain size distribution and shape of grains, and stratification of the soil.t [en 1997-1 §10.4(5)P and (6)P]

In other words:

Regrettably, Eurocode 7 does not give a partial factor for determining id, but based on previous experience this should be at least equal to 4.0.

In order to reduce the potential for particles to be moved through filter materials, much lower design hydraulic gradients are required to resist internal erosion than to resist heave.

7.5.3 Piping

Piping is a form of internal erosion that begins, for example, at the surface of a reservoir and then regresses until a pipe-shaped discharge tunnel is formed in the soil, between the soil and the foundation, or at the interface between cohesive and non-cohesive strata. Failure occurs when the upstream end of the eroded tunnel reaches the bottom of the reservoir.

Areas susceptible to piping must be inspected regularly during periods of extremely unfavourable hydraulic conditions, such as floods, so that t§10.4(5)P wrongly says 'it shall be verified that the critical hydraulic gradient is well below the design value of the gradient at which soil particles begin to move' — this is a known error that will be corrected in a future corrigendum.

measures can be taken immediately to mitigate the conditions (using materials stored in the vicinity).

Prevention of piping must be achieved by providing sufficient resistance against internal soil erosion in the areas where water outflow may occur. Joints or interfaces between the structure and the ground, which may provide preferential seepage paths, must be considered when determining hydraulic conditions in those outflow areas.

Piping is a special case of internal erosion and is of particular significance in the design of embankment dams and/or dams founded on granular fine soils. It is extremely important that hydraulic gradients and the potential for seepage to concentrate in particular areas of the structure is avoided. To mitigate against such problems, careful control of the earthworks is required and seepage paths should be controlled using suitably permeable materials and carefully designed and constructed filter drainage systems.

7.6 Summary of key points

Limit states EQU, UPL, and HYD involve failure of the ground due to an imbalance of forces when the resistance of the ground does not govern.

Verification of these limit states is demonstrated by ensuring:

Ed ,dst — Ed ,stb + Rd where Ed,dst = destabilizing design effects of actions, Edstb = stabilizing design effects, and Rd = design resistance.

The differences between ultimate limit states EQU, UPL, and HYD are determined by which terms dominate the equation above. In EQU, the resistance is of minor importance; in UPL, only vertical actions are considered; and HYD focuses on microscopic rather than macroscopic stability.

7.7 Worked examples

The worked examples in this chapter look at the static equilibrium of a wind turbine subject to wind loads (Example 7.1); equilibrium of a double-walled cofferdam subject to water loads (Example 7.2); uplift of a box caisson (Example 7.3); uplift of the basement of a buried structure (Example 7.4); hydraulic stability of a weir (Example 7.5); and piping due to heave of an embedded retaining wall (Example 7.6).

Specific parts of the calculations are marked O, ©, ©, etc., where the numbers refer to the notes that accompany each example.

7.7.1 Wind turbine

Example 7.1 considers the foundation design for the wind turbine9 shown in Figure 7.10, which is subject to a permanent vertical force VGk and imposed variable horizontal force HQk and moment MQk. The base, which is square on plan, is set at a depth D below ground surface.

Magnel Diagram

The vertical loads are relatively low, resulting in small bearing pressures. Because the turbine is sitting on rock, the bearing resistance of the ground will be high. This example is therefore likely to be governed by the EQU limit state, since the properties of the ground are insignificant to the stability of the wind turbine.

Notes on Example 7.1

O Strength and stiffness properties are not relevant in limit state EQU in this example.

© The self-weight of the foundation (concrete and backfill sitting on it) is a stabilizing permanent action. The other stabilizing action is the self-weight of the turbine, VGk.

© Pore water pressures acting on the underside of the foundation are destabilizing. Here we take a conservative estimate of ground water level (at ground level) and treat the uplift force as a permanent action. Alternatively, a lower water table could be assumed and some component of the uplift force considered variable.

© Partial factors > 1.0 are applied to destabilizing actions (thereby increasing their design values) and factors < 1.0 are applied to stabilizing actions (decreasing their values) . Stabilizing variable actions are ignored.

© The design destabilizing moment comprises: 1) the moment caused by the variable horizontal action HQk multiplied by the distance D of its point of action from the foundation base; 2) the moment applied at the top of the foundation; and 3) the moment owing to uplift from ground water.

© The stabilizing moment is a function of the foundation weight WGk and the imposed load from the turbine VGk, multiplied by their lever arm B/2.

© The design destabilizing moment is more than the design stabilizing moment (degree of utilization > 100%), which means that this design does not meet the requirements of EN 1997-1.

© IEC 61400 is a commonly used design standard for wind turbines. A key difference from Eurocode 7 is that it applies a single partial factor to permanent and variable destabilizing loads.

© The original calculation on which this Example 7.1 is based treats the uplift from groundwater as a negative stabilizing force, rather than as a positive destabilizing force. Combined with lower partial factors, IEC 61400 implies the design is satisfactory and hence some power engineers may regard the design to EN 1997-1 as too conservative.

® The traditional lumped factor of safety for this foundation is 1.17 if the water thrust is treated as a destabilizing force, and 1.32 if is treated as a negative stabilizing force. The perceived safety of the structure clearly depends on the assumption made about the effect of water pressures.

Example 7.1 Wind turbine Verification of stability against overturning (EQU)

Design situation

Consider the foundation of a wind turbine, which is required to carry imposed forces in two directions, vertical VGk = 2000kN (permanent) and horizontal

HQk = 1500kN (variable), and an imposed moment MQk = 50000kNm

(variable), all of which act at the top of the foundation.

The base is square with width B = 15m at its bottom and b = 5.5m at its top. The narrowest part of the base has thickness t = 1500mm and the widest part T = 600mm. The underside of the foundation is at depth D = 3.0m. The kN

characteristic weight density of reinforced concrete is Yck = 25-(as per m

EN 1991-1-1 Table A.1). The backfill that sits on top of the base has kN

characteristic weight density Ykf = 1®-. Groundwater is at ground level m kN

with characteristic weight density Yw = 9.81-. V


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