Mat Design and Construction

MAT Foundation Design and Construction

ম্যাট ডিজাইন যেহেতু বিএসসিতে বেশী শিখানো হয়না সিভিল ইঞ্জিনিয়াররা রিয়েল লাইফে ডিজাইন করতে যেয়ে সমস্যায় পড়েন । বিশেষ করে যারা জিওটেকনিক্যাল বইয়ের শরনাপন্ন হন তারা আরো বেশী সমস্যায় পড়েন । ম্যাট এর ডিজাইনের দুইটা দিক । একটা হল জিওটেকনিক্যাল ডিজাইন । আরেকটা হল স্ট্রাকচারাল ডিজাইন । ম্যাট এর ডিজাইন সম্পর্কে বইতে অনেক পুরনো কিছু মেথড আছে যা এখন আর ব্যাবহার করা কোন মতেই উচিত না । জিওটেকনিক্যাল ফাইনাইট এলেমেন্ট সফটওয়্যার ব্যাবহার করে ম্যাট ডিজাইন করতে পারলে সবচেয়ে ভাল হয় । কিন্তু এটা সময়সাপেক্ষ এবং ব্যয়বহুল । সুতরাং ETABS or STAAD Pro দিয়ে যদি ম্যাট ডিজাইন করা যায় সিভিল ইঞ্জিনিয়াররা অনেক সহজে 80-90% Accuracy তে ম্যাট ডিজাইন করতে পারবে । এর জন্য যা দরকার সব আছে এই কোর্সটিতে ।

Mat foundation or raft foundation is not taught enough at the undergraduate level. Civil engineers are facing difficulties in mat foundation or raft foundation design. They try to find the solution in the Geotechnical textbooks. But there is not up to date methodology of raft foundation design in those textbooks. So, they are in real trouble in designing the mat foundation. There are two aspects of mat foundation design; (i) geotechnical design of mat foundation and (ii) structural design of mat foundation. Textbooks contain traditional methods of raft foundation design which should not be used anymore. The best method is to use Geotechnical FEM software where you can model the soil, foundation and structure all together. However, it is expensive and time-consuming process. This short course will teach you how to model the raft foundation and structure together in structural FEM softwares, like ETABS and STAADpro.

What you'll learn

  • Bearing capacity calculation of Mat foundation on sand and clay
  • Settlement calculation of Mat foundation on sand and clay soil
  • Structural design of Mat foundation
  • Structural design of basement wall
  • Software modeling of raft foundation
  • Modulus of subgrade reaction
  • Construction difficulties of Mat foundation

Prerequisite / Eligibility

  • BSc, MSc or PhD in Civil Engineering
  • Level 4 or 4th year student of bachelor’s in civil engineering
  • AMIEB students of IEB

Course Teacher

Professor Dr. Jahangir Alam, Department of Civil Engineering, BUET, Dhaka, Bangladesh

Brief Biography of Course Teacher

Education

  • PhD in Geotechnical Earthquake Engineering, the University of Tokyo, Japan, 2005
  • MSc in Civil and Geotechnical Engineering, BUET, Dhaka, Bangladesh, 2002
  • BSc in Civil Engineering, BUET, Dhaka, Bangladesh, 1998

Biography

Professor Dr. Engr. Md. Jahangir Alam is faculty member at the Department of Civil Engineering, BUET, Dhaka-1000, since 1999. He completed his PhD from University of Tokyo in Geotechnical Earthquake Engineering in 2005 as a Monbu-Kagaku-sho Scholar. He was research fellow in Ecole Centrale Paris in 2008. Professor Jahangir did his BSc in Civil Engg with major in Structure and MSc in Civil and Geotechnical Engineering from BUET.

Professor Jahangir has multidisciplinary research interests and has publications in international journals and conferences. His current research topics are “Risk Sensitive Land Use Planning of Mega City”, Physical and Numerical Modeling of Liquefaction Hazard, Mitigation against Seismic Liquefaction, Cyclic Behavior of Non-plastic silt, Reinforced Earth, Earthquake Resistant Foundation in Soft Soil, Climate Resilient Concrete, Climate Resilient Road.

Professor Jahangir was involved in many consultancy projects where he designed/checked high rise RCC buildings, Communication towers, Jetty, Shore Pile, Embankment, Container Terminal, Ground Improvement, Bridge Foundation etc. He supervised many MSc and PhD students. He was involved in pile load testing, pile integrity testing, concrete mix design and development of laboratory and field-testing equipment.

Professor Jahangir actively involved in National and International professional bodies. He is life member and was Treasurer of Bangladesh Society for Geotechnical Engineering (BSGE), which is Bangladesh Chapter of ISSMGE. He is life fellow of Institute of Engineers Bangladesh (IEB). He is life member of Bangladesh Earthquake Society (BES). He was Treasurer of Bangladesh Earthquake Society (BES).

