Foundation_HU_Lec_5 Design of Shallow Foundations Lec#1.pptx

Foundation Engineering I
Hawassa University Institute of Technology
Department of Civil Engineering
Bereket Bezabih
beackon@gmail.com
2018/19

Chapter Four
Design of Shallow Foundations
Lecture One

Contents
• Introduction
• Design Approach: Limit Equilibrium
• Design Methods : WSD,LFD and Limit State Design
• Limit State Design
• Performance Requirements
• Factors to Consider in Foundation Design
• Geotechnical Design [Proportioning]
• References
Friday, October 28, 2022 HU-IOT Department of Civil Engineerig 3

Introduction
• Limit Equilibrium Method
• The limit equilibrium method is an iterative process by
which one speculates a possible failure mechanism and
use equilibrium equations for each mechanism the
collapse or failure load
• Field observations and laboratory tests reduce the number of
possible failure mechanisms
• Remember the possible failure mechanism in determining the
bearing capacity equations
• In foundation, design the method is applied in
geotechnical design i.e. soil bearing capacity and
settlement and structural design i.e. flexure, shear etc…
• Other design methods include analytical and numerical
methods here only limit equilibrium is covered

Introduction
• Design Methods
• Three basic methods using factors of safety to achieve
safe, workable structures have been developed;
• Permissible Stress Method/Working Stress Method
in which ultimate strengths of the materials are divided by
a factor of safety to provide design stresses which are
usually within the elastic range
• Load Factor Method
in which the working loads are multiplied by a factor of
safety
• Limit State Method/LRFD
which multiplies the working loads by partial factors of
safety and also divides the materials' ultimate strengths by
further partial factors of safety

Introduction
• Limit State Design/LRFD
• The purpose of design is to achieve acceptable
probabilities that a structure will not become unfit for its
intended use i.e., it will not reach a limit state
• Thus, any way in which a structure may cease to be fit for use
will constitutes a limit state and the design aim is to avoid any
such condition being reached during the expected life of the
structure
• The two principal types of limit state are the ultimate
limit state and the serviceability limit state
• Ultimate limit states include
• Loss of equilibrium of the structure,
• Internal failure of the structure,
• Failure due to excessive deformation in soil,
• Loss of equilibrium due to uplift and
• Failure due to hydraulic gradient

Geotechnical Design
• Limit State Design
• Ultimate Limit State
• This requires that the structure must be able to withstand, with an
adequate factor of safety against collapse, the loads for which it is
designed
• Serviceability Limit States
• Generally the most important serviceability limit states are:
• Deflection, settlement, heave, tilt etc
• the appearance or efficiency of any part of the structure must
not be adversely affected by deflections
• Cracking
• local damage due to cracking and spalling must not affect the
appearance, efficiency or durability of the structure
• Durability
• this must be considered in terms of the proposed life of the
structure and its conditions of exposure
• Often one of the limit states control the design ,but is
considered good practice to check the others are satisfied

Introduction
• Performance Requirements for Engineering
Structures
• Design of an engineering structure must ensure that
• Under the worst loadings the structure is safe, and
• During normal working conditions the deformation of the
members does not detract from the appearance,
durability or performance of the structure
• Despite the difficulty in assessing the precise
loading, variations in the strength of the concrete
and steel and uncertainty in the geotechnical
properties of soils, these requirements have to be
met

Factors to Consider in Foundation
Design
• Footing Depth from Surface
• The depth of embedment must be at least large enough to
accommodate the required footing thickness, measured from
the lowest adjacent ground surface to bottom of the footing
• Depth of footing is determined after considerations of the
following factors
• Zone of high volume change/expansive soils
• Top organic soil
• Peat or Muck
• Unconsolidated materials
• Footings in soils prone to Scouring
• Footings located on or near the top of slopes i.e. possibility of land
slide, soil creep downhill
• Location of ground water (possibility of working under water

