751.38 Spread Footings - Revision history

Hoskir: updated old math code

2026-01-15T19:34:11Z

updated old math code

Hoskir: /* 751.38.8.3.1 Spread Footing Reinforcement */ updated per RR4033

2025-04-18T18:15:19Z

751.38.8.3.1 Spread Footing Reinforcement: updated per RR4033

← Older revision		Revision as of 13:15, 18 April 2025
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	\| '''FRONT ELEVATION''' \|\| '''SIDE ELEVATION'''		\| '''FRONT ELEVATION''' \|\| '''SIDE ELEVATION'''
	\|-		\|-
	\| colspan="2" style="text-align:left" \| '''*''' Use same area of steel in the top of the footing as is required for the bottom.		\| colspan="2" style="text-align:left" \| '''**''' Use same area of steel in the top of the footing as is required for the bottom.
	\|-		\|-
	\| colspan="2" style="text-align:left" \| For spread footing joint shear reinforcement requirement for SDC C and D, see [[751.9_Bridge_Seismic_Design#751.9.1.2.4.2_Footing_(Spread_Footing_and_Pile_Cap_Footing)_Joint_Shear_Reinforcement\|EPG 751.9.1.2.4.2 Footing (Spread Footing and Pile Cap Footing) Joint Shear Reinforcement]].		\| colspan="2" style="text-align:left" \| For spread footing joint shear reinforcement requirement for SDC C and D, see [[751.9_Bridge_Seismic_Design#751.9.1.2.4.2_Footing_(Spread_Footing_and_Pile_Cap_Footing)_Joint_Shear_Reinforcement\|EPG 751.9.1.2.4.2 Footing (Spread Footing and Pile Cap Footing) Joint Shear Reinforcement]].

Hoskir: /* 751.38.8.3.1 Spread Footing Reinforcement */ updated per RR4033

2025-04-14T16:28:54Z

751.38.8.3.1 Spread Footing Reinforcement: updated per RR4033

← Older revision		Revision as of 11:28, 14 April 2025
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	{\|border="0" align="center" style="text-align:center"		{\|border="0" align="center" style="text-align:center"
			! colspan="2" \|'''Reinforcement Details - Seismic Design Category A'''
	\|~~[[Image:751.38_Reinforcement_Front_Elevation.gif]]~~
	~~\|[[Image:751.38_Reinforcement_Side_Elevation.gif]]~~
	\|-		\|-
	\|~~'''FRONT ELEVATION'''~~\|\|~~'''SIDE ELEVATION'''~~		\| [[Image:751.38_Reinforcement_Front_Elevation.gif]] \|\| [[Image:751.38_Reinforcement_Side_Elevation.gif]]
	\|-		\|-
	\|~~colspan="2"~~\|'''~~Fig. 751.38.8.4 Schematic showing typical reinforcement detail in front elevation and side elevation.~~'''		\| '''FRONT ELEVATION''' \|\| '''SIDE ELEVATION'''
	\|-		\|-
	\|colspan="2"\| '''*''' Footing depths > 36 in. may require the side faces to have shrinkage and temperature reinforcement. See Structural Project Manager.		\| colspan="2" style="text-align:left" \| '''*''' Footing depths > 36 in. may require the side faces to have shrinkage and temperature reinforcement. See Structural Project Manager.
			\|-
			! colspan="2" \|'''Reinforcement Details - Seismic Design Category B, C & D'''
			\|-
			\| [[Image:751.38.8.3.1_04-2025.png\|400px]] \|\| [[Image:751.38.8.3.1_04-2025.png\|400px]]
			\|-
			\| '''FRONT ELEVATION''' \|\| '''SIDE ELEVATION'''
			\|-
			\| colspan="2" style="text-align:left" \| '''*''' Use same area of steel in the top of the footing as is required for the bottom.
			\|-
			\| colspan="2" style="text-align:left" \| For spread footing joint shear reinforcement requirement for SDC C and D, see [[751.9_Bridge_Seismic_Design#751.9.1.2.4.2_Footing_(Spread_Footing_and_Pile_Cap_Footing)_Joint_Shear_Reinforcement\|EPG 751.9.1.2.4.2 Footing (Spread Footing and Pile Cap Footing) Joint Shear Reinforcement]].
	\|}		\|}