Certificate of Attendance

Certificate of attendance will be awarded after completion of all video lessons and quizzes

Related Courses

  • Footing design and construction
  • Pile Design and Construction
  • Shore Pile and Braced Excavation Design

Free Courses

  • Design Issues for Large Earth Structures: Stress, Deformation, FOS and Liquefaction
  • Quality Control of Cast in Situ Piling

Features of ourPROFESSORs.com

Frequently Asked Questions (FAQ)

Course Preview

Detail Course Outline

Introduction to Mat/Raft Foundation

  • The necessity of raft foundation
  • Compensated raft foundation
  • Advantages of mat foundation
  • Types of raft foundation: Based on support or structural system
  • Load combination for bearing capacity and settlement
  • Bearing pressure
  • Bearing capacity
  • Factor of safety
  • Settlement
  • Examples
  • Modulus of subgrade reaction and modulus of elasticity
  • Problems of mat foundation

Differential Settlement of Mat Foundation

  • Modulus of Subgrade Reaction, Vertical Spring Constant
  • Differential Settlement
  • Rigidity Factor & Distortion factor

Seismic Design of Mat Foundation

  • Basic Foundation Design Procedures
  • Proportioning
  • Punching Shear Strength of Mat
  • Beam Shear Strength of Mat
  • One-Way Shear and Vertical Reinforcement
  • Analysis
  • Typical Modeling Practice

Structural Design of Mat

  • Design Steps of Mat Foundation
  • Control Settlement
  • Methods of Structural Design: Conventional Rigid Method, Approximate Flexible Method OR Beam on Elastic Foundation, Simplified Elastic (Flat Slab) Method, Finite Difference Method, Finite Element Method by Modeling Mat and Superstructure, Finite Element Method by Modeling Soil, Mat and Superstructure.
  • FoS against overturning
  • Limit of eccentricity
  • Thickness from Punching Shear
  • ETABS or safe modeling

Structural design of basement wall

  • Lateral earth pressure determination
  • The thickness of Basement Retaining Wall

Construction Issues of Mat Foundation

  • Concrete of Basement Wall
  • Construction Joint in Mat and Wall
  • Water Proofing of Mat & Retaining Wall
  • King Post Removal

Introduction of Mat Foundation

1
Introduction of Mat Foundation, Part-1

Mat/Raft Foundation



NECESSITY OF RAFT FOUNDATION

·        sum of footing area > 50% of building footprint – then RAFT is preferred

·        But this concept is not accepted by all professionals


Raft foundation is generally suggested in the following situations:

·        Building load is heavy

·        Allowable bearing capacity of soil is so small that individual footings would cover more than 50% or 80% of floor area

·        Soil contains compressible lenses or the soil is sufficiently erratic

·        When it is difficult to define and assess the extent of each of the weak pockets or cavities

·        When it is difficult to estimate the overall and differential settlement.

·        When structures and equipment to be supported are very sensitive to differential settlement.

·        Where structures naturally lend themselves for the use of raft foundation such as silos, chimneys, water towers, etc.

·        Floating foundation cases wherein soil is having very poor bearing capacity and the total weight of the super-structure is proposed to be balanced by the weight of the soil removed.

·        The amount of differential settlement between various parts of a structure supported on a mat foundation is much lower than individual footings but undergone the same amount of maximum settlement.

·        Maximum total settlement which can be allowed for a particular structure on mat foundation is more than the structure is resting on individual footings

·        Where basements are to be provided



COMPENSATED RAFT FOUNDATION

·        100% compensated foundation=floating foundation or buoyancy raft foundation

·        Very soft and highly compressible soil

·        In normal circumstances building construction is not possible, it may be possible to provide the building with a compensated foundation

·        The relief of stress due to the excavation is approximately balanced by the applied stress of the foundation, resulting in a negligible net stress

·        The structure acts in a similar way to a ship’s hull

·        As a result there may be little consolidation settlement experienced

·        Compensated foundations normally comprise a deep basement and/or are used to support tall buildings or swimming pools, where a very large amount of material is excavated.



ADVANTAGES MAT FOUNDATION

·        Ultimate bearing capacity increases with increasing width of the foundation bringing deeper soil layers in the influenced zone.

·        Consolidation Settlement decreases with increased depth of basement

·        Minimizes differential settlement



TYPES OF RAFT FOUNDATION

Based on the method of their support

1.      Raft supported on soil

2.      Buoyancy raft or floating raft or fully compensated mat foundation

3.      Raft supported on soils and piles (Piled Mat)


Based on structural system

1.      Plain slab rafts which are flat concrete slabs having a uniform thickness throughout. This can be with pedestals or without pedestals.

2.      Beam and slab raft which can be designed with downstand beam or upstand beam systems.

3.      Voided mat or Cellular raft or Framed raft with foundation slab, walls, columns and one of the floor slabs acting together to give a very rigid structure.



LOAD COMBINATION FOR BEARING CAPACITY

Design Load

(a) Shallow foundation design considering bearing capacity due to shear strength shall consider the most unfavorable effect of the following combinations of loading:


(i) D + L

(ii) 0.75*(D + L + W or E)

(iii) 0.9*D + Buoyancy Pressure

(iv) 0.6*D + W



LOAD COMBINATION FOR SETTLEMENT

(b) Shallow foundation design considering settlement shall consider the most unfavourable effect of the following combinations of loading:


Cohesionless

 D + L


Cohesive soil

D + 0.5*L



Bearing Capacity of Mat Foundations

Safe bearing capacity = Ultimate / FS< bearing pressure under mat [FS = 3]


Settlement must be calculated and compared with allowable limit



FULLY COMPENSATED AND PARTIALLY COMPENSATED MAT FOUNDATION

1.      Figure indicate that the net pressure increase in the soil under a mat foundation can be reduced by increasing the depth of the mat.

2.      This approach is generally referred to as the compensated foundation design and is extremely useful when structures are to be built on very soft clays.

3.      In this design, a deeper basement is made below the higher portion of the superstructure, so that the net pressure increase in soil at any depth is relatively uniform



Allowable Bearing Capacity of Mat Foundations at Limiting Settlement

The net allowable bearing capacity for mats constructed over granular soil deposits can be adequately determined from SPT value.


