For the maximum limiting value for the differential settlement of a mat foundation under the surcharge of an RC building you should consider more parameters such as soil type.That value that you mentioned based on the maximum differential settlement was limited to 50 mm according to Skempton and McDonald (1956) is a small part of solution for this issue. please consider the issue more widely and see the following items.

The assessment of limiting settlements of structures is more complex than that of limiting deformation as it brings in the behavior of the ground and its interaction with the structure.

The problem is essentially one of estimating the maximum relative deflections and rotations likely to be experienced by the structure. Nevertheless, the practicing engineer needs to know when it is reasonable for him to proceed in a routine manner and for this he uses simple guidelines based on previous experience.

All too often such guidelines are interpreted as providing rigid rules for "allowable maximum settlements". Terzaghi (1956) issued a stern warning against such proposals , The problem is to provide safe simple guides without inhibiting the search for optimum solutions when appropriate. It is therefore suggested that the term 'Routine Limits' be used when such guidelines are proposed.

Following Terzaghi and Peck (1948), foundations on sand will be treated separately from those on clayey soils. Such a division does, of course, leave out a wide range of types of ground for which the engineer must use his judgement and experience:

1- The mat foundation on Sand:

Terzaghi and Peck (1948) suggested that for footing on sand the differential settlement is unlikely to exceed 75 per cent of the maximum settlement and since most ordinary structures can withstand 20 mm of differential settlement between adjacent columns , a limiting maximum settlement of about 25 mm was recommended.

For raft foundations the limiting maximum settlement was increased to 50 mm, Skempton and MacDonald (1956) correlated measured maximum relative rotation (angular distortion) Beta with total and differential settlement for eleven buildings founded on sand. They concluded that for a safe limit of Beta = 1 /500 the limiting maximum differential settlement is about 25 mm and the limiting total settlements are about 40 mm for isolated foundations and 40 mm to 65 mm for mat foundations,

2 - Mat foundation on Clayey soils:

Using similar procedures to those described previously Skempton and MacDonald concluded that for foundations on clay the design limit for maximum differential settlement is about 40 mm. The recommended design limit for total settlements are about 65 mm for isolated foundation and 65 mm to 100 mm for mat foundations. These recommendations were criticized by Terzaghi on the grounds that the relationship between maximum relative rotation Beta and maximum settlement in clay is dependent on too many factors for a single value to be assigned to it. Grant, Christian and Vanmarcke have added a number of case records to the original data. These confirm that there is no simple correlation between maximum relative rotation and maximum settlement in clay soils. Nevertheless, we must consider whether Skempton and MacDonald's recommendations are acceptable as routine limiting values.

I hope it was useful for you.

All the best.

It is more difficult to predict the differential settlement; thus, it is obtained directly from the total settlement. The differential settlement is automatically controlled if the total settlement is controlled. Observation of existing buildings showed that the differential settlement < 50% total settlement.

The following is the design limits for maximum settlements

Raft on clay: 65 to 100 mm

Raft on sand: 45 to 65 mm

Dear Navid Yeganeh,

The maximum load that may be safely applied to a foundation unit, considering both the strength and settlement of the soil, under expected loading and soil conditions and the expected un‐factored load to a foundation unit is much concern here.

Differential settlement is the difference in total settlement between two foundations or two points in the same foundation. It occurs as a result of relative movement between two parts of a building. The related terms describing the effects of differential settlement on the structural as a whole or on parts of it are tilt, rotation and angular distortion/relative rotation. As a general rule, a total settlement of 25 mm and a differential settlement of 20 mm between columns in most buildings shall be considered safe for buildings on isolated pad footings on sand for working load (unfactored). A total settlement of 40 mm and a differential settlement of 20 mm between columns shall be considered safe for buildings on isolated pad footings on clay soil for working load. Buildings on raft can usually tolerate greater total settlements. Limiting tolerance for distortion and deflections introduced in a structure is necessarily a subjective process, depending on the status of the building and any specific requirements for serviceability.

****For isolated foundations, RCC Structures for sand and hard clay, Maximum Settlement (mm) is 50 mm and Differential Settlement (mm) is 0.0015 L. Similarly for Plastic Clay, Maximum Settlement (mm) is 75mm and Differential Settlement (mm) is 0.0015 L. angular distoration for both (sand and hard clay) and (plastic clay) is 1/666 same. A factor of safety shall be applied to all estimates of failure load after considering allowable total and differential settlement of the structure. Settlement is to be limited or differential settlement avoided (i.e., for accurately aligned machinery or a fragile finish of superstructure). In case of submerged loose sands, vibration caused by earthquake may cause liquefaction or excessive total and differential settlements.

Ashish

Dear Navid Yeganeh,

The maximum load that may be safely applied to a foundation unit, considering both the strength and settlement of the soil, under expected loading and soil conditions and the expected un‐factored load to a foundation unit is much concern here.

Differential settlement is the difference in total settlement between two foundations or two points in the same foundation. It occurs as a result of relative movement between two parts of a building. The related terms describing the effects of differential settlement on the structural as a whole or on parts of it are tilt, rotation and angular distortion/relative rotation. As a general rule, a total settlement of 25 mm and a differential settlement of 20 mm between columns in most buildings shall be considered safe for buildings on isolated pad footings on sand for working load (unfactored). A total settlement of 40 mm and a differential settlement of 20 mm between columns shall be considered safe for buildings on isolated pad footings on clay soil for working load. Buildings on raft can usually tolerate greater total settlements. Limiting tolerance for distortion and deflections introduced in a structure is necessarily a subjective process, depending on the status of the building and any specific requirements for serviceability.

****For isolated foundations, RCC Structures for sand and hard clay, Maximum Settlement (mm) is 50 mm and Differential Settlement (mm) is 0.0015 L. Similarly for Plastic Clay, Maximum Settlement (mm) is 75mm and Differential Settlement (mm) is 0.0015 L. angular distoration for both (sand and hard clay) and (plastic clay) is 1/666 same. A factor of safety shall be applied to all estimates of failure load after considering allowable total and differential settlement of the structure. Settlement is to be limited or differential settlement avoided (i.e., for accurately aligned machinery or a fragile finish of superstructure). In case of submerged loose sands, vibration caused by earthquake may cause liquefaction or excessive total and differential settlements.

Ashish

Dear Mr. Ashish Thakur,

Could you pls. furnish a reference for the allowable differential settlement of 0.0015L and angular distortion of 1/666.

Regards,

Kedar Birid

It depends on type of structure and the standards you are complying with. For example; in EuroCode EN1997, the limiting value of angular distortion for framed buildings and load bearing brick walls ranges between 1/300 to 1/2000

in Egyptian code (ECP202/2007-Part 3), the allowable angular distortion ranges between 1/150 to 1/750 depending on type of structures