Design Example: Rectangular Balanced Foundation.

A five-storey concrete-framed office building has columns located on a regular 6 m × 6 m grid. The soil is a sandy clay with a net allowable bearing pressure, na = 150 kN/m2.
 
Loadings
The column loads are as follows:
Internal column: 2000 kN
Perimeter column: 1000 kN
Corner column: 500 kN

The imposed load may be taken to be 55% of the total load for all columns. Thus, from Fig. 10.20, the combined partial load factor γP = 1.51.

Fig. 10.20 Combined partial safety factors for dead +
imposed loads.

Size of isolated pad bases
Normal internal column foundations have been chosen to be isolated pad foundations, with an area given by

which for a square base gives plan dimensions of 3.65 m × 3.65 m. This size will be used for internal columns,  with proportionally smaller sizes for perimeter and corner columns.

The building is however built tight to the site boundary along two sides, as shown in Fig. 12.9. To keep foundations within the site boundary, the four columns adjacent  to the corner will share a combined base.
The base  will be designed as a rectangular balanced foundation  in order to minimize bearing pressures and differential  settlements.

Fig. 12.9 Rectangular balanced foundation design example.

Size of combined base
Superstructure total load, ∑ P = 2000 + 1000 + 1000 + 500 = 4500 kN

Taking moments about grid line 2 to calculate the distance of the centroid of the column loads from this grid line,

Similarly, by symmetry, Y = 2.0 m.

To achieve a balanced foundation, it is necessary to provide a base whose centre of gravity coincides with the centroid of the applied loads. The distance, in either direction, from the centroid of loads to the site boundary edge of the base  is 6.5  − X = 4.5 m: therefore if the opposite edge is like- wise located 4.5 m from the centroid of loads, the two will coincide. Thus a 9 m × 9 m base will provide a balanced foundation in this situation.

The base will only remain exactly balanced if all four columns have the same level of imposed loading. From a foundation point of view this is unlikely to be critical unless extreme variations in the distribution of imposed loads occur. Where such variations are expected, these should be designed for as a separate load case.

Bearing pressure 
The actual bearing pressure will be equal to

The value of p (= 56 kN/m2) indicates that, although the  balanced foundation would limit differential settlement between the four columns sharing the base, it would not, for this particular building example, reduce differential  settlements between columns on this base and those on adjacent bases. Adjacent bases would be sized to give bearing pressures close to the allowable value of na = 150 kN/m2.

The superstructure would therefore be required to accom- modate the differential settlement between the combined corner base and the adjacent isolated bases. If it is unable  to accommodate these differential settlements, the bearing pressure on the balanced foundation could be increased, within limits, by turning the foundation into a holed balanced foundation. In this particular example this would involve cutting a hole out of the centre of the base, thus reducing the area of the base. Provided the centre of gravity of the base remains in line with the centroid of applied loads, the bearing pressure would remain uniform, but its magnitude would increase.

Ultimate design pressure
The ultimate design pressure for reinforcement design  is given by pu =γPp, where  γP is the combined dead and imposed partial load factor.

Balanced foundations (rectangular, cantilever, trapezoidal and holed) Design.

Design decisions
The decision to use a combination of column loads to produce a combined balanced foundation would depend upon a number of factors, for example:

(1) The spacing of the point loads.
(2) The combination of loads being considered.
(3) The restrictions of projections due to site boundaries.
(4) The overall eccentricities produced from the resultant of the loads.
(5) The bearing area available.
(6) The need to produce a uniform pressure.
(7) The economics compared to other possible alternatives, if any. For example, in some situations a combination of column loads can be used to balance out eccentric loads which would otherwise extend isolated foundations beyond the boundaries of the site. Balancing out these column loads means that the boundaries can be maintained within a base giving uniform pressure and this may prove more economic than say a piled solution.

In other situations an attempt to balance out the loads may produce cantilevers which would extend beyond the site boundaries therefore making it necessary to look at alternative column combinations or alternative means of support such as piling.

In most cases where these foundations are adopted they relate to: boundaries which are restrictive; foundations which would otherwise overlap; or situations where, by introducing a load from other columns onto the same  foundation, bending moments are reduced and pressures become more uniform.

Sizing up the design

(1) Rectangular balanced foundations
The foundation base is designed by calculating the position of the resultant applied load and making the centre of gravity of the base coincide with that of the downward load.

This is done by first calculating the area of the base required to resist the resultant load and then finding the most  economic rectangular pad to achieve this. The pad is then located so that its centre of gravity is in the same position as the resultant load (see Fig. 12.6).

Fig. 12.6 Rectangular balanced pad base.

The base is then designed to resist the bending moments and shear forces produced by the solution, and the depth and reinforcement are determined and detailed accordingly.

(2) Cantilever balanced foundations
The design of the cantilever balanced foundation is carried out by assuming locations for the pad supports based upon the physical considerations and calculating the reactions from the cantilever beam. The reactions are then accommodated by calculating the required size of rectangular pads for each reaction based upon a uniform bearing pressure.

The beam is then designed to support the loads from the superstructure taking account of the induced bending and shear forces, etc. (see Fig. 12.7 for a typical example).

Fig. 12.7 Bending and shear diagram for typical
cantilever base.

(3) Trapezoidal balanced foundations
The design is carried out by first of all calculating the area of the base required for a uniform pressure to resist the total applied load. The resultant load and its point of application is then calculated. By fixing the dimensions for the length of the base, the dimensions A and B (see Fig. 12.8 (a)) can be calculated to give a centre of gravity which coincides with the location of the resultant load.