Hoskir: /* 751.38.5.1 Modifications to Footing Dimensions for Eccentric Loads */

2025-03-18T17:51:30Z

751.38.5.1 Modifications to Footing Dimensions for Eccentric Loads

← Older revision		Revision as of 12:51, 18 March 2025
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	In cases where spread footings will be subjected to eccentric loads, the minimum footing dimensions established in accordance with EPG 751.38.3 and EPG 751.38.4 shall be determined using reduced dimensions, ''B' '' and ''L' '', instead of the actual dimensions, ''B'' and ''L'', where		In cases where spread footings will be subjected to eccentric loads, the minimum footing dimensions established in accordance with EPG 751.38.3 and EPG 751.38.4 shall be determined using reduced dimensions, ''B' '' and ''L' '', instead of the actual dimensions, ''B'' and ''L'', where

	{\| ~~style="margin: 1em auto 1em auto"~~ width="~~700~~"		{\| width="500"
	\|-		\|-
	\|align="left"\|''B' = B - 2e<sub>B</sub>''\|\|align="center"\| (consistent units of length)\|\|align="right"\|Equation 751.38.5.3		\|align="left"\|''B' = B - 2e<sub>B</sub>''\|\|align="center"\| (consistent units of length)\|\|align="right"\|Equation 751.38.5.3

Hoskir: /* 751.38.5.2 Limiting Eccentricity in Soil and Cohesive Intermediate Geomaterials */

2025-03-18T17:49:10Z

751.38.5.2 Limiting Eccentricity in Soil and Cohesive Intermediate Geomaterials

← Older revision		Revision as of 12:49, 18 March 2025
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	:The location of the resultant of the reaction forces shall be within the middle two-thirds of the base width (B) and length (L), or (e<sub>B</sub> ≤ 0.33B) and (e<sub>L</sub> ≤ 0.33L) for γ<sub>EQ</sub> = 0.0. For γ<sub>EQ</sub> refer to LRFD 3.4.		:The location of the resultant of the reaction forces shall be within the middle two-thirds of the base width (B) and length (L), or (e<sub>B</sub> ≤ 0.33B) and (e<sub>L</sub> ≤ 0.33L) for γ<sub>EQ</sub> = 0.0. For γ<sub>EQ</sub> refer to LRFD 3.4.

	Note: Seismic design shall be performed for γ<sub>EQ</sub> = 0.0		:Note: Seismic design shall be performed for γ<sub>EQ</sub> = 0.0

	Eccentricity, (e) Limit for Extreme Event II:		Eccentricity, (e) Limit for Extreme Event II:

Hoskir: /* 751.38.5.3 Limiting Eccentricity in Cohesionless Intermediate Geomaterials and Rock */ updated per RR4024

2025-03-18T17:48:57Z

751.38.5.3 Limiting Eccentricity in Cohesionless Intermediate Geomaterials and Rock: updated per RR4024

← Older revision		Revision as of 12:48, 18 March 2025
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	===751.38.5.3 Limiting Eccentricity in Cohesionless Intermediate Geomaterials and Rock===		===751.38.5.3 Limiting Eccentricity in Cohesionless Intermediate Geomaterials and Rock===
			For footings founded in cohesionless intermediate geomaterials and rock, the load eccentricity shall be as shown below.

			Eccentricity, (e) Limit for Strength Limit State: LRFD 10.6.3.3
			:The location of the resultant of the reaction forces shall be within 0.45 of the base width (B) and length (L), or (e<sub>B</sub> ≤ 0.45B) and (e<sub>L</sub> ≤ 0.45L).

	~~For footings founded in cohesionless intermediate geomaterials~~ and ~~rock,~~ the ~~load eccentricity~~ shall be ~~restricted to~~ the middle ~~three~~-~~quarters~~ of the ~~footing. Minimum footing dimensions satisfying this criterion are:~~		Eccentricity, (e) Limit for Extreme Event I (Seismic): LRFD 10.6.4.2 and 11.6.5.1
	~~{\| style="margin: 1em auto 1em auto"~~ width~~="800"~~		:The location of the resultant of the reaction forces shall be within the middle two-thirds of the base width (B) and length (L), or (e<sub>B</sub> ≤ 0.33B) and (e<sub>L</sub> ≤ 0.33L) for γ<sub>EQ</sub> = 0.0. For γ<sub>EQ</sub> refer to LRFD 3.4.
	\|-
	~~\|align="left"\|~~<~~math~~>B ~~\ge \frac{8 \cdot e_B}{3}~~</~~math~~> and <~~math~~>L ~~\ge \frac{8 \cdot e_L}{~~3}</~~math~~>~~\|\|align~~=~~"center"\|~~ (~~consistent units~~ of length)~~\|\|align="right"\|Equation 751~~.38.5.6		:Note: Seismic design shall be performed for γ<sub>EQ</sub> = 0.0
	\|}
			Eccentricity, (e) Limit for Extreme Event II:
			:The location of the resultant of the reaction forces shall be within the middle eight-tenths of the base width (B) and length (L), or (e<sub>B</sub> ≤ 0.40B) and (e<sub>L</sub> ≤ 0.40L).