N_60=Standard Penetration Resistance

B=Least dimension of Mat is not to be large

F_d=depth factor=1+0.33 Df/B≤1.33

S_e=Allowable settlement (mm)



How to calculate Ks

First elastic settlement will occur then consolidation settlement will take place

Therefore, Ks should be determined by considering both of the settlements

This can be done as follows


Considering elastic settlement

ks=Q0/∆H

Where, ??= pressure due to axial force of the vertical member

∆?= Elastic settlement of the foundation


Although the base contact pressure ?? remains constant the total settlement is

Where, ∆?? is the consolidation settlement

So, modulus of subgrade reaction is


If ?? is known then ?? can be calculated by as follows

worked out example (previously calculated)



Mat Settlement

Mat foundations are commonly used where settlements may be a problem. The settlement tends to be controlled by the following:

1.      Use of a larger foundation to produce lower soil contact pressures

2.      Use fully or partially compensated mat

3.      Bridging effects attributable to

a.      Mat rigidity

b.      Contribution of superstructure rigidity to the mat



Differential Settlement of Mat

In 1988, the American Concrete Institute Committee 336 suggested a method for

calculating the differential settlement of mat foundations. According to this method,

 the rigidity factor Kr is calculated as

Kr=EI/EB



Important notes on differential settlement of mat

1.      Kr significantly related to modulus of elasticity of soil – E?

2.      If mat thickness is determined using punching shear, then usually, mat becomes rigid – means no differential settlement

3.      In Etabs/SAFE model, Ks should vary from center to edge

4.      Voided or cellular mat is best to make the mat rigid



Typical Modeling Practice

Depending on the subgrade behavior, dishing may have a relatively small effect on soil pressure distribution but may have a more significant effect on bending moments in the mat foundation (Horvilleur and Patel 1995).



Problems of mat foundation

1.      Overturning of high rise building at extreme wind load or EQ load

2.      Liquefaction of foundation soil (loose sand + non plastic silt) during EQ

3.      Gradual tilting of building due to non-uniformity of soil under mat

4.      Overstressing and cracking of structural members due to differential settlement of flexible mat

2
Introduction of Mat Foundation, Part-2
3
Introduction of Mat Foundation, Part-3
4
Introduction of Mat Foundation, Part-4
5
All documents of Mat design and construction

Geotechnical design of Mat

1
Basics about Bearing Capacity
2
Bearing Capacity of Mat Foundations
3
Ultimate Bearing Capacity Example
4
Allowable Bearing Capacity of Mat Foundations at Limiting Settlement
5
Bearing Capacity Considering Settlement, Part-1
6
Bearing Capacity Considering Settlement, Part-2
7
Calculation of consolidation settlement
8
Effect of size of foundation on settlement
9
Mat Settlement, Part-1
10
Mat Settlement, Part-2
11
Mat Consolidation Settlements Example, Part-1
12
Mat Consolidation Settlements Example, Part-2
13
Conclusion

Differential Settlement of Mat Foundation

1
Differential Settlement of Mat Foundation, Part-1

Differential Settlement of Mat Foundation




Modulus of Subgrade Reaction (Ks)

Ks = q/δ

q=Stress on Plate in kN/m2

δ = settlement of Plate in m



Vertical Spring Constant (Kz)

Vertical Spring Constant (Kz) in kN/m =P/ δ

P=Load on column in kN

δ = settlement of footing in m



Differential Settlement of Mat as per ACI Committee 336 (1988)

Rigidity Factor, Kr

In 1988, the American Concrete Institute Committee 336 suggested a method for calculating the differential settlement of mat foundations. According to this method, the rigidity factor Kr is calculated as



Distortion Factor and Differential Settlement Proposed by Professor Jahangir Alam

D=EIEs/B3



Ks for Flexible Mat

Depending on the subgrade behavior, dishing may have a relatively small effect on soil pressure distribution but may have a more significant effect on bending moments in the mat foundation (Horvilleur and Patel 1995).



Structural Design of Mat

·        Determine settlement of mat at center

·        Determine differential settlement of mat considering rigidity of mat using any method

·        Determine ks for center, edge and corner

·        Analyses the mat including superstructure which will consider the soil-structure interaction approximately (if possible, use Geotechnical FEM software)



Conclusions

·        Differential settlement and angular distortion of mat can be calculated using rigidity factor (ACI) or distortion factor (proposed by us) or Fraser and Wardle (1976) Method

·        Subgrade modulus at center and edge is different and should be determined considering mat rigidity

2
Differential Settlement of Mat Foundation, Part-2
3
Differential Settlement of Mat Foundation, Part-3
4
Differential Settlement of Mat Foundation, Part-4

Bearing capacity calculation

1
Bearing capacity calculation, Part-1

Bearing Capacity

 

 

 

LOAD COMBINATION FOR SETTLEMENT

(b) Shallow foundation design considering settlement shall consider the most unfavourable effect of the following combinations of loading:

Cohesionless D + L

Cohesive soil D + 0.5*L

 

Notes: The values given in the Table may be taken only as a Guide and the permissible Total settlement, Differential settlement and tilt (angular distortion) in each cash should be decided as per requirement of the designer.

L denotes the length of deflected part of wall / raft or centre to centre distance between columns.

H denotes the length of wall from foundation footing.

* For intermediate ratios of L/H, the values can be interpolated. 