Fig. 12.8 Trapezoidal and holed balanced foundation.

The applied bending moments and shear forces are then calculated and the reinforced foundation designed to suit.

(4) Holed balanced foundations
The design is carried out by first calculating the resultant load and its location. The area required for the base is then determined by dividing the resultant load by the allowable bearing pressure. By fixing the length of the base an average width can hence be determined, and by inspection  of the eccentricity of the resultant load, an allowance can  be made for an approximate size of hole and a trial width determined (see Fig. 12.8 (b)).

From this trial width a size and location for the hole can  be calculated to give a centre of gravity for the base which will coincide with that of the applied loads and result in a uniform pressure.

Having determined the base dimensions the bending moments and shear forces can be calculated and the foundation design completed.

(5) General sizing considerations
The size of the sections involved is based upon bending moments, shear forces and bond stresses in a similar manner to any other reinforced concrete section. With foundations, however, due to the slightly reduced shuttering cost for concrete below ground compared to elevated sections,  it is often more economic to go for slightly larger concrete sections to avoid the use of excessive shear reinforcement or large-diameter bars.
Each condition will demand dif- ferent sizes and therefore the engineer will need to deter- mine the initial size from a feel of engineering, which will develop with experience. The design may then be finalized by trial and error.

Design Example: Tied Portal Frame Base.

The pad bases for a single-bay portal frame are to be joined by a horizontal tie to take out the horizontal thrusts from the portal legs. The portal is similar to the one which was designed as an untied portal in section 11.3.4. Loads and dimensions are shown in Fig. 12.4.

Loadings
From section 11.3.4,

vertical superstructure load, P = (dead load)
                                                + (imposed load)
                                               = G + Q
                                               = 175 + 225
                                               = 400 kN

Q as a percentage of P is 100 Q/P = (100 × 225)/400 = 56%.

From Fig. 10.20, the combined partial factor for dead and imposed loads is γP = 1.51.

Horizontal thrust, H = 50 kN

The horizontal thrust H arises from vertical loads G and Q, and will therefore have the same combined partial load  factor γP = 1.51.
 
Size of base
From section 11.3.4, the net allowable bearing pressure, na = 300 kN/m2.

On the basis that the horizontal thrust will be taken out by the tie joining the portal feet, the minimum area of foundation required is

A base 1.2 m × 1.2 m will therefore be chosen. Comparison with the example in section 11.3.4 shows that the introduction of the horizontal tie has reduced the base size.

Design of horizontal tie
The tie will be a mild steel bar, as shown in Fig. 12.5, encased in concrete for durability.

Ultimate tensile force in bar, Hu =γPH
                                               = 1.51 × 50
                                                = 76 kN

From BS 8110, the characteristic tensile stress fy = 250 N/mm2 for hot rolled mild steel. The partial material factor γs = 1.05.

The required cross-sectional area of bar is

Provide one number 25 mm diameter mild steel bar (area  = 491 mm2 ) to act as the tie. This will need to be  adequately anchored into the pad base as shown in Fig. 12.5.

To prevent possible foundation spread from lack of fit, the tie will incorporate a turn-buckle, to take up any slack prior to steel erection.

Fig. 12.5 Tied base design example – tie rod detail.

Tied foundations - Design.

Introduction
Tied foundations are often adopted as a means of exploiting to advantage opposing forces. This is achieved by linking them together via a tie or tie beam. The effect this has on  the design is to reduce the horizontal force requiring to be resisted by the ground (see Fig. 12.1 (a)).

The use of a tie can reduce the amount of movement likely to occur in developing the reaction and reduce the cost of the foundation.

Fig. 12.1 Tied foundation.

Design decisions
In any situations where horizontal forces, such as thrusts from portal frames, etc., act in opposite directions, consideration should be given to connecting the forces via a tie in order to reduce or totally react a horizontal force. For example, if the forces are equal and opposite then the total force can be reacted. On the other hand, if the forces are opposite and not equal, the smaller of the two forces can be tied and the remainder left to be reacted by foundation 1 or, if a higher tie force is used, foundation 2 can also be utilized, thereby reducing the force to be taken in passive pressure (see Fig. 12.1 (b)).

Sizing the foundations
The main pad foundations are designed in the same way as those previously discussed in Chapter 11 but taking into account the tie force reaction in accordance with the above considerations. The tie itself must be designed to resist the force H1 or H2, as the case may be, and must be detailed to
transfer this force without excessive slip or failure between the bases of the stanchions.

This is usually achieved by designing a tie rod for the total force using appropriate permissible tensile stresses for the steel and ensuring that suitable mechanical anchorage or bond anchorage is achieved in the details between the  stanchion and tie (see Fig. 12.2).

In detailing these ties, the detailer should ensure that the  tie acts on the centreline of the horizontal thrust force or that any eccentricity produced is designed into the foundation by the designer. The tie rod itself could contain a turn-buckle for tensioning in order to reduce lateral movement due to possible slackness in the rod, alternatively, if adjustment is not required, a reinforced concrete tie beam as shown in Fig. 12.3 could be used. Care should be taken  to ensure axial tension across any connections which may  be required in the tie by the use of turn-buckle or male/ female-type plate connectors. In the case of portal framed factories it is often desirable to construct the floor slab after
erection and cladding of the building. In this case the engineer must ensure that all tie members are constructed and covered prior to the erection of the steelwork, in order that the presence of the tie members does not impede the construction process.