	==751.38.6 Design for Lateral Loading==		==751.38.6 Design for Lateral Loading==

Hoskir: /* 751.38.5.2 Limiting Eccentricity in Soil and Cohesive Intermediate Geomaterials */ updated per RR4024

2025-03-18T17:45:24Z

751.38.5.2 Limiting Eccentricity in Soil and Cohesive Intermediate Geomaterials: updated per RR4024

← Older revision		Revision as of 12:45, 18 March 2025
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	===751.38.5.2 Limiting Eccentricity in Soil and Cohesive Intermediate Geomaterials===		===751.38.5.2 Limiting Eccentricity in Soil and Cohesive Intermediate Geomaterials===
			For footings founded in soil or cohesive intermediate geomaterials, the load eccentricity shall be as shown below.

	~~For footings founded in soil or cohesive intermediate geomaterials~~, the ~~load eccentricity~~ shall be ~~restricted to the middle~~ one-~~half~~ of the ~~footing~~. ~~Minimum footing dimensions satisfying this criterion are:~~		Eccentricity, (e) Limit for Strength Limit State: LRFD 10.6.3.3
			:The location of the resultant of the reaction forces shall be within one-third of the base width (B) and length (L), or (e<sub>B</sub> ≤ 0.33B) and (e<sub>L</sub> ≤ 0.33L).

	~~{\| style="margin~~: ~~1em auto 1em auto" width="800"~~		Eccentricity, (e) Limit for Extreme Event I (Seismic): LRFD 10.6.4.2 and 11.6.5.1
	\|-		:The location of the resultant of the reaction forces shall be within the middle two-thirds of the base width (B) and length (L), or (e<sub>B</sub> ≤ 0.33B) and (e<sub>L</sub> ≤ 0.33L) for γ<sub>EQ</sub> = 0.0. For γ<sub>EQ</sub> refer to LRFD 3.4.
	~~\|align="left"\|''~~B ~~≥ 4e~~<sub>B</sub>'' and ''L ~~≥ 4e~~<sub>L</sub>~~''\|\|align~~=~~"center"\|~~ (~~consistent units~~ of length)~~\|\|align="right"\|Equation 751~~.38.5.5
	\|}		Note: Seismic design shall be performed for γ<sub>EQ</sub> = 0.0

			Eccentricity, (e) Limit for Extreme Event II:
			:The location of the resultant of the reaction forces shall be within the middle eight-tenths of the base width (B) and length (L), or (e<sub>B</sub> ≤ 0.40B) and (e<sub>L</sub> ≤ 0.40L).

	===751.38.5.3 Limiting Eccentricity in Cohesionless Intermediate Geomaterials and Rock===		===751.38.5.3 Limiting Eccentricity in Cohesionless Intermediate Geomaterials and Rock===

Hoskir: /* 751.38.5.1 Modifications to Footing Dimensions for Eccentric Loads */ updated per RR4024

2025-03-18T17:36:44Z

751.38.5.1 Modifications to Footing Dimensions for Eccentric Loads: updated per RR4024

← Older revision		Revision as of 12:36, 18 March 2025
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	===751.38.5.1 Modifications to Footing Dimensions for Eccentric Loads===		===751.38.5.1 Modifications to Footing Dimensions for Eccentric Loads===

	In cases where spread footings will be subjected to eccentric loads, the minimum footing dimensions established in accordance with EPG 751.38.3 and EPG 751.38.4 shall be determined using reduced dimensions, ''B' '' and ''L' '', instead of the actual dimensions, ''B'' and ''L'', where		In cases where spread footings will be subjected to eccentric loads, the minimum footing dimensions established in accordance with EPG 751.38.3 and EPG 751.38.4 shall be determined using reduced dimensions, ''B' '' and ''L' '', instead of the actual dimensions, ''B'' and ''L'', where

	{\| style="margin: 1em auto 1em auto" width="~~800~~"		{\| style="margin: 1em auto 1em auto" width="700"
	\|-		\|-
	\|align="left"\|''B' = B - 2e<sub>B</sub>''\|\|align="center"\| (consistent units of length)\|\|align="right"\|Equation 751.38.5.3		\|align="left"\|''B' = B - 2e<sub>B</sub>''\|\|align="center"\| (consistent units of length)\|\|align="right"\|Equation 751.38.5.3
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	\|}		\|}

	where ''e<sub>B</sub>'' and ''e<sub>L</sub>'' are the load eccentricity due to the factored load in the width and length dimensions, respectively.		where ''e<sub>B</sub>'' and ''e<sub>L</sub>'' are the load eccentricity due to the factored load in the width and length dimensions, respectively.

