FOUNDATION ON ROCK

1. Introduction1.1 Type of Foundation on Rock1.2 Input Parameter For Bearing Capacity Calculation 1.3 Loadings From Upper Structures Analysis For Foundation

2. Shallow Foundation2.1 Bearing capacity

- Strength Properties Based on Rock Mass Classification System ( RMR)

- Hoek And Brown Bearing Capacity- Empirical Formula

2.2Stability Of Shallow Foundation - Under Vertical Load- Under Vertical, Horizontal And Moment Load

3 Deep Foundation3.1 Bearing Capacity

3.1.1 Piles on intact ( unweathered ) rocks. 3.1.2 Piles on weathered rocks.

3.2Stability Of Deep Foundation - Single Pile- Piles In Group

1. INTRODUCTION

1.1 Type of foundation on rock

Foundations may rests on soil or rock, it can be shallow ( footing foundation) or deep foundations ( pile foundation ), deep foundation might be in single pile or pile in group.In this chapter, the description is focused on foundation on rock. Two types of rock foundation each requiring different design procedures, are illustrated in fig.1 . the upper photograph shows spread footings for a cut and cover structure founded on an interbedded sequence of very weak sandstone and shale. With each footing surrounded by a considerable extent of intact rock, the primary design task for these foundation is determination of the allowable bearing pressure and the magnitude of the settlement. The lower photograph shows a bridge foundation located near the crest of vertical slope of a very strong granite. The rock has adequate bearing capacity for the applied loads and settlement will be elastic and negligible. Therefore, the primary design task is to ensure that blocks of rock in the foundation formed by continuous joints are stable against toppling and sliding.

fig.1 Shallow foundation on rock

The design of footing on rock encompass the following three tasks that examine different aspects of foundation performance :

1. The bearing capacity of the rock to ensure that there will be no crushing or creep of the material within the loaded zone.

2. Settlement of the foundation which will result from both elastic and inelastic strain of the rock, and possibly compression of weak seams within the volume of rock compressed by the applied load.

3. Stability of the footing by examination of sliding and shear failure of blocks of the rock formed by intersecting discontinuity within the foundation.

The performance of a foundation must be checked with respect to all three of this conditions because they are independent of each other.

1.2 Input parameter for bearing capacity calculation

Bearing capacity ( BC) is a capacity and capability of soil or rock and foundation either shallow or deep foundation to retain loading from upper structure.The upper structure can be bridge, tower, building or any structure which resting on the foundation.In design and analysis of foundation, three steps as mentioned above should be performed, in order to calculate bearing capacity, some aspects should be taken into account.Bearing capacity can be obtained from site investigation to the area of soil or rock where any structure will be built resulting in some parameters.

1. BC from building codeBC taken from this method is very rough value, only recommended when site investigation data not available.

2. BC from the measurement of particular parameter in in-situ test and laboratory test.

1.3 Loadings From Upper Structures Analysis For Foundation

The figure 2 shows how the load is transferred into the rock, the loading from upper structure ( dead load and live load ) is collected in the column of the building, at the same time the column is attached to the top part of the foundation then the loading is given by the foundation to the soil / rock resulting in a system of equilibrium.

2. SHALOW FOUNDATION

2.1 Bearing capacity

The usual method of determining allowable bearing pressures is to use published tables or building codes relating allowable values to rock type. However, in a circumstances where the rock conditions do not match description on the building code, it is more appropriate to use limit equilibrium or numerical methods incorporating appropriate rock mass strength parameters.Most of the foundations lay on the following geological conditions :

1. Fractured and weathered rock2. Shallow dipping bedding plane3. layered formation4. karstic formation.

To calculate bearing capacity of footing, the geological condition should be determined in advance to select the appropriate bearing capacity formulation.

1. BC using building code.

The allowable bearing pressure for three classes of rock ( soft rock, medium rock and hard rock ) can be used using building code as shown in the fig.3

High rise building

Soil / rock Foundation

Fig.2 Transfer of loading to the soil

fig.3 BC from building code

The effect of fractured intensity on bearing capacity of the above rock types can be estimated from RQD of drill core as follow :

a) RQD > 90 % : no reductionb) 50 %< RQD < 90 % reduced BC by factor of about 0.25 – 0.7c) RQD < 50 % reduced BC by a factor of about 0.25 – 0.1 ; reduce BC further if extensive clay seams present.

Fig . 4 Allowable bearing pressure for intact rock

2. BC of fractured rock ( Hoek and Brown formula )

- Compressive strength of fractured rock

Fractured rock will of course have a much lower compressive strength than intact rock.A strength criterion Has been developed by Hoek and Brown :

Where :

Maximum principal effective stressminimum principal stress or confining stressuniaxial compressive strength of intact rock

m and s dimensionless constant from the table 1 Hoek and Brown

Table 1 : Rock mass quality vs material constant

The typical shape of the strength envelope defined by equation above, is shown in the figure 5 . The steep gradient of this curve clearly demonstrates that increasing confining pressure has a significant effect on improving the strength and bearing capacity of the rock.

Fig 5 Strength of fractured rock

The formula of allowable BC using Hoek and Brown expression :

Where : Cf1 = correction factor for foundation shape shown in the table 2. SF = safety factor 2 – 3 m and s = material factor of discontinuity = uniaxial compressive strength

In the case of footing which recessed into the rock surface, it is necessary to modify equation above to account for the increase in the stress as a results of confining stress applied at the ground surface.