Fig. 12.2 Tie anchorage.

Fig. 12.3 Reinforced concrete tie beam.

Tied and Balanced Foundations.

General Introduction
Tied and balanced foundations are used to combine a number of superstructure loads in order to achieve acceptable bearing pressure. The combined base is used to balance out or tie together difficult eccentricities of loading or horizontal forces. Such foundations usually result from an engineering study of the superstructure loads to be transmitted onto the foundation. The engineer’s aim is to make the best use of the magnitude and direction of such forces in balancing out or tying together eccentric reactions and horizontal thrust to economically achieve the required ground bearing pressures.

Particular problems exist where large lateral forces are transferred at the top edge of a foundation from say portal frames or when large column loads occur at or near site boundaries. Fortunately portal frames tend to have an equal and opposite leg with similar opposing horizontal forces which can be reacted against each other. Buildings with large column loads near to the boundary tend also to have other large column loads either internal to the building or on an opposite boundary. The internal or opposite columns can therefore be used to stabilize the moments produced  by the eccentricity from the outer perimeter frame. Typical examples are given in the following sections.

Tied and Balanced Foundations.

General introduction
Tied and balanced foundations are used to combine a number of superstructure loads in order to achieve acceptable bearing pressure. The combined base is used to balance out or tie together difficult eccentricities of loading or horizontal forces. Such foundations usually result from an engineering study of the superstructure loads to be transmitted onto the foundation. The engineer’s aim is to make the best use of the magnitude and direction of such forces in balancing out or tying together eccentric reactions and horizontal thrust to economically achieve the required ground bearing pressures.

Particular problems exist where large lateral forces are transferred at the top edge of a foundation from say portal frames or when large column loads occur at or near site boundaries. Fortunately portal frames tend to have an equal and opposite leg with similar opposing horizontal forces which can be reacted against each other. Buildings with large column loads near to the boundary tend also to have other large column loads either internal to the building or on an opposite boundary. The internal or opposite columns can therefore be used to stabilize the moments produced  by the eccentricity from the outer perimeter frame. Typical examples are given later.

Design - Jacking Raft

Introduction
Raft foundations suitable for jacking are specifically designed versions of crust rafts, cellular rafts, lidded cellular rafts, beam strip rafts or other foundations whose stiffness and behaviour is designed to resist the jacking forces and moments involved in the process of re-levelling.

The raft is designed to cater for the bending and shear forces likely to be produced during subsidence and relevelling activity. Jacking points are built into the foundation to allow for re-levelling and the type of raft and
number of jacking points depends to a large extent on the proposed use, the size of the structure and the predicted subsidence likely to occur.

The need for a jacking raft tends to be determined by the unpredictability of subsidence and the practicalities for the building user of re-levelling within the life of the building.

As mentioned previously, domestic sites in areas of brine mining are typical of sites where such foundations have been adopted and basically two design conditions need to be considered.

(1) To design for the normal subsidence condition for the site including bending moments and forces as previously discussed for the raft type.
(2) Additional analysis and design to incorporate the structural requirements to resist stresses and distortions during the jacking operations.

Sizing the design
It can be seen that the initial sizing of the foundation for trial design would be to adopt generous sizes for a standard raft of the type being proposed in anticipation of embracing the jacking stresses.

The stresses produced during jacking are dependent on the restrictions and methods of jacking and therefore tend to be one-off designs for set conditions.

Design - Buoyancy Raft.

Introduction
The buoyancy raft works on a similar principle to that of a floating structure where the support for the raft is mainly obtained by displacing the weight of earth or overburden by the volume of a large voided foundation.

The raft  is described previously and is often economically achieved by making use of the voids as a basement structure (see Fig. 13.42).

Fig. 13.42 Buoyancy foundation/basement.

It is designed so that sufficient overburden is removed to allow the superstructure load to be applied to the ground with little or no increase in the original stress which existed on the sub-strata prior to excavation and construction. Thus the structure floats like a ship – which displaces water equal to its own weight.

The bottom slab can form the basement of the proposed building, and be combined with the ground slab and retaining walls to act as the raft. It can also be of cellular form (see Fig. 13.43).

Fig. 13.43 Cellular buoyancy foundation.

The raft design takes into account any eccentricity of load and aims to keep differential settlements and tilting within acceptable limits (see Fig. 13.44), which shows how eccentric resultant loads can be caused by the basement projections, producing a uniform bearing pressure.

Fig. 13.44 Eccentrically loaded buoyancy raft.

Since buoyancy foundations are expensive compared to more traditional forms they tend only to be used where suitable bearing strata is at too great a depth for other more traditional alternatives. For this reason the foundation tends to be restricted to sites on very deep alluvial deposits such as soft sands and silts and where loads on the foundations can be kept concentric. Examples of such building types would be schemes where deep basements can be economically incorporated into the design or where underground tanks are required.
The cases therefore where the engineer would adopt such solutions tend to be limited.

2 Sizing the design
The overall sizing of the design would generally involve:

(1) Calculating the depth plan size and centre of gravity required for the overburden removal to suit structural buoyancy.
(2) Comparing the results of (1) with the requirements for tanks or basements to suit client’s needs.
(3) Calculating the water pressure for (1) to check for  flotation.
(4) Combining the requirements of (1), (2) and (3) into a mutually suitable voided foundation.
(5) Designing the external walls, floors, roof and separating wall elements for the pressures, bending moments and shear forces including any projections to prevent flotation.

Design - Beam Strip Raft.