LOAD COMBINATION FOR BEARING CAPACITY

Design Load

Shallow foundation design considering bearing capacity due to shear strength shall consider the most unfavorable effect of the following combinations of loading:  

(i) D + L

 (ii) 0.75*(D + L + W or E)

 (iii) 0.9*D + Buoyancy Pressure

 (iv) 0.6*D + W



Ultimate // Safe // Allowable Bearing Capacity

1.           Ultimate bearing capacity = soil pressure at which failure occur

2.           Safe bearing capacity = ultimate/FS; so safety margin exist, no failure; but may have excessive settlement

3.           Allowable bearing capacity = soil pressure at which settlement of footing will be within permitted limit

4.           settlement governs for most of the soils

5.           Ultimate bearing capacity is determined using any formula = 600 kPa

6.           Safe Bearing Capacity = Ultimate / FS = 200 kPa

7.           Say footing size is 3 m x 3 m using safe bearing capacity and calculated settlement is 150 mm

8.           To limit the settlement within allowable limit (say 50 mm), footing size need to be increased. Say, 4 m x 4 m is ok at 100 kPa

9.           So, Allowable bearing capacity = 100 kPa



Bearing capacity vs. bearing pressure

Bearing capacity

1.           Ultimate bearing capacity is determined using any formula = 600 kPa

2.           Safe Bearing Capacity = Ultimate / FS = 200 kPa

3.           Say footing size is 3 m x 3 m using safe bearing capacity and calculated settlement is 150 mm

4.           To limit the settlement within allowable limit (say 50 mm), footing size need to be increased. Say, 4 m x 4 m is ok at 100 kPa

5.           So, Allowable bearing capacity = 100 kPa


Bearing pressure

1.           Bearing pressure = pressure applied on soil at the bottom of footing = soil pressure

2.           Applied load divided by footing area

3.           Bearing pressure may be less, equal or more than Allowable bearing capacity

4.           Bearing pressure should be less than Allowable bearing capacity

 

 

General shear failure

·        When ultimate bearing pressure is reached, footing will undergo a very large settlement

·        Bulging at both side of footing

·        Slip surface extends upto ground level

·        Zone a is pushed down, zone b is pushed laterally and zone c is pushed upward



Local shear failure

·        When ultimate bearing pressure is reached, footing will undergo a very large settlement

·        Small Bulging at both side of footing

·        Slip surface does not extends upto ground level

·        Zone a is pushed down, zone b is pushed laterally and zone c is not developed


Punching shear failure

·        When ultimate bearing pressure is reached, footing will undergo a very large settlement

·        No bulging at both side of footing

·        Slip surface does not form

·        Zone a is pushed down, zone b is pushed down


General Bearing Capacity Equation

The gross ultimate bearing capacity of a footing can be determined by the equation below:


Bearing capacity equation for local shear failure

Use the same equation which is given for general bearing capacity, but modify c and φ

 

Effect of ground water table

Three cases

Case I: above footing

Case II: at footing level

Case II: below footing level

    


General Bearing Capacity Equation

The term B in above equation is the smallest dimension of the mat.

 The net ultimate capacity of a footing is

The factor of safety against bearing capacity failure of mats on sand is very large

Bearing Capacity Factors

 

Ø>0 For cohesive soil and undrained condition, Ø =0.01            

 

Bearing Capacity Factors

 

Bearing Capacity Factors

 

Shape Factors

 

Depth Factors

 

Inclination Factors

 

Safe bearing capacity = Ultimate / FS

< bearing pressure under mat [FS = 3]

 

Settlement must be calculated and compared with allowable limit

 

Ultimate Bearing Capacity Example (Clay)

 

Ultimate Bearing Capacity Example (Sand)

2
Bearing capacity calculation, Part-2
3
Bearing capacity calculation, Part-3
4
Bearing capacity calculation, Part-4
5
Bearing capacity calculation, Part-5
6
Bearing capacity calculation, Part-6
7
Bearing capacity calculation, Part-7

Interaction of Nearby Footings under Building

1
Interaction of Nearby Footings under Building, Part-1

Effect of Interaction of Nearby Footings on Settlement of Foundation under Building



Which option is correct?

1.Settlement of footing under building

= Settlement of individual footing.

2.Settlement of footing under building

≠ Settlement of individual footing.



Engineering Properties of Subsoil

Constitutive model-Mohr-Coulomb

Saturated Unit Weight=18 kN/m3

Initial void ratio=0.800

Modulus of Elasticity=12 – 60 MPa

Poisson’s ratio=0.3

Cohesion=5 kN/m2

Drained Angle of Friction=35 degree


Vertical Settlement of Individual footing model at isolated location


Vertical settlement of Individual footing model under building for 5x5 matrix


Effect of Footing Interaction Parameter


Effect of Footing Interaction Parameter


Effect of Footing Interaction Parameter


Effect of modulus of elasticity and building size


Effect of distance from center of building


Effect of pressure on footing



Conclusions

The following conclusions may be drawn from the results of this parametric study.

1.     Settlement of individual footings under building = 1.5 to 5 times the settlement of individual footing at isolated location.

2.     Settlement individual footings under a building vary with the distance from center of the building. Maximum settlement was found at center of building.

3.     Scenter/Sind is highly sensitive with Footing Interaction Parameter (B/L) and Building size. Scenter/Sind increases with the increase of B/L and building size.

4.     Scenter/Sind α Footing Interaction Parameter.

5.     Scenter/Sind α Building Size For increased pressure, settlement increases. However, Scenter/Sind decreases with the increase of applied pressure on footing.

6.     Scenter/Sind α (1/Applied Pressure)

7.     Scenter/Sind is not sensitive with Modulus of Elasticity. However, settlement increases with the decrease of Modulus of Elasticity. 