The modified value of allowable bearing pressure is as follows :

Where :

table 2 shape factor

3. BC from Bell

For weak rock with little fracturing , Bell provide the formula which utilizes the bearing capacity factor Nc Nq Nγ described in the fig 6

Where :

Nc = 2 Nθ1/2(Nθ+1)

Nq = Nθ2

Nγ = 0.5 Nθ1/2(Nθ

2 – 1 )

Nθ= tan2(45 + )

BC of shallow dipping bedded formations

Nθ1= tan2(45 + )

Nθ2= tan2(45 + )

fig.6 BC factors

If the rock surface around the footing is subjected to a surcharge pressure qs , as might be the case if the footing were recessed into the ground surface, then the BC is increase due to the confinement provided to the passive wedge.

Example 1

Consider a 2 m wide strip footing bearing on the surface of a fair quality limestone in which the average discontinuity spacing is 400 mm and contain some clay. The strength properties of rock are as follows :

1. Unconfined compressive strength of intact rock, = 75 MPa2. Curve strength envelope parameter m=0.128 and s = 0.000093. Rock density = 0.022 MN/m3

For a strip footing, the correction shape factor Cf1 and Cf2 = 1.

a. Building code

From the table 5.1 and 5.2 a bearing capacity of about 1 – 2 MPa can be interpreted for rock which is moderately strong and has a moderate discontinuity spacing

b. Hoek and Brown

using the formula :

qa = 1.14 Mpa

c. Bell solution

Bell solution needs c and of rock mass. For an average pressure on the foundation = 2 MPa , the instantaneous values for c and are 0.54 and 25 o

respectively. Then Nθ = 2.47Nc = 10.92 and Nγ = 4.01.

Assuming strip foundation of width 2 m and SF = 3, qa = = 2 MPa.

2.2 Stability of shallow foundation

To control the structure is safe under such loading, the stability analysis is performed by comparison between the loading from upper structure with allowable bearing capacity.The allowable bearing capacity is ultimate bearing capacity divided by safety factor. qall = qult / SFthe value of SF is recommended 2 – 3 depends on standard requirement.

1. Stability Under Vertical Load

Fig.8

Fig.7 Stability under V Loading only

The structure is safe when

V

Column

Footing

Rock

Where : V = vertical load, A contact area between footing and rock qall = allowable bearing capacity

2. Stability Under Vertical, Horizontal And Moment Load

Fig.8 Stability under VHM Loading

Under this circumstances, 2 analysis should be performed.1. Stability under horizontal load

2. Stability under moment load

DEEP FOUNDATION

3.1 BEARING CAPACITY

V

H M

Piles foundation on rock consist of :a. Bored and rock socketed pileb. Piles driven to rock

Rocks may be either unweathered and intact or may be in weathered state, pile design criteria will be different for both two rock conditions.

3.1.1 Piles on intact ( unweathered ) rocks.

As shown in the figure 9 , two types of piles are generally installed on rock.The measurement of bearing capacity can be based on RQD value and properties of rock cores.

fig 9 type of pile foundation on rock

a. Allowable BC based on RQD value.

The table 3 can be used to obtain qa , for this contact pressure, the settlement of foundation should not exceed 0.5 in ( 12.5 mm ).

table 3 Allowable contact pressure

b. Allowable BC based on properties of rock cores.

The qa for cast in place or rock socketed piles in rock can be evaluated by relating it to rock core strength as given by equation :

Where :

(qu)core = average unconfined compressive strengthKsp = empirical factor given in figured = depth factor given by equation

Ls = pile length that is socketed in rock having a strength qu and B is diameter of pileSd = spacing of discontinuitytd = thickness of discontinuity

fig 10 value for Ksp

c. Allowable BC derived from the bond between rock and concrete

Qall = p Ls Cbs

p = pile perimeter ( = πB for circular pile )Ls = socketed pile length in the rockCbs = allowable bond strength between concrete and rock.

table 4 allowable strength of skin friction and end bearing

3.1.2 Piles on weathered rocks.

Weathered rocks exhibit a great variety of physical properties. In situations where weathering is extensive and rock fragments are surrounded by decomposed soil, the foundation should be designed as if supported on soil matrix.

3.2 STABILITY OF DEEP FOUNDATION

a. Single Pile

The control to stability either shallow or deep foundation is defined as a comparison of strength of rock and foundations against service load multiplied by Safety factor.Under simple condition single pile with vertical load, the control of pile stability is :

where Qult = Capacity of single pile under vertical load

b. Piles In Group

The control of pile stability in group requires complex analysis, will be described in the next subject.

Example :

A 36 in ( 900 mm ) diameter drilled pile is supported on unweathered rock by socketting 6 ft into it. The rock was sandstone with qu core of 90 t/ft2. Estimate the allowable BC of the pile.

Solution: a) Allowable BC from table : For group c in table presumed allowable BC for medium to high sandstone is 10 to 40 t/ft2 ( 1000 to 4000 kN/m2)

b) Allowable BC From properties of rock

Ls = 6 ft ; B = 3 ft ; d = 0.8 + 0.2( 6/3 ) = 1.2

In the absence of information on sizes and spacing of discontinuities, assume Ksp = 0.3 from figure , then from equation qa = ( qu )core Ksp d = 90 x 0.3 x 1.2 t/ft2 = 32 t/ft2

c) Allowable BC derived from the bond between rock and concrete

Qv(all) = p Ls Cbs

The value for a allowable bond stress Cbs is not available for unweathered Sandstone and the pile material ( concrete ). A conservative value of 4.5 t/ft2

Can be estimated from table.

Cbs = 4.5 t/ft2 ; p = x B ; Ls = 6 ft

Qv(all) = p Ls Cbs = x 3 x 6 x 4.5 = ; qall = Qv(all) / Area

qall = 36 t / ft2

From the case b and c , the lower value of allowable BC = 32 t/ft2 can be obtained.