Introduction
The beam strip raft is described in section 9.4.7 and consists of downstand beams in two directions tied together by a ground bearing slab. The beam and the slab are designed as separate elements which are combined together to finalize the rafted design.

These rafts are used where the bearing capacity below the beams is relatively good as is the bearing capacity of the ground below the slab and therefore there is no need to design the total raft foundation when the two are linked  in the final drawing.

The two are generally linked because of the added performance from the two separate elements when they are cast monolithic. The beams may be required due to the point loads from column structures around the edge of the raft  or within the body of the raft and beams are designed to span horizontally between these point loads. Similarly the raft slab is designed to float on the ground between the beams but since the bearing capacity where these rafts  are adopted is relatively good then a nominal design incorporating a top and/or bottom mesh is all that is required  in the slab.

These foundations are generally used in areas where quite shallow sand deposits occur below the topsoil and where there is no need to go to excessive depths around the edges of these rafts for heave or other problems. They can also be used where the strata changes slightly from perhaps clayey sands to sandy/silty clays.

Sizing of the design
The sizing of the sections is carried out by treating the beam strips as independent beams, designed previously.

These two parts for the foundation are then tied as shown in Fig. 13.39.

Fig. 13.39 Beam strip raft.

Any necessary adjustments that the engineer may feel are required due to the changes in behaviour resulting from combining the elements are then made in the detailing of the raft. For example, the linking together will generally improve the raft performance by reducing the stresses in the two elements from those applicable if they acted alone.

However, there will be some occasions, for example, when a local heavy load occurs on a downstand, where a local detail could become critical due to the change in behaviour, and additional reinforcement or a slight adjustment to a detail may be needed.

Design - Lidded Cellular Raft.

Introduction
The lidded cellular raft is described previously and due to its formation tends to be a little less stiff than the true  cellular raft. The design calculations however follow similar lines with the exception that the cross-section of the beams tends to be restricted to inverted T and L shapes.

The advantage of this form over the pure cellular raft is that the upper slab can be detailed to allow it to be re-levelled should the floor tilt or distortion become excessive for the building’s use. Also in some locations the top of the lidded raft can be constructed in precast units and may prove  more economic, avoiding the possible need for permanent formwork.

The raft is usually designed as a number of intersecting inverted  T beams taking advantage of the lower ground slab as the flange of the  T but ignoring the upper slab  which could be constructed in timber joists and boards or other form to suit the design requirements (see Fig. 13.37).

Fig. 13.37 Lidded cellular raft.

Remember that the strength advantage of the T beam can only be used for midspan, where compression occurs in the bottom of the beam. The section below the column must be designed as rectangular.

The detail at the seating of the upper floor depends upon the need for re-levelling and the possible number of times adjustments may need to be made.

As explained in section 9.4.6, the upper floor of the lidded raft is a separate structure to the main inverted  T and  L beams forming the concrete raft.

Sizing the design
The design procedure is similar to that of the cellular raft except that the upper deck is simply designed to span as  a floor between the up-standing ribs. The remainder of  the design follows the same procedure as before with the exception already mentioned that the element sections become inverted T or L beams rather that I or box sections.

Design - Cellular Raft.

Introduction
Cellular rafts are used where valuable increases in bearing capacity can be achieved by the removal of overburden or where severe bending moments may be induced due to mining activity, seismic loadings, etc.

The cellular form in such situations can perform two functions (see Fig. 13.31).

The foundation while being economic for such situations is one of the most expensive foundation types used.

Fig. 13.31 Cellular raft.

Sizing the design
In the case of overburden removal the depth required may relate more to the excavation required to produce adequate reduction in load than to the bending moment resistance of the cellular form (see Fig. 13.32).

Fig. 13.32 Raft depth dictated by bearing
requirements.

On the other hand it is more common for the raft depth to relate to the moments likely to be induced and the reduced overburden load to be a resulting bonus. For example, a raft designed to resist seismic loads or mining subsidence may need to be designed to span two-thirds of its total length and to cantilever one-third of its length. Similarly rafts on variable ground subjected to large differential settlements may require such design parameters. This requirement  on a building plan which is restricted to say 20 m on any one side can produce very large shear forces and bending moments thus requiring deep rectangular, I or box sections.

The size of these beams can often be reduced by jointing buildings into smaller units (see Chapter 6). Cellular rafts or other rafts which are formed from beams crossing at right angles are difficult to assess since loads are resisted in two directions by the framework. The designer must start by calculating the design column loads and relating these to the overall plan and ground pressures.

The calculations for the ground pressures based upon the centre of gravity of the loads and the relative stiffness of the raft foundation is then considered. In the case of the cellular raft a stiff raft would normally be assumed (see Fig. 13.33). With reference to Fig. 13.33, the centre of gravity of the load would be calculated in the normal way and the resultant load would be the total addition of the loads on the frame- work for the design conditions being considered.

Fig. 13.33 Centre of gravity of load on stiff raft.

The ground pressures at the corners of the raft would then be determined. Assume the resultant total load to be T, the total area to be A, the moment in each of the two directions to be Mx and My, the eccentricity in each direction to be ex and ey, and the section modulus in those directions assum- ing symmetrical plan to be Zx and Zy. The stress at each corner would equal

Mx and My, being the resultant moments, equal T × ex and  T × ey, respectively (see Figs 13.34 and 10.18).

Fig. 10.18 Foundation in biaxial bending.