2
Interaction of Nearby Footings under Building, Part-2

Short term and long term bearing capacity of Footing

1
Short term and long term bearing capacity, Part-1

Footing on Clay


Plate load test may mislead you 

Use of test results – which one?

UCS (Cu = Su = qu/2)

UU triaxial (Cu = Su = ?)

CU triaxial (C and phi)

CD triaxial (C and Phi)


Which condition properly represent

bearing capacity of footing of building?


·        UCS / UU triaxial (most conservative)

·        CU (most appropriate)

·        CD (long term capacity)


UCS or UU Triaxial Test


Consolidated Undrained Triaxial Test Result (CU Test)

NC Clay

Consolidated Drained Triaxial Test Result (CD Test)


OC Clay


Failure Envelope of Clay in Drained Triaxial Test


Peak – and residual- strength envelopes for clay


Effective Stress Friction Angle of Cohesive Soils


Plasticity index (%)

Variation of sin  with plasticity index (PI) for several normally

(Bjerrum and Simons, 1960; Kenney, 1959)


Important note on Effective Stress Friction Angle of Cohesive Soils


Phi (CU) = 0.66*phi (CD) (approx.)

From personal experience


Now you can explain: why some buildings did not fail even it was under designed


Loads are redistributed to adjacent footings if it is subjected excessive settlement

2
Short term and long term bearing capacity, Part-2
3
Short term and long term bearing capacity, Part-3
4
Short term and long term bearing capacity, Part-4

Seismic design of Mat

1
Seismic design of Mat, Part-1

Seismic Design of Mat




Reference

·        NEHRP Seismic Design Technical Brief No. 7

·        Seismic Design of Reinforced Concrete Mat Foundations. A Guide for Practicing Engineers

·        By Ron Klemencic, Ian S. McFarlane, Neil M. Hawkins, Sissy Nikolaou

·        NEHRP (National Earthquake Hazards Reduction Program) Technical Briefs are published by NIST, the National Institute of Standards and Technology, as aids to the efficient transfer of NEHRP and other research into practice, thereby helping to reduce the nation’s losses from earthquakes.



Introduction

·        Seismic design of reinforced concrete mat foundations has advanced significantly in the last twenty years.

·        As analytical capabilities have improved, primarily in the form of finite element analysis, the mathematical modeling of these continuous structural elements has led to seemingly more precise designs.

·        Yet, fundamental questions still remain regarding the seismic performance of these thick foundation systems.



Following Aspects Must be Considered during Mat Design

1.      Liquefaction

2.      Soft soil and site amplification

3.      FoS against overturning and sliding

4.      Drift due to soil deformation during EQ and wind

5.      Rebar detailing

6.      Punching shear reinforcement



Basic Foundation Design Procedures

1.      ACI 318 (ACI-ASCE Committee 326)

·        Foundations are designed using allowable stress for the soil and strength design (USD) for the concrete foundation

 

2.      Failures

·        Bearing failure of the soil under the foundation

·        serviceability failure because of excessive differential settlements causing nonstructural or structural damage to the superstructure

·        Excessive total settlements


3.      Limiting conditions

·        local flexural failure of the foundation (including reinforcement anchorage failure)


4.      shear failure of the foundation

·        Soil pressures were traditionally calculated by assuming linear elastic action of the soil in compression and no tension capacity offered by the soil.


5.      The stress under the foundation is given by:

q = P/A ± My/I

where, as illustrated in Figure 2-1(a) and Figure 2-1(b):

P = axial force

A = area of contact surface between the soil and the foundation

I = moment of inertia of contact area A

M = moment about centroidal axis of area A

y = distance from centroidal axis to position

where q is calculated


6.      If separation (uplift) between the soil and the foundation is to be avoided, the eccentricity e = M/P must lie within the kern of the contact surface.

The kern area, which is shaded area in Figure 2-1(c), is the area for which applied loads within that region will produce only compression over the area of the footing.



ACI 336.2R-88

·        American Concrete Institute 1988

The suggested design procedure using strength methods for proportioning the mat was as follows:


1.      Proportion the mat plan using unfactored loads and overturning moments as:

The value q is then scaled to a pseudo “ultimate” value as:


2.      Compute the minimum required mat thickness based on punching shear at critical columns and walls without the use of shear reinforcement


3.      Design the reinforcing steel for bending based on the strip methods described in the ACI 336.2R-66 report.


4.      Run a computer analysis of the resultant mat, such as with the finite element method as described in the ACI 336.2-88 report. Revise the rigid body design as necessary.




Punching Shear Strength of Mat

Two-Way Shear (Punching Shear)

Punching shear tests of slabs have shown that Equation 11-33 of ACI 318, Vc = 4√( f ’c)bod can be unconservative for thick members with low reinforcement ratios (Guandalini et al. 2009). *****

In addition, ACI 318 §11.11.3.1 requires that Vc ≤ 2√( f ’c)bod when reinforcement is provided for punching shear resistance. *****

Therefore, a value of Vc = 2√( f’c)bod is recommended for design purposes



Beam Shear Strength of Mat

One-Way Shear (Beam Shear)

Peak shear stresses have traditionally been considered as 2√f ’c , while some research (Reineck et al., 2003) suggests that for thick structural elements in one-way shear this is unconservative, and √f’c is a more appropriate shear stress threshold when no vertical reinforcement is provided


One-Way Shear and Vertical Reinforcement

When vertical reinforcement in accordance with ACI 318 §11.4.6 is provided in a mat foundation, aggregate interlock is maintained, and it is recommended to use Vc = 2√f ’c bod in combination with Vs corresponding to the vertical reinforcement provided. Therefore, a thinner mat may be possible by providing a nominal amount of vertical reinforcement as compared to a mat without vertical reinforcement



ACI 318 – 08 >>> 11.4.6 — Minimum shear reinforcement

11.4.6.1 — A minimum area of shear reinforcement, Av,min, shall be provided in all reinforced concrete flexural members (prestressed and nonprestressed) where Vu exceeds 0.5φVc, except in members satisfying one or more of (a) through (f):

(a) Footings and solid slabs; (b) ……….