Design
• Minimum Depth of Square, Rectangular or Continuous
footings, Df
• The depth of footing measured from the lowest adjacent ground
surface shall be at least equal to thickness of the footing, d [Cudato
page 260-261]
Load, P(kN) Minimum Depth Df
(mm)
Load,
P(kN/m)
Minimum Depth Df
(mm)
Square/Rectangular Continuous
0-300 300 0-170 300
300-500 400 170-250 400
500-800 500 250-330 500
800-1100 600 330-410 600
1100-1500 700 410-490 700
1500-2000 800 490-570 800
2000-2700 900 570-650 900
2700-3500 1000 650-740 1000

Design
• Maximum Embedment depth
• Some times maximum embedment depth is specified for
the following reasons
• Potential undermining of existing foundations, structures,
streets, utility lines etc
• Presence of soft layers beneath a harder stronger near surface
stratum and the desire to support the stratum on it
• The desire to avoid below the ground water level and avoid
dewatering expenses
• The desire to avoid excavation costs

Design
• Footing Spacing
• Footings adjacent to existing structures
• The distance m indicated should be greater than or equal to
the depth difference zf
𝑧𝑓 =
2𝑐
(𝐹𝑆)𝛾 𝐾
−
𝑞𝑜
𝐹𝑆 𝛾
𝑞𝑜 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑓𝑟𝑜𝑚 𝑒𝑥𝑖𝑠𝑖𝑡𝑖𝑛𝑔 𝑓𝑜𝑜𝑡𝑖𝑛𝑔
K is lateral earth pressure coefficient ka<k<kp
• If the soils is a sand(no cohesion) one can not excavate to a depth
more the existing footing
• If the soil is a c-φ soil, the maximum depth is given by zf

Geotechnical Design
• Geotechnical Design: Proportioning
• A geotechnical engineer must ensure the
foundation satisfies the following requirements
• The foundation must not collapse or became
unstable (both locally and globally) under any
conceivable loading
• i.e. safety during ultimate limit state[ULS]
• Settlement of the structure should be within
tolerable limits
• i.e. Safety against serviceability limit state[SLS]
• The values of ultimate and serviceability limit states
are provided in building codes like EBCS

Geotechnical Design
• Geotechnical design [Proportioning]
• The ultimate bearing capacity of soils can be determined
as discussed in chapter 3 of this lesson using bearing
capacity equations
• Partial safety factors as per Euro Code for geotechnical
material properties
Angle of
Internal
Friction (apply
to 𝐭𝐚𝐧 𝛟)
Effective
Cohesion
Undrained
Shear Strength
Unconfined
Strength
Bulk
Density
Symbol 𝛾𝜙 𝛾𝑐′ 𝛾𝑐𝑢
𝛾𝑞𝑢
𝛾𝛾
Combination 1 1.0 1.0 1.0 1.0 1.0
Combination 2 1.25 1.25 1.4 1.4 1.0

Geotechnical Design
• Proportioning Isolated Footing
• For collapse(bearing capacity failure) i.e.
ultimate limit state considerations, the
factored loads shall be used
• For settlement considerations, the least
amount of permanent and variable load
shall be used as the settlement takes place
over a long period of time
Example 4.1: Proportioning Spread
Footing
• Design a spread footing for the average soil
conditions and footing load given below.
Note the geotechnical consultant provided
qa =220kPa.
• Permanent load=350kN Variable Load=450kN
• Soil profile Show in the figure
𝑠𝑢 = 100𝑘𝑃𝑎, 𝐸𝑠(𝑐𝑙𝑎𝑦) = 1000𝑠𝑢 𝐸𝑠(𝑠𝑎𝑛𝑑) = 500(𝑁55 + 15)

Geotechnical Design
• Footing Width
• Most structures require many footings hence it is often
inconvenient to compute bearing capacity for each
footing
• often geotechnical engineers provide design criteria
applicable to the entire site
• Two such methods are presented hereunder
• Allowable Bearing Capacity Method
• Design Chart Methods