As usual in design calculations these theoretical pressures will not necessarily be achieved on site and the difficulty then arises when the engineer tries to assess the actual ground pressures. These pressures will be dependent on the sub- strata, the flexibility of the raft, the actual loads occurring at any time and the time at which these pressures are considered relative to the original application of the load.

None of these conditions can be assessed accurately nor is it necessary to do so. The procedure to be adopted is for the engineer to apply the art of foundation design in producing calculations and details for the raft. This means taking consideration of these variables as part of the refinement of the design at the detailing stage. Adjustments must be made  to sections, reinforcement, location of joints and to the number of beams on plan to produce a more realistic and practical solution. The authors make no apology for suggesting that foundation engineering is an art as well as  a science since they have learnt this art from long and bitter
experience. The engineer doing this exercise therefore would begin by preparing a rough layout from practical experience indicating rough sizes likely to be required.

Assumptions are then made, for example:

(1) The raft will be assumed to be stiff.
(2) The bearing pressure will be assumed to be trapezoidal, as indicated in Fig. 13.34.
(3) The load from the structure will be assumed to be fixed at the design load for the analysis.
(4) The reactions to each beam line will be assumed to be proportional to the bearing area and ground pressure on that line and when both directions are totalled they must be equal to the applied load at that point from the structure.

Fig. 13.34 Corner pressure below stiff raft with
resultant load as Fig. 13.3.

Many methods of analysing foundations have been proposed, some assuming springs below the foundations, some assuming uniform bearing pressure, some assuming non- linear bearing pressures, some trying to take into account the stiffness of the raft foundation.

At the end of the day the experienced engineer fully under- stands that all these calculated methods, while being  reasonable and theoretically logical, are not realistic. The foundation which the engineer designs will not sit on the soil which was taken to the laboratory for testing, it will  not for its total life be resisting the loads calculated, it willnot be of the stiffness assumed, it will not be subjected to
the settlements or movements anticipated by calculation.

With all this in mind the engineer uses analysis as one of the tools in the kit bag. The above knowledge produced by design and calculation is taken into account and the design adjusted in a direction which is more realistic.

To achieve this practical engineers will often make simple assumptions to produce a quicker analysis while satisfying themselves of the foundation requirements without the need for complicated and often less accurate methods of analysis. A typical design approach for a cellular raft is shown in the following example.

Design Example: Slip Sandwich Raft.

The nominal crust raft for a pair of semi-detached properties in Design Example 1 is now assumed to be located in a mining area. It will therefore be reworked as a slip sandwich raft, to accommodate the associated ground strains.

The slip sandwich raft is designed on the assumption that the two halves of the raft – on either side of the centreline – are moving away from each other (tension), or towards each other (compression). The maximum horizontal force across the centreline of the raft, arising from the horizontal strains in the underlying ground, is equal to the maximum frictional force which can be transmitted across the slip-plane into one half of the raft.

Vertical loadings
Loads are as Design Example 1 (see Fig. 13.15):

Fig. 6.15 Raft detail – low-rise/lightly loaded buildings.

Horizontal force across raft centreline
The raft is 10.0 m × 12.0 m. With reference to Fig. 13.30, the total ultimate vertical load on one half of the raft is




located at the level of the underside of the raft thickenings to act as a slip-plane (see Fig. 13.30). The raft will be assumed to behave as illustrated in Fig. 6.14 and Fig. 13.27.

Fig. 6.14 Effect of ground strain on raft.

The Coal Authority guidelines(4) recommend the use of a coefficient of friction of µ= 0.66 for a sand slip-plane. The length of the centreline is B = 10.0 m. The horizontal force per metre length across the centreline of raft is therefore given by

Reinforcement design for raft tension
Provide high yield reinforcement to resist this force in  tension such that

Provide two layers of A193 mesh throughout, as shown in Fig. 13.30.

Design for raft compression
The same tensile force calculated above can also act in com- pression. By inspection the raft concrete can accommodate this magnitude of compressive stress.

Design - Slip Sandwich Raft.

1. Introduction
This raft is mainly used in active mining areas or where  clay is creeping on inclined sand beds where the horizontal  ground strains set up during subsidence or creep movements would cause damage to the structure, if allowed to be transferred up to it via the foundation (see Fig. 13.23).

Fig. 13.23 Effects on foundations from horizontal
ground strains.

By using a slip-plane of known resistance, the maximum force which can be transferred from the ground to the building before the plane ruptures can be calculated, and the raft designed to resist this force in any direction that it is likely to occur.

The raft can be a flat slab profile thus avoiding the use  of downstand thickenings which may pick up excessive passive load from the ground strain. Alternatively a slab with medium thickenings incorporating a design which provides a slip-plane below the hardcore dumplings (i.e. the raised areas of hardcore protruding up between the beam lines) can be used (see Fig. 13.24).

Fig. 13.24 Alternative slip sandwich rafts.

The ideal ground (i.e. uniform firm layers of non-frost- susceptible low shrinkability sub-strata) to facilitate a flat slab rarely occurs on the site to be developed. Therefore,  to prevent damage from frost, clay heave or differential  settlement, thickenings are often necessary. In such situ- ations the ground strains being picked up either have to  be designed to be resisted by the raft or a slip-plane layer  provided below the level of the downstands to reduce  the forces being transferred. The upper raft (above the  slip plane layer) of a slip sandwich raft can be any of the other rafts already designed and discussed in earlier sections  of this part.

The difference between the slip sandwich raft and the other rafts relates to the slip-plane layer below the slab and the horizontal forces produced from the ground strains transferred through the slip-plane.