Reason of Conservative Design of Mat

1.      There is great difficulty in predicting subgrade responses and in assigning even approximate properties to the soils

2.      Because of soil-strata thickness, variations in soil properties both horizontally and vertically, and rate of loading.

3.      There are effects of mat shape and variation in superstructure loads and their development, and there are effects of superstructure stiffness on mat response and vice versa.

4.      For those reasons, mats were conservatively designed to ensure adequate performance.



Analysis

Now a days, analysis of a mat foundation is typically performed using finite element analysis software

1.      Inputs

·        Geometry

·        loading

·        soil spring properties


2.      Analysis results

·        bearing pressure distributions

·        mat deformations

·        moment and shear diagrams

·        Details flexural reinforcement



Typical Modeling Practice

1.      Finite element analysis of mat foundations typically assumes gross section concrete stiffness with no cracking.

2.      Developing a numerical model for a mat foundation analysis model, stiffness of the complete structure should be considered

3.      For shear walls or basement walls above a mat foundation, the in-plane flexural stiffness should be added to the analysis model

4.      This can be accomplished with a very deep beam or slab element

5.      At elevator pits, the pit configuration should be reflected in the analysis model

6.      Where the pit depth is less than the mat thickness, a reduced mat thickness should be used

7.      For pits that extend below the mat foundation, a combination of reduced mat thickness and flexural releases should be used to reflect the pit configuration

8.      Dishing (or cupping) can be visualized by considering the difference in pressure at the center of a uniformly loaded mat as compared to the very edge of the mat

9.      The pressure at the edge of the mat dissipates quickly into the soil continuum because of lack of pressure on the adjacent soil, but the pressure at the center of the mat dissipates more slowly because of the adjacent loaded soil

10.  To accurately model this effect, a variable subgrade modulus may need to be used in the analysis model

11.  To select the appropriate modulus, iterations must be performed between the structural engineer and geotechnical engineer

12.  Dishing (or cupping) can be visualized by considering the difference in pressure at the center of a uniformly loaded mat as compared to the very edge of the mat

13.  The pressure at the edge of the mat dissipates quickly into the soil continuum because of lack of pressure on the adjacent soil, but the pressure at the center of the mat dissipates more slowly because of the adjacent loaded soil

14.  To accurately model this effect, a variable subgrade modulus may need to be used in the analysis model

15.  To select the appropriate modulus, iterations must be performed between the structural engineer and geotechnical engineer

16.  Depending on the subgrade behavior, dishing may have a relatively small effect on soil pressure distribution but may have a more significant effect on bending moments in the mat foundation (Horvilleur and Patel 1995).

2
Seismic design of Mat, Part-2
3
Seismic design of Mat, Part-3

Structural Design of Mat

1
Basics of Structural Design of Mat, Part-1

Structural Design of Mat





Problems of mat foundation

  • Overturning of high rise building at extreme wind load or EQ load
  • Liquefaction of foundation soil (loose sand + non plastic silt) during EQ
  • Gradual tilting of building due to non-uniformity of soil under mat
  • Overstressing and cracking of structural members due to differential settlement of flexible mat



Design Steps of Mat Foundation

  • Determine bearing capacity of the mat foundation
  • Determine total settlement of mat foundation
  • Determine the differential settlement
  • Determine stress / contact pressure distribution beneath the mat foundation
  • Design the structural component of the mat foundation



Comments of Tomlinsion

Structural Design of Mat need Compromise between two aspects

1. Keeping the differential settlement within allowable limit

2. Avoiding excessive stiffness in the raft structure

Flexible mat is economic because of low bending moment. But it leads to

  1. large differential settlement and
  2. increase the superstructure cost



How to Control Total Settlement of Mat Foundation

  • Extending mat outline
  • Increasing depth of foundation (increasing number of basements)

ú Better soil at greater depth

ú Increase of stress compensation

  • Use of piles under mat



How to Control Differential Settlement of Mat Foundation

  • Increasing mat thickness
  • Use of voided mat
  • Use of shear wall along perimeter and column lines
  • Ground improvement under mat foundation
  • Use of pile foundation
  • Increasing depth



Methods of Structural Design of Mat

  1. Conventional Rigid Method
  2. Approximate Flexible Method OR Beam on Elastic Foundation
  3. Simplified Elastic (Flat Slab) Method
  4. Finite Difference Method
  5. Finite Element Method by Modeling Mat and Superstructure
  6. Finite Element Method by Modeling Soil, Mat and Superstructure



Conventional Rigid Method

  • The mat is divided into strips loaded by a line of columns and resisted by soil pressure.
  • This strip is then analyzed as a combined footing.
  • The mat is assumed to be infinitely rigid.
  • Soil pressure is distributed in a straight line, and the centroid of the soil pressure is coincident with the line of action of the resultant column loads.
  • This method can be used where the mat is very rigid and the column pattern is fairly
  • uniform in both spacing and loads.