			Note: When the value of eccentricity e is negative then use ''e = 0''.

	===751.38.5.2 Limiting Eccentricity in Soil and Cohesive Intermediate Geomaterials===		===751.38.5.2 Limiting Eccentricity in Soil and Cohesive Intermediate Geomaterials===

Smithk: Per BR, minor clarifications

2021-06-29T13:09:03Z

Per BR, minor clarifications

← Older revision		Revision as of 08:09, 29 June 2021
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	\|}		\|}

	These guidelines address procedures for design of spread footings used as foundations for bridge piers, bridge abutments, retaining structures and other miscellaneous structures. The guidelines were established following load and resistance factor design (LRFD) concepts. The provisions provided herein are intended to produce foundations that achieve target reliabilities established by MoDOT for structures ~~located on~~ different ~~classes of roadways~~. The ~~different~~ classes of ~~roadways/bridges considered~~ include minor ~~roads~~, major ~~roads~~, major ~~bridges~~ costing less than $100 million, and major ~~bridges~~ costing greater than $100 million. Additional background regarding development of these provisions and supportive information regarding use of these provisions is provided in the accompanying commentary.		These guidelines address procedures for design of spread footings used as foundations for bridge piers, bridge abutments, retaining structures and other miscellaneous structures. The guidelines were established following load and resistance factor design (LRFD) concepts. The provisions provided herein are intended to produce foundations that achieve target reliabilities established by MoDOT for structures of different operational importance. The four classes of operational importance include minor or low volume route, major route, major bridge costing less than $100 million, and major bridge costing greater than $100 million. Additional background regarding development of these provisions and supportive information regarding use of these provisions is provided in the accompanying commentary.

	===751.38.1.1 Dimensions and Nomenclature===		===751.38.1.1 Dimensions and Nomenclature===
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	Spread footings shall be dimensioned so that there is a small likelihood that footings will settle more than tolerable settlements, generally established from consideration of span length. This shall be accomplished by determining minimum footing dimensions for the appropriate site conditions in accordance with the content of this article.		Spread footings shall be dimensioned so that there is a small likelihood that footings will settle more than tolerable settlements, generally established from consideration of span length. This shall be accomplished by determining minimum footing dimensions for the appropriate site conditions in accordance with the content of this article.

	Resistance factors provided in this ~~subarticle~~ were established to produce factored settlements that have a target probability of being exceeded. Target probabilities of exceedance were established by MoDOT for structures ~~located on four~~ different ~~classes of roadways~~. Additional information regarding development of the resistance factors and application of the resistance factors for settlement calculations are provided in the commentary that accompanies these guidelines.		Resistance factors provided in this article were established to produce factored settlements that have a target probability of being exceeded. Target probabilities of exceedance were established by MoDOT for structures of different operational importance. Additional information regarding development of the resistance factors and application of the resistance factors for settlement calculations are provided in the commentary that accompanies these guidelines.

	The method for determining minimum footing dimensions based on serviceability considerations shall be selected based on the material type present beneath the base of the footing. In general, EPG 751.38.4.1 shall be followed for footings founded in rock with uniaxial compressive strengths (q<sub>u</sub>) greater than 100 ksf; EPG 751.38.4.2 shall be followed for footings founded in weaker rock with q<sub>u</sub> greater than 5 ksf but less than 100 ksf. The provisions in EPG 751.38.4.3 and EPG 751.38.4.4 shall be followed for footings founded in soil.		The method for determining minimum footing dimensions based on serviceability considerations shall be selected based on the material type present beneath the base of the footing. In general, EPG 751.38.4.1 shall be followed for footings founded in rock with uniaxial compressive strengths (q<sub>u</sub>) greater than 100 ksf; EPG 751.38.4.2 shall be followed for footings founded in weaker rock with q<sub>u</sub> greater than 5 ksf but less than 100 ksf. The provisions in EPG 751.38.4.3 and EPG 751.38.4.4 shall be followed for footings founded in soil.
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	the limit state is satisfied and the probability of footing settlement exceeding the tolerable settlement is less than or equal to the target probability established by MoDOT. If the factored total settlement is determined to exceed the tolerable settlement, the probability of footing settlement exceeding the tolerable value is greater than the target probability established by MoDOT. In such cases, the footing dimensions shall be increased until the factored total settlement is less than or equal to the tolerable settlement.		the limit state is satisfied and the probability of footing settlement exceeding the tolerable settlement is less than or equal to the target probability established by MoDOT. If the factored total settlement is determined to exceed the tolerable settlement, the probability of footing settlement exceeding the tolerable value is greater than the target probability established by MoDOT. In such cases, the footing dimensions shall be increased until the factored total settlement is less than or equal to the tolerable settlement.