The additional stresses are analysed by calculating the forces transferred from the ground strain and these forces are added to the design conditions already discussed for other rafts.

2 Design decisions
The design decision to use a slip sandwich raft will depend totally on the possible existence of critical horizontal ground strains in the sub-strata during the life of the building and the need to restrict these forces to prevent them being trans- ferred in total to the superstructure. The use of jointing to reduce the overall building into small independent robust units is part of the design process. In addition the possible need to incorporate compressible aprons around the raft requires consideration in the design and it is dependent upon the directions and magnitude of the ground strains (see Fig. 13.25).

Fig. 13.25 Section through raft and compressive apron.

3 Sizing the design
The basic sizing of the raft to sit on the slip-plane would  follow the principles already discussed in other sections of this part.

The additional requirements for the slip sandwich raft however relate to the compressive and tensile forces likely to be transferred through the slip-plane from the ground strains. If a simple rectangular plan shape raft is considered as shown in Fig. 13.26 (which would be the ideal plan shape for such a raft) and a 150 mm thick sand slip-plane, the  following simple analysis can be applied. Assume the total weight of the building and foundations to equal T and the frictional resistance of the sand slip-plane layer to be equal to µ (see Fig. 13.27), the largest horizontal force which can be transferred up from the ground strain through the slip-plane will be equal to (µT)/2. The reason for the total load acting down being halved is that the maximum force that can be transferred as tension through the building must be reacted by the other half of the load. This formula assumes that no other passive forces are being transferred to the foundation, i.e. that all forces are transferred via the sand as a frictional force. In practice the downstand beams would be cast with sloping internal faces as in Fig. 13.30.

Fig. 13.26 Simple rectangular raft.

Fig. 13.27 Forces on foundation from ground strains.

Fig. 13.30 Slip sandwich raft design example.

If however downstands project below the raft then the  slip-plane layer should be positioned below such down-stands and the downstands kept to a minimum. In addition if compressive ground strains are occurring then an apron must be introduced to prevent or restrict the amount of strain transferred from passive pressure on the raft edges. If such pressures cannot be avoided then they must be added
to the force indicated above and allowed for in the design.

Any eccentricities of such forces should also be taken into account in the design of the raft since these will produce bending in the raft foundation (see Fig. 13.28) which indicates an eccentric force on a downstand raft thickening.

Fig. 13.28 Passive forces on raft downstands.

If the plan shape adopted is not rectangular, for example, the L shape as shown in Fig. 13.29, then the two halves of the building producing the force (µT)/2 from frictional resistance below the surface will produce tensile or com- pressive forces across a line which passes through the  centre of gravity of the building and which will tend to rotate towards a line parallel to the subsidence wave.

Consideration must be given therefore to the additional stresses produced by these forces including any bending moments across this face or on lines parallel to the face  (see Fig. 13.29). Division of the slab into two separate  rectangular rafts by the incorporation of a movement joint could be considered as an alternative approach. The significant movements likely to occur here would however have to be allowed for in the detailing of the joint through the structure.

Fig. 13.29 Direction of tensile failure dependent on
direction of wave face.

PIPING FAILURES IN SAND CUTS.

Sheet piling is used for cuts in sand and the excavation must be dewatered by pumping from the bottom of the excavation. Sufficient penetration below the bottom of the cut must be provided to reduce the amount of seepage and to avoid the danger of piping.

Piping is a phenomenon of water rushing up through pipe-shaped channels due to large upward seepage pressure. When piping takes place, the weight of the soil is counteracted by the upward hydraulic pressure and as such there is no contact pressure between the grains at the bottom of the excavation. Therefore, it offers no lateral support to the sheet piling and as a result the sheet piling may collapse. Further the soil will become very loose and may not have any bearing power.

It is therefore, essential to avoid piping. For further discussions on piping.

Permeability and Seepage. Piping can be reduced by increasing the depth of penetration of sheet piles below the bottom of the cut.

BRACED CUTS.

General Considerations
Shallow excavations can be made without supporting the surrounding material if there is adequate space to establish slopes at which the material can stand. The steepest slopes that can be used in a given locality are best determined by experience. Many building sites extend to the edges of the property lines. Under these circumstances, the sides of the excavation have to be made vertical and must usually be supported by bracings.

Common methods of bracing the sides when the depth of excavation does not exceed about 3 m are shown in Figs 20.26(a) and (b). The practice is to drive vertical timber planks known as sheeting along the sides of the excavation. The sheeting is held in place by means of horizontal beams called wales that in turn are commonly supported by horizontal struts extending from side to side of the excavation. The struts are usually of timber for widths not exceeding about 2 m. For greater widths metal pipes called trench braces are commonly used.

When the excavation depth exceeds about 5 to 6 m, the use of vertical timber sheeting will become uneconomical. According to one procedure, steel sheet piles are used around the boundary of the excavation. As the soil is removed from the enclosure, wales and struts are inserted. The wales are commonly of steel and the struts may be of steel or wood. The process continues until the excavation is complete. In most types of soil, it may be possible to eliminate sheet piles and to replace them with a series of//piles spaced 1.5 to 2.5 m apart. The //piles, known as soldier piles or soldier beams, are driven with their flanges parallel to the sides of the excavation as shown in Fig. 20.26(b). As the soil next to the piles is removed horizontal boards known as lagging are introduced as shown in the figure and are wedged against the soil outside the cut. As the general depth of excavation advances from one level to another, wales and struts are inserted in the same manner as for steel sheeting.