Advantage of conventional rigid method

  • Easy to perform hand calculation
  • No computer program is needed



Disadvantage of conventional rigid method

  • Crude method
  • Most conservative design – foundation cost will be high
  • This method can be used where the mat is very rigid and the column pattern is fairly uniform in both spacing and loads.
  • This method is not recommended at present because of the substantial amount of approximations and the wide availability of computer programs that are relatively easy to use.



APPROXIMATE FLEXIBLE METHOD

  • The mat is divided into strips loaded by a line
  • of columns and resisted by soil pressure.
  • The strip is modeled as beam on elastic foundation
  • This method is better than Conventional Rigid Method



APPROXIMATE FLEXIBLE METHOD

  •  Compute the plate rigidity D
  • Compute the radius of effective stiffness L
  • Compute the radial and tangential moments, the shear, and deflection.
  • Hand calculation is cumbersome. Computer program should be used.

Alternatively, FEM software may be used to apply this method



Simplified Elastic (Flat Slab) Method

  • Mat is considered as inverted flat slab
  • At column locations, x, y, z are restrained
  • Under the mat uniform or linear soil pressure is applied
  • Hand calculation is possible. FEM software should be used.



Comments of Tomlinsion

It is wrong in principle to assume that a raft acts as an inverted floor slab on unyielding supports

To design the mat on the assumption that its whole area is loaded to the maximum safe bearing pressure on the soil can lead to wasteful and sometimes dangerous designs



FINITE DIFFERENCE METHOD

The finite-difference method uses the fourth-order differential equation based on the theory of plates and shells Timoshenko and Woinowsky-Krieger (1959)



ADVANTAGES OF FINITE DIFFERENCE METHOD

  • It has been widely used (and should be used as a check on alternative methods where it is practical).
  • It is reliable if the mat can be modelled using a finite-difference grid.
  • It is rapid since the input data are minimal compared with any other discrete method, and the computations to build the stiffness array are not so extensive as other methods. Usually only three to five lines of input data are needed compared with up to several hundred for the other methods.



Disadvantages of Finite Difference Method

  • It is extremely difficult to model boundary conditions of column fixity.
  • It is very difficult to model notches, holes, or re-entrant corners.
  • It is difficult to apply a concentrated moment (as from a column) since the difference model uses moment/unit of width.



Finite Element Method by Modeling Mat and Superstructure

  • Mat and superstructure is modeled together
  • Subgrade modulus / area spring is used under mat
  • At column locations, x, y are restrained
  • FEM software should be used.


Finite Element Method by Modeling Soil, Mat and Superstructure

  • Soil, Mat and superstructure is modeled together
  • Soil properties are input as per constitutive model of soil
  • Boundary conditions are applied at outer surface of soil model
  • Geotechnical FEM software must be used



K from Plate Load Test

Subgrade Modulus is needed in many methods which can be obtained from plate load test and modified as follows

Limitation: plate load test gives stiffness of soil within shallow depth

 




K for Approximate Flexible Method

For long beams, Vesic (1961) proposed an equation for estimating subgrade reaction



Structural Design of Mat Foundation using Conventional Rigid Method


So the modified column loads are 

This modified loading on the strip under consideration is shown in Figure 6.10b. The shear and the moment diagram for this strip can now be drawn, and the procedure is repeated in the x and y directions for all strips.

Step 6: Determine the effective depth d of the mat by checking for diagonal tension shear near various columns.According to ACI Code 318-95 (Section 11.1.1.1c, America concrete Institute, 1995). for the critical section.


Step 7. From the moment diagram of all strips in one direction (x or y), obtain the maximum positive and negative moments per unit width (i.e.M’=M/B1).

Step 8. Determine the areas of steel per unit width for positive and negative reinforcement in the x and y directions, we have


Mu=(M’) (load factor)= Ф Asfy (d-a/2)

And a =Asfy/(0.85 f^' cb)

Where

As=area of steel per unit width

Fy=yield stress of reinforcement in tension

Mu= factor moment

Ф= 0.9= reduction



Conventional Rigid Method Example


Problem:

The plan of a mat foundation is shown in Figure 6.14. Calculate the soil pressure at points A,B, C,D,E and F. (Note: All column sections are planned to be

0.5 m x 0.5 m.)


Hence, the resultant line of action is located to the left of the center of the mat.

My=Q*ex= (11000)(0.44)= 4840kn-m


My=Q*ex= (11000)(0.44)= 4840kn-m

he location of the line of action of the resultant column


Note that the column loads shown in this figure have been multiplied bf F=0.9322.Also the load per unit length of the beam is equal to B1qav (modified)= (4.25)(38.768)=164.76KN/m.


Determination of the Thickness of the Mat

For this problem, the critical section for diagonal tension shear will be at the column carrying 1500 kN of load at the edge of the mat Figure-6

 

Assuming a minimum cover of 75 mm over the steel reinforcement and also assuming that the steel bars to be used are 25 mm in diameter, the total thickness of the Mat is

H=0.68+0.075+0.025/2=0.768m


Bending moment diagram

At strip GIJH

M-ve=1620.89 KN-m, M+ve=637.94 KN-m, M-ve=1620.89 KN-m, M-ve=1620.89 KN-m, M+ve=637.94 KN-m



Limit of eccentricity

If separation (uplift) between the soil and the foundation is to be avoided, the eccentricity e = M/P must lie within the kern of the contact surface.

The kern area, which is shaded area in Figure, is the area for which applied loads within that region will produce only compression over the area of the footing.