	Resistance factors provided in this ~~subarticle~~ were established to produce factored settlements that have a target probability of being exceeded. Target probabilities of exceedance were established by MoDOT for structures ~~located on four~~ different ~~classes of roadways~~. Additional information regarding development of the resistance factors and application of the resistance factors for settlement calculations are provided in the commentary that accompanies these guidelines.		Resistance factors provided in this article were established to produce factored settlements that have a target probability of being exceeded. Target probabilities of exceedance were established by MoDOT for structures of different operational importance. Additional information regarding development of the resistance factors and application of the resistance factors for settlement calculations are provided in the commentary that accompanies these guidelines.

	'''Tolerable settlement'''		'''Tolerable settlement'''
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	These guidelines were developed from prior EPG guidelines with notable changes to the general approach for application of LRFD techniques as well as updated resistance factors based on probabilistic calibrations. Calibration analyses were performed following generally accepted procedures for calibration of resistance factors for geotechnical applications, but with modifications to permit several enhancements to be included in the guidelines. The most notable enhancements provided in the guidelines include:		These guidelines were developed from prior EPG guidelines with notable changes to the general approach for application of LRFD techniques as well as updated resistance factors based on probabilistic calibrations. Calibration analyses were performed following generally accepted procedures for calibration of resistance factors for geotechnical applications, but with modifications to permit several enhancements to be included in the guidelines. The most notable enhancements provided in the guidelines include:

	:* ~~use~~ of resistance factors that are contingent upon the variability and uncertainty that exists in select design properties ~~and~~		:* Use of resistance factors that are contingent upon the variability and uncertainty that exists in select design properties.
			:* Adoption of different target reliability levels for foundations of structures of different operational importance.

	~~:* adoption of different target reliability levels for foundations of structures located on different classes of roadways.~~

	Both of these enhancements are expected to produce efficient foundation designs while still maintaining appropriate safety and reliability for all classes of ~~structures~~. Additional information regarding development of the methods provided in these guidelines can be found in Abu El-Ela et al. (2011) and Song et al. (2011). Additional information regarding target reliability values established for different classes of ~~roadways~~ is provided in Bowders et al. (2011).		Both of these enhancements are expected to produce efficient foundation designs while still maintaining appropriate safety and reliability for all classes of operational importance. Additional information regarding development of the methods provided in these guidelines can be found in Abu El-Ela et al. (2011) and Song et al. (2011). Additional information regarding target reliability values established for different classes of operational importance is provided in Bowders et al. (2011).

	The ~~different~~ classes of ~~roadways considered in the guidelines~~ include:		The four classes of operational importance include:
			:* Minor and low volume route
			:* Major route
			:* Major bridge costing less than $100 million
			:* Major bridge costing greater than $100 million.

	~~:* major roads,~~		These classifications are based on common MoDOT designations. The target reliability levels established for each limit state and operational importance were generally based upon consideration of highway bridges. However, the methods in this article can also be utilized for design of foundations for other structures including retaining walls and roadway signs.

	~~:* minor roads,~~

	~~:* major bridges costing less than $100 million and~~

	~~:* major bridges costing greater than $100 million.~~

	These classifications are based on common MoDOT designations. The target reliability levels established for each limit state and ~~roadway classification~~ were generally based upon consideration of highway bridges. However, the methods in this article can also be utilized for design of foundations for other structures including retaining walls and roadway signs.