If the width of a deep excavation is too great to permit economical use of struts across the entire excavation, tiebacks are often used as an alternative to cross-bracings as shown in Fig. 20.26(c). Inclined holes are drilled into the soil outside the sheeting or H piles. Tensile reinforcement is then inserted and concreted into the hole. Each tieback is usually prestressed before the depth of excavation is increased.

Figure 20.26 Cross sections, through typical bracing in deep excavation, (a) sides
retained by steel sheet piles, (b) sides retained by H piles and lagging, (c) one of
several tieback systems for supporting vertical sides of open cut. several sets of
anchors may be used, at different elevations (Peck, 1969)

ANCHORAGE OF BULKHEADS.

Sheet pile walls are many times tied to some kind of anchors through tie rods to give them greater stability as shown in Fig. 20.21. The types of anchorage that are normally used are also shown in the same figure.

Anchors such as anchor walls and anchor plates which depend for their resistance entirely on passive earth pressure must be given such dimensions that the anchor pull does not exceed a certain fraction of the pull required to produce failure. The ratio between the tension in the anchor T and the maximum pull which the anchor can stand is called the factor of safety of the anchor.

The types of anchorages given in Fig. 20.21 are:

1. Deadmen, anchor plates, anchor beams etc.: Deadmen are short concrete blocks or continuous concrete beams deriving their resistance from passive earth pressure. This type is suitable when it can be installed below the level of the original ground surface.

2. Anchor block supported by battered piles: Fig (20.21b) shows an anchor block supported by two battered piles. The force Ta exerted by the tie rod tends to induce compression in pile P1 and tension in pile P2. This type is employed where firm soil is at great depth.

3. Sheet piles: Short sheet piles are driven to form a continuous wall which derives its resistance from passive earth pressure in the same manner as deadmen.

4. Existing structures: The rods can be connected to heavy foundations such as buildings, crane foundations etc.

Figure 20.21 Types of anchorage: (a) deadman; (b) braced piles; (c) sheet piles; (d)
large structure (after Teng, 1969)

Location of Anchorage
The minimum distance between the sheet pile wall and the anchor blocks is determined by the failure wedges of the sheet pile (under free-earth support condition) and deadmen. The anchorage does not serve any purpose if it is located within the failure wedge ABC shown in Fig. 20.22a.

If the failure wedges of the sheet pile and the anchor interfere with each other, the location of the anchor as shown in Fig. 20.22b reduces its capacity. Full capacity of the anchorage will be available if it is located in the shaded area shown in Fig. 20.22c. In this case

1. The active sliding wedge of the backfill does not interfere with the passive sliding wedge of the deadman.

2. The deadman is located below the slope line starting from the bottom of the sheet pile and making an angle 0 with the horizontal, 0 being the angle of internal friction of the soil.

Figure 20.22 Location of deadmen: (a) offers no resistance; (b) efficiency greatly
impaired; (c) full capacity, (after Teng, 1969)

Crust Raft - Design.

1 Introduction
The crust raft is discussed  previously where it is explained that it is a stiffer and stronger version of the
nominal crust raft. In this chapter it is intended to take this a stage further through the design procedure and to an actual example.

2 Design decisions
The crust raft is used where normal ground bearing substrata is relatively poor, where the depth to good load-bearing soils is excessive, but where by dispersing the  loads differential settlements can be controlled. It is more attractive where these conditions exist on a relatively level site, i.e. where few steps or changes in level exist.

The considerations for thickening layout and profile are as for the nominal crust (see section 13.2).

The design of the crust raft and its element cross-sections tends to be based on a similar simplified analysis to that of the nominal crust raft but adopting a slightly more analytical approach. However, in order to arrive at a suitable span and depression diameter a more detailed analysis of the ground conditions would be carried out. For example, if the raft was to span over possible swallow-holes or shallow
mine workings a detailed study of borehole information particularly with regard to the existence of voids below ground, combined with historical evidence of previous  collapses/depressions would be carried out. Excessively large voids or voids which were creating particular prob- lems in the design of the raft could be considered for grouting in order to reduce the risk of collapse and reduce the diameter of design depressions. If grouting was to be adopted then this would be carried out prior to construction of the raft foundation.

When studying old shallow mine workings reference should be made to Chapter 6. Historical details of pillar and stall workings may be used in the anticipation of the maximum diameter of collapse at cross-over positions, etc. (see Fig. 13.16).

Fig. 13.16 Subsidence prediction for shallow
mine working.

A word of caution should be given at this stage with regard to the reliance on mining records since, as was emphasized previouly, while shaft locations are often quite accurate any records of pillar and stall workings tend to be less reliable. This is due to disintegration during oxidation of the pillars, and/or the practice of robbing pillars at the end  of the workings’ normal life. These actions result in a tendency for larger depressions to occur but usually within  a shorter period after completion of the mine workings.

The earlier completion of subsidence is an advantage. In some cases, however, if pit props have remained in position un-rotted, early subsidence is prevented. These sorts of conditions will be taken into account by the experienced engineer in assessing the borehole records and other records of the possible collapse mechanism and type and size of void or depression to be spanned or grouted.

Design Example: Nominal Crust Raft.

A new housing estate, consisting of two-storey semi- detached properties, is to be built on a green field site.
The ground conditions consist of a soft to firm clayey sand.

The net allowable bearing pressure for raft design is estimated at na = 100 kN/m2.

The foundation for each pair of houses is to be designed  as a raft foundation. Taking into account the ground conditions and the relatively light loading, a nominal crust raft  is considered adequate. The wall layout, loadings, and  corresponding raft layout are shown in Fig. 13.15.

Fig. 13.15 Nominal crust raft design example.

Loadings
The foundation load due to slab self-weight and imposed
load is

fQ as a percentage of  f is 100fQ/f = 42%. From Fig. 10.20,  the combined partial safety factor for the foundation load is γF = 1.48.

Wall line load, P = (wall dead load) + (wall imposed load)
     = G + Q
     = 15.5 + 10.5
     = 26.0 kN/m

Q as a percentage of P is 100Q/P = 40%. From Fig. 10.20, the combined partial safety factor for the superstructure loads is γP = 1.48.

Fig. 13.20 Blanket raft construction.

Bearing pressure design
Because of the low level of loading, no explicit check on bearing capacity is considered necessary.

Design span for local depressions
With reference to Table 13.1, the soil conditions are taken  to be medium Class B. From Fig. 13.5, assuming 150 mm of hardcore, the design span L is 1.6 m.

Table 13.1 Design diameter for local depressions

Slab design
It is intended for the slab to have top mesh reinforcement only. Figure 13.5 indicates that, for a design span of 1.6 m,  a minimum average effective depth of 100 mm is required to comply with the deflection requirements of BS 8110:  Part 1(2). A slab thickness of 125 mm will therefore be adopted, with 20 mm top cover. For shrinkage purposes, Table 13.2 indicates, for a 12 m long slab, that A142 mesh is adequate.

Table 13.2 Shrinkage reinforcement for raft slabs

Because of the low level of distributed load, and the absence of any significant wall line loads on the slab, there is no need to carry out a local spanning check on the slab under ultimate loads. (If however, the internal thickenings were omitted, and the slab required to carry their load, a check should be carried out in a similar manner to Design Example 2 in section 13.3.3.)

Beam thickening design
Similarly, the low level of loading, and the absence of concentrated point loads on the thickenings, indicate that these can be sized and reinforced on a nominal basis.

For external thickenings, use pre-bent B503 mesh, as shown in Fig. 13.15, with the main T8 bars at 100 mm centres  running along the length of the beam. This will result in  at least three T8 longitudinal bars in the top and bottom  of the beam.

For internal thickenings, again use pre-bent B503 mesh,  as shown in Fig. 13.15, with the main bars again running longitudinally to help span over local depressions.

Design - Nominal Crust Raft – Semi-Flexible

1 Design decisions
As discussed previouly the nominal crust raft is used where loadings are relatively light and ground conditions reasonable. The raft is lightly reinforced and consists of a basic ground slab with nominal thickenings (see  Fig. 13.15).

Fig. 13.15 Nominal crust raft design example.

2 Sizing the design
Such rafts can be designed either from experience simply by adopting a known raft which has performed successfully on similar ground conditions and subjected to similar loadings or by calculation as discussed previously.

Many local authorities have ‘standard’ designs which have been approved for use and are often agreed as ‘deemed to satisfy’ building insurers’ requirements. It is wise to agree with building control the design methodology prior to preparation of detailed calculations.

The calculated design assumes that the slab and thickening should be capable of spanning and cantilevering over any local depressions which may occur as a result of the loading and/or sub-strata conditions.

Such rafts are used generally for relatively lightly loaded conditions on reasonable ground. In such conditions these lightly reinforced rafts can prove more economic than strip footings particularly where the ground is reasonably level, where the basic ground slab is used as the main body of  the raft and where small straight thickenings replace  complicated layouts of wall strips.

The layout of the downstands is determined from the  overall raft stiffness requirements and while heavy load lines and point loads will have a bearing on the location  of such downstands they should not be allowed to dictate the design. For example, the strip wall loadings, shown in Fig. 13.10, zig-zags across the building and if the downstand thickenings were made to follow these lines an overall weakness in the thickenings would result at each change in direction and hence the overall behaviour of the raft would be adversely affected.

Fig. 13.10 Zig-zag wall layout.

It is therefore important that a common straight line across the building is used for the downstand which caters for  the local heavy loads and overall stiffness (see Figs 13.11 and 13.12).

Fig. 13.11 Straight thickenings below raft.

Fig. 13.12 Irregular wall layout but straight
thickenings.

With regard to overall thickening layouts it may be necessary when considering total raft behaviour to introduce thickenings purely for stiffness and in locations where no vertical load lines exist (see Fig. 13.13).

Fig. 13.13 Thickening layout for raft stiffness.

For raft foundations adequate protection from weathering and frost effects on most granular soils, sandy clays and insensitive clays can be achieved with 450 mm cover, similar to road construction. Over-emphasis on clay shrinkage must not be allowed to change the engineering judgement in such soils particularly where past performance has been proven.

The raft is considered as a single element in determining overall behaviour taking account of the stiffness of the  raft, and then breaking the foundation down into a num- ber of small elements to simplify the design. These local conditions tend to dictate the cross-section dimensions of the foundations with the overall behaviour being devel- oped and incorporated into the design on the drawing board. For example, if we take the raft shown in Fig. 13.13 and adopt the internal thickening layout discussed it can be seen that the reinforcement details for overall slab behaviour should ensure that beam thickenings can act continuously. In particular the design should avoid local weakenings in the concrete profile or reinforcement in vulnerable locations such as the internal angles of the raft (see Fig. 13.14). The detail therefore must ensure strong inter-sections at these locations where the overall shape of the raft tends to weaken structural behaviour.

Fig. 13.14 Weak and improved thickening layouts.