Approximate flexible method

This method, as proposed by the American Concrete Institute Committee 336 (1988), is described step by step. The use of the design procedure, which is based primarily on the theory of plates, allows the effects (i.e., moment, shear, and deflection) of a concentrated column load in the area surrounding it to be evaluated. If the zones of influence of two or more columns overlap, superposition can be employed to obtain the net moment, shear, and deflection at any point.

Step 1. Assume a thickness h for the mat, according to Step 6 of the conventional rigid method. (Note: h is the total thickness of the mat.)

Step 2. Determine the flexural rigidity R of the mat as given by the formula


Step 3. Determine the radius of effective stiffness—that is,


Step 4. Determine the moment (in polar coordinates at a point) caused by a column load (see Figure 6.13a). The formulas to use are


Step 5. For the unit width of the mat, determine the shear force V caused by a column load:


Step 6. If the edge of the mat is located in the zone of influence of a column, determine the moment and shear along the edge. (Assume that the mat is continuous.)

Moment and shear opposite in sign to those determined are applied at the edges to satisfy the known conditions.

Step 7. The deflection at any point is given by


Alternative solution of Approximate Flexible Method

Area

 1.          Model the strip as thick shell area in ETABS

2.           Apply column loads

3.           Apply subgrade modulus under strip

4.           Restrain x, y at column points


Beam

1.           Model the strip as beam in ETABS

2.           Apply column loads

3.           Apply line spring under beam

4.           Restrain x, y at column points



ETABS or safe modeling

Typical Modeling Practice

Depending on the subgrade behavior, dishing may have a relatively small effect on soil pressure distribution but may have a more significant effect on bending moments in the mat foundation (Horvilleur and Patel 1995).

Ks at edge and corner must be finalized by trial



Typical Modeling Practice

•     At elevator pits, the pit configuration should be reflected in the analysis model

•     Where the pit depth is less than the mat thickness, a reduced mat thickness should be used

•     For pits that extend below the mat foundation, a combination of reduced mat thickness and flexural releases should be used to reflect the pit configuration



Important note on structural design of mat

•        Thickness from punching shear

•        Mostly minimum reinforcement govern

•        Minimum rebar = temperature and shrinkage rebar OR 1.33 times of flexural rebar (Larger One)

•        Mat rebar should be designed modeling in Etabs/Safe

•        Reduction of mat thickness by providing punching shear rebar is not recommended



Steps of mat design using FEM

  1. Matching cg of mat area and cg of columns and shear wall loads (as close as possible)
  2. Determine thickness from punching shear
  3. Calculating bearing capacity and Check bearing pressure of mat under gravity and lateral loads
  4. Estimate settlement at center, edge and corner
  5. Estimate differential settlement and compare with limits
  6. Check FoS against overturning of whole building/str; FoS>1.5
  7. Calculate ks at center, edge and corner
  8. Model the whole structure and mat together with 3 diff ks. Finalize ks after trials so that settlement and diff settlement match with calculation 


2
Basics of Structural Design of Mat, Part-2
3
Basics of Structural Design of Mat, Part-3
4
Basics of Structural Design of Mat, Part-4
5
Conventional Rigid Method, Part 1
6
Conventional Rigid Method, Part 2
7
Conventional Rigid Method, Part 3
8
Approximate flexible method
9
Structural design of basement wall

Design of Basement Wall




Design of basement retaining wall

•     As shear wall of super-structure – from Etabs model as shear wall

•     As retaining wall (flexural stress) to support lateral earth pressure – as beam supported at each floor level

•     Whichever rebar governs?


·        Lateral earth pressure for basement wall


·        Lateral pressure for basement wall due to ground water


·        Lateral pressure due to soil and ground water


·        Thickness of Basement Retaining Wall

o  Minimum 300 mm

10
Water proofing and king post removal

Construction Issues of Mat Foundation



Concrete of Basement Wall

•     w/c ratio < 0.45

•     Strength > 4000 psi

•     Cement: CEM-II

•     Water proofing admixture

•     Membrane or other treatment at outer side of wall

•     FA = Sylhet sand

•     CA = stone chips



Construction Joint in Mat and Wall

Water Proofing of Mat & Retaining Wall


  1. Under mat: use 0.150 mm thick HDPE Geo-membrane sheet. if it is not available, may use any other polythene of about same thickness. 
  2. Outside of basement retaining wall: at first use a thin layer of emulsified bitumen, then attach 0.150 mm thick HDPE Geo-membrane sheet. If bitumen is difficult to handle, you may eliminate it. because, we use water proofing admixture in concrete. then you can attach membrane by any kind of glue.
  3. Basement wall (option 2): use new material at outer surface of wall

***** basement wall is most important for water proofing – because it is thin section (250 mm +). Min 300 mm recommended.


King Post Removal

Seismic design of Mat Foundation using ETABS

1
Modeling of B G 9 storied Building according to BNBC 2017, Part-1
2
Modeling of B G 9 storied Building according to BNBC 2017, Part-2
3
Modeling of B G 9 storied Building according to BNBC 2017, Part-3
4
Modeling of B G 9 storied Building according to BNBC 2017, Part-4
5
Analysis of Mat foundation, Part-1
6
Analysis of Mat foundation, Part-2
7
Analysis of Mat foundation, Part-3
8
Analysis of Mat foundation, Part-4
9
Seismic design of mat foundation, Part-1
10
Seismic design of mat foundation, Part-2
11
Seismic design of mat foundation, Part-3
5
5 out of 5
2 Ratings

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Stars 5
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