	Calibration analyses performed to establish the resistance factors presented in this subarticle were performed using the latest knowledge of variability and uncertainty of applied loads (Kulicki et al., 2007), as well as using load factors that are currently in effect. The resistance factors provided in these guidelines are intended to produce foundations with reliabilities that are approximately equal to the target reliabilities established by MoDOT when utilized with current load factors. Since it is the combined effect of load and resistance factors that produce this reliability, the resistance factors provided are inherently coupled with current load factors and are contingent upon the uncertainty and variability in the applied loads that was presumed for the calibrations. As such, recalibration of resistance factors is required if alternative load factors are adopted, or if substantial revisions to current estimates of load variability and uncertainty are found.		Calibration analyses performed to establish the resistance factors presented in this subarticle were performed using the latest knowledge of variability and uncertainty of applied loads (Kulicki et al., 2007), as well as using load factors that are currently in effect. The resistance factors provided in these guidelines are intended to produce foundations with reliabilities that are approximately equal to the target reliabilities established by MoDOT when utilized with current load factors. Since it is the combined effect of load and resistance factors that produce this reliability, the resistance factors provided are inherently coupled with current load factors and are contingent upon the uncertainty and variability in the applied loads that was presumed for the calibrations. As such, recalibration of resistance factors is required if alternative load factors are adopted, or if substantial revisions to current estimates of load variability and uncertainty are found.
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	This limiting value of angular distortion is based on theoretical consideration of the onset of deck cracking (Duncan and Tan, 1991). This limit is implicitly included in the methods provided in EPG 751.38.4.1 and EPG 751.38.4.2, while it is explicitly included in EPG 751.38.4.3.		This limiting value of angular distortion is based on theoretical consideration of the onset of deck cracking (Duncan and Tan, 1991). This limit is implicitly included in the methods provided in EPG 751.38.4.1 and EPG 751.38.4.2, while it is explicitly included in EPG 751.38.4.3.

	The target probabilities of exceedance reflected in the resistance factors provided in EPG 751.38 correspond to the target values established by MoDOT based on economic considerations. While use of alternative limits for tolerable settlement is possible, such use is not strictly appropriate since the target probabilities adopted by MoDOT for different classes of ~~roadways~~ were established based on consequences associated with the limit provided in Equation Commentary 751.38.4.1. Other limits would generally require different target probabilities, and thus different resistance factors to achieve the same economic balance.		The target probabilities of exceedance reflected in the resistance factors provided in EPG 751.38 correspond to the target values established by MoDOT based on economic considerations. While use of alternative limits for tolerable settlement is possible, such use is not strictly appropriate since the target probabilities adopted by MoDOT for different classes of operational importance were established based on consequences associated with the limit provided in Equation Commentary 751.38.4.1. Other limits would generally require different target probabilities, and thus different resistance factors to achieve the same economic balance.

	As was the case in EPG 751.38.3, design procedures within this subarticle are categorized according to material type, including methods for design of spread footings founded upon “rock”, “weak rock”, “cohesive soil”, and “cohesionless soil”. While these categories serve to logically separate the guidelines according to design method, complexities present at some sites may lead to cases where multiple methods could potentially be used. In such cases, designers should utilize the method that is most appropriate for the conditions encountered, rather than selecting the method that produces the smallest or largest footing dimensions.		As was the case in EPG 751.38.3, design procedures within this subarticle are categorized according to material type, including methods for design of spread footings founded upon “rock”, “weak rock”, “cohesive soil”, and “cohesionless soil”. While these categories serve to logically separate the guidelines according to design method, complexities present at some sites may lead to cases where multiple methods could potentially be used. In such cases, designers should utilize the method that is most appropriate for the conditions encountered, rather than selecting the method that produces the smallest or largest footing dimensions.

Smithk: Per BR, clarified terminology in figures

2021-06-28T18:10:47Z

Per BR, clarified terminology in figures

← Older revision		Revision as of 14:34, 15 January 2026
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	:''L'' = minimum footing length (consistent units of length),		:''L'' = minimum footing length (consistent units of length),

	:<math>\~~boldsymbol~~ \gamma Q</math> = factored load for the appropriate strength limit state (consistent units of force) and		:<math>\mathbf \gamma Q</math> = factored load for the appropriate strength limit state (consistent units of force) and

	:''q<sub>R</sub>'' = factored bearing resistance (consistent units of stress).		:''q<sub>R</sub>'' = factored bearing resistance (consistent units of stress).
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	:<math>\overline{q_u}</math> = mean value of the uniaxial compressive strength of intact rock core (consistent units of stress).		:<math>\overline{q_u}</math> = mean value of the uniaxial compressive strength of intact rock core (consistent units of stress).