Geotechnical Design
• Footing Width
• Allowable Bearing Capacity Method
• Allowable bearing capacity is the largest bearing capacity that
satisfies both bearing capacity and settlement(total &
differential) qall
• Use the following procedure to develop allowable bearing
capacity
1. Select depth of embedment, D if different depth are required
for different footings use the depth of the shallowest
groundwater level
2. Determine the required factor of safety
3. Use bearing capacity equations and perform bearing capacity
analysis on a footing with the smallest applied normal load

Geotechnical Design
• Footing Width: Allowable bearing capacity method
• Use the following procedure to develop allowable bearing
capacity cont….
4. Use the equation below to write the bearing capacity q as a
function of B
𝒒 =
𝑸 + 𝑾𝒇
𝑨
− 𝒖𝑫
Where q is bearing pressure
Q vertical column load
Wf weight of footing including weight of any backfill
A area of the footing
UD pore water pressure at depth D
5. Using appropriate bearing capacity equation and write the
bearing capacity qa as a function of B
6. Set q=qa and solve for B
7. Using bearing capacity equation, determine qa for B value in step
6

Geotechnical Design
• Footing Width: Allowable bearing capacity method
• Use the following procedure to develop allowable
bearing capacity cont….
8. Determine the total and differential settlement 𝛿𝑎 & 𝛿𝐷𝑎𝑙𝑙
9. Using local experience or the following table determine 𝛿𝐷
𝛿
Design Values for 𝜹𝑫
𝜹 for spread footing foundations
Predominant Soil Type Below
Footings
Design Values for 𝜹𝑫
𝜹 for spread footing foundations
Flexible Structure Rigid Structure
Sand Natural Soils 0.9 0.7
Compacted Fills 0.5 0.4
Clay Natural Soils 0.8 0.5
Compacted Fills 0.4 0.3

Geotechnical Design
• Footing Width: Allowable bearing capacity Method
• Use the following procedure to develop allowable
bearing capacity cont….
10. If 𝛿𝐷𝑎 ≥ 𝛿𝑎(𝛿𝐷
𝛿),then designing the footing to satisfy the
total settlement requirement (𝛿 ≤ 𝛿𝑎) will implicitly satisfies
the differential settlement requirement (𝛿𝐷 ≤ 𝛿𝐷𝑎) as well,
hence proceed to the next step
• If 𝛿𝐷𝑎 < 𝛿𝑎
𝛿𝐷
𝛿 it is necessary to reduce 𝛿𝑎 to keep
differential settlement under control. Hence, revise
𝛿𝑎 = 𝛿𝐷𝑎(𝛿𝐷
𝛿) and continue
11. Using the 𝛿𝑎 step 10 perform a settlement analysis on the
footing with the largest applied normal load. Determine the
maximum bearing pressure q that keeps the total settlement
within tolerable limits i.e. 𝛿 ≤ 𝛿𝑎
12. Set the allowable bearing pressure 𝒒𝒂 equal to the lower of
qa from step 7 or step 11

Geotechnical Design
• The structural design shall be based on the criteria that
𝑞 ≤ 𝑞𝑎,thus for square, rectangular, circular or continuous
footings
𝑞 =
𝑃+𝑊𝑓
𝐴
− 𝑈𝐷 ≤ 𝑞𝑎
Setting 𝑞 = 𝑞𝐴 𝑖𝑚𝑝𝑙𝑖𝑒𝑠
𝐴 =
𝑃 + 𝑊𝑓
𝑞𝑎 + 𝑈𝐷
𝑢𝐷 = 0 𝑖𝑓 𝑡ℎ𝑒 𝑔𝑟𝑜𝑢𝑛𝑑𝑤𝑎𝑡𝑒𝑟 𝑎𝑡 𝑑𝑒𝑝𝑡ℎ 𝐷 𝑜𝑡ℎ𝑒𝑤𝑖𝑠𝑒
𝑢𝐷 = 𝛾𝑤(𝐷 − 𝐷𝑤)

Geotechnical Design
• Example 4.2
• A new parking garage is proposed on a site previously used by a
two story office building, which is demolished and backfilled
with well graded sand. The design column loads range between
1112kN to 4000kN.The allowable total and differential
settlement are 25mm and 15mm.A serious of boring show the
soil is primarily a backfilled soil underlain by alluvial sand
deposit. The groundwater table is located at 61m depth.
• A laboratory shear test shows the compacted fill has
𝑐′ = 0 𝑎𝑛𝑑 𝜙′ = 35𝑜
• Determine the allowable bearing capacity 𝑞𝑎 for square and
continuous footing and determine the dimension of square
footing that will support 1350kN column load.
Assume the first 1m of back fill will be removed. Unit weight of sand
for the first 3m is 19.7kN/m3 and below that 17.6kN/m3
Depth
(m)
Modulus of
Elasticity
(kPa)
0-3 52,700
3-6 47900
>6 81400

Introduction
• Design for Eccentric or Moment Loads
• It may be necessary to design footing which support
eccentric loads or moments

Geotechnical Design
• Design for Eccentric or Moment Loads cont….
• One way Eccentricity
• If the footing has a base area A and supporting a load P with
footing weight Wf the eccentricity e is given by
𝑒 =
𝑃𝑒1
𝑃 + 𝑊𝑓
𝑒 =
𝑀
𝑃 + 𝑊𝑓

Geotechnical Design
• One way Eccentricity
𝑒 < 𝐵/6 𝑒 = 𝐵/6 𝑒 > 𝐵/6
𝑞𝑚𝑎𝑥 =
𝑃 + 𝑊𝑓
𝐴
− 𝑈𝐷 1 +
6𝑒
𝐵
𝑞𝑚𝑖𝑛 =
𝑃 + 𝑊𝑓
𝐴
− 𝑈𝐷 1 −
6𝑒
𝐵

Geotechnical Design
• Two way Eccentricity
• The load has eccentricity or support a two way moment the
eccentricity will be contained within the kernel if the following
condition is met
6𝑒𝐵
𝐵
+
6𝑒𝐿
𝐿
≤ 1.0
• The magnitude of q on the four corners of the footing is given
by
𝑞 =
𝑃+𝑊𝑓
𝐴
− 𝑈𝐷 1 ±
6𝑒𝐵
𝐵
±
6𝑒𝐿
𝐿

Geotechnical Design
• Use the following procedure to proportion footings with eccentric
loads or moments
1. Develop a preliminary values for the plan dimension B and L.
2. Determine the resultant of the load that acts within the middle third
(for one-way) of the footing or the kern (for two way) footing. If this is
the case the length/width of footing shall be increased
3. Using the following procedure determine B’ and L’.
4. Determine eB bad eL
5. Compute effective footing dimensions
𝐵′
= 𝐵 − 2𝑒𝐵 & 𝐿′
= 𝐿 − 2𝑒𝐿 hence 𝐴′
= 𝐵′
𝑥𝐿′
5. Compute the equivalent bearing pressure
𝑞𝑒𝑞𝑢𝑖𝑣 =
𝑃 + 𝑊𝑓
𝐵′𝐿′ − 𝑢𝐷
6. Compare 𝑞𝑒𝑞𝑢𝑖 with 𝑞𝑎𝑙𝑙.If 𝑞𝑒𝑞𝑢𝑖 ≤ 𝑞𝑎𝑙𝑙 the design is satisfactory if not
increase the dimensions

Geotechnical Design
• Example 4.3
• Proportion a footing for the following loading conditions
Loads Permanent Variable Column Dimensions
P 800kN 950kN wx 500mm
Moments wy 600mm
Mx 300kNm 500kNm Allowable Soil Pressure
My 400kNm 650kNM qall 250kPa

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