	Resistance factors (<math>\~~boldsymbol~~ \phi_b</math>) to be applied to the nominal resistance values (''q<sub>n</sub>'') determined according to the provisions of this article shall be established from Figure 751.38.3.1 based on the coefficient of variation of the mean uniaxial compressive strength, <math>COV_{\overline{q_u}}</math>. Values for ''q<sub>u</sub>'' and <math>COV_{\overline{q_u}}</math> shall be determined in accordance with methods described in [[321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation\|EPG 321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation]] for the site and location in question. Values for design parameters ''q<sub>u</sub>'', ''m'' and ''s'' shall be taken as mean values for the rock between the base of the footing and a depth of ''B'' below the base of the footing. Values for <math>COV_{\overline{q_u}}</math> should similarly reflect the variability of the mean uniaxial compressive strength for the rock over the same depth range.		Resistance factors (<math>\mathbf \phi_b</math>) to be applied to the nominal resistance values (''q<sub>n</sub>'') determined according to the provisions of this article shall be established from Figure 751.38.3.1 based on the coefficient of variation of the mean uniaxial compressive strength, <math>COV_{\overline{q_u}}</math>. Values for ''q<sub>u</sub>'' and <math>COV_{\overline{q_u}}</math> shall be determined in accordance with methods described in [[321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation\|EPG 321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation]] for the site and location in question. Values for design parameters ''q<sub>u</sub>'', ''m'' and ''s'' shall be taken as mean values for the rock between the base of the footing and a depth of ''B'' below the base of the footing. Values for <math>COV_{\overline{q_u}}</math> should similarly reflect the variability of the mean uniaxial compressive strength for the rock over the same depth range.

	[[image:751.38.3.1 2021.jpg\|center\|775px\|thumb\|<center>'''Fig. 751.38.3.1 Resistance factors for bearing resistance of spread footings on rock.'''</center>]]		[[image:751.38.3.1 2021.jpg\|center\|775px\|thumb\|<center>'''Fig. 751.38.3.1 Resistance factors for bearing resistance of spread footings on rock.'''</center>]]
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	:''i<sub>c</sub>'' = correction factor to account for inclination of the factored load (dimensionless).		:''i<sub>c</sub>'' = correction factor to account for inclination of the factored load (dimensionless).

	Resistance factors (<math>\~~boldsymbol~~ \phi_b</math>) to be applied to the nominal resistance values (''q<sub>n</sub>'') determined according to the provisions of this subarticle shall be established from Figure 751.38.3.2 based on the coefficient of variation of the mean uniaxial compressive strength <math>COV_{\overline{q_u}}</math>. Values for <math>\overline{q_u}</math> and <math>COV_{\overline{q_u}}</math> shall be determined in accordance with methods described in [[321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation\|EPG 321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation]] for the site and location in question. Values for design parameter ''q<sub>u</sub>'' shall be taken as the mean value of the parameter for the rock between the base of the footing and a depth of ''B'' below the base of the footing. Values for <math>COV_{\overline{q_u}}</math> shall similarly reflect the variability of the mean uniaxial compressive strength over the same depth range.		Resistance factors (<math>\mathbf \phi_b</math>) to be applied to the nominal resistance values (''q<sub>n</sub>'') determined according to the provisions of this subarticle shall be established from Figure 751.38.3.2 based on the coefficient of variation of the mean uniaxial compressive strength <math>COV_{\overline{q_u}}</math>. Values for <math>\overline{q_u}</math> and <math>COV_{\overline{q_u}}</math> shall be determined in accordance with methods described in [[321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation\|EPG 321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation]] for the site and location in question. Values for design parameter ''q<sub>u</sub>'' shall be taken as the mean value of the parameter for the rock between the base of the footing and a depth of ''B'' below the base of the footing. Values for <math>COV_{\overline{q_u}}</math> shall similarly reflect the variability of the mean uniaxial compressive strength over the same depth range.

	[[image:751.38.3.2 2021.jpg\|center\|thumb\|700px\|<center>'''Fig. 751.38.3.2 Resistance factors for bearing resistance for spread footings on weak rock.'''</center>]]		[[image:751.38.3.2 2021.jpg\|center\|thumb\|700px\|<center>'''Fig. 751.38.3.2 Resistance factors for bearing resistance for spread footings on weak rock.'''</center>]]
Line 267:		Line 267:
	:''i<sub>c</sub>'' = correction factor to account for inclination of the factored load (dimensionless).		:''i<sub>c</sub>'' = correction factor to account for inclination of the factored load (dimensionless).

	Resistance factors (<math>\~~boldsymbol~~ \phi_b</math>) to be applied to the nominal resistance values (''q<sub>n</sub>'') determined according to the provisions of this subarticle shall be established from Figure 751.38.3.3 based on the coefficient of variation of the mean undrained shear strength, <math>COV_{\overline{s_u}}</math>. Values for <math>\overline{s_u}</math> and <math>COV_{\overline{s_u}}</math> shall be determined in accordance with methods described in [[321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation\|EPG 321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation]] for the site and location in question. Values for design parameter <math>\overline{s_u}</math> shall be taken as the mean value for the soil between the base of the footing and a depth of ''B'' below the base of the footing. Values for <math>COV_{\overline{s_u}}</math> shall similarly reflect the variability of the mean soil shear strength over the same range of depths.		Resistance factors (<math>\mathbf \phi_b</math>) to be applied to the nominal resistance values (''q<sub>n</sub>'') determined according to the provisions of this subarticle shall be established from Figure 751.38.3.3 based on the coefficient of variation of the mean undrained shear strength, <math>COV_{\overline{s_u}}</math>. Values for <math>\overline{s_u}</math> and <math>COV_{\overline{s_u}}</math> shall be determined in accordance with methods described in [[321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation\|EPG 321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation]] for the site and location in question. Values for design parameter <math>\overline{s_u}</math> shall be taken as the mean value for the soil between the base of the footing and a depth of ''B'' below the base of the footing. Values for <math>COV_{\overline{s_u}}</math> shall similarly reflect the variability of the mean soil shear strength over the same range of depths.

	The value of ''N<sub>c</sub>'' shall be taken as 5.0. The respective correction factors shall be computed using Equations 751.38.3.8, 751.38.3.9 and 751.38.3.10.		The value of ''N<sub>c</sub>'' shall be taken as 5.0. The respective correction factors shall be computed using Equations 751.38.3.8, 751.38.3.9 and 751.38.3.10.
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	:''L'' = minimum footing length (feet),		:''L'' = minimum footing length (feet),

	:<math>\~~boldsymbol~~\gamma Q</math> = factored load for the appropriate serviceability limit state (kips)		:<math>\mathbf\gamma Q</math> = factored load for the appropriate serviceability limit state (kips)

	:''v'' = mean value of Poisson’s ratio (dimensionless),		:''v'' = mean value of Poisson’s ratio (dimensionless),
Line 390:		Line 390:
	:''L'' = minimum footing length (feet),		:''L'' = minimum footing length (feet),

	:<math>\~~boldsymbol~~\gamma Q</math> = factored load for the appropriate serviceability limit state (kips)		:<math>\mathbf\gamma Q</math> = factored load for the appropriate serviceability limit state (kips)

	:''v'' = mean value of Poisson’s ratio (dimensionless),		:''v'' = mean value of Poisson’s ratio (dimensionless),
Line 525:		Line 525:
	\|}		\|}

	where <math>M^_B</math> and <math>M^_L</math> are moments attributed to ''factored'' load effects in the ''B'' and ''L'' directions (consistent units of force times length), respectively, and <math>\~~boldsymbol~~\gamma Q</math> is the resultant factored load (consistent units of force) for the strength limit state (Figure 751.38.5.1). Here the moment, <math>M^_B</math>, is a moment about the ''y''-axis and moment, <math>M^_L</math>, is a moment about the ''x''-axis.		where <math>M^_B</math> and <math>M^_L</math> are moments attributed to ''factored'' load effects in the ''B'' and ''L'' directions (consistent units of force times length), respectively, and <math>\mathbf\gamma Q</math> is the resultant factored load (consistent units of force) for the strength limit state (Figure 751.38.5.1). Here the moment, <math>M^_B</math>, is a moment about the ''y''-axis and moment, <math>M^_L</math>, is a moment about the ''x''-axis.

	[[image:751.38.5.1.jpg\|center\|725px\|thumb\|<center>'''Fig. 751.38.5.1 Nomenclature used for load eccentricity for spread footings.'''</center>]]		[[image:751.38.5.1.jpg\|center\|725px\|thumb\|<center>'''Fig. 751.38.5.1 Nomenclature used for load eccentricity for spread footings.'''</center>]]
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	:''h'' = depth of footing (in.)		:''h'' = depth of footing (in.)

	:<math>\~~boldsymbol~~\gamma_e</math> = 1.0 for Class 1 exposure condition		:<math>\mathbf\gamma_e</math> = 1.0 for Class 1 exposure condition


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	===Commentary on [[#751.38.3 Design for Axial Loading at Strength Limit States\|EPG 751.38.3 Design for Axial Loading at Strength Limit States]]===		===Commentary on [[#751.38.3 Design for Axial Loading at Strength Limit States\|EPG 751.38.3 Design for Axial Loading at Strength Limit States]]===

	Throughout EPG 751.38, factored loads are denoted as <math>\~~boldsymbol~~\gamma Q</math>. This notation should not be taken to suggest inclusion or exclusion of specific load effects, but rather is simply intended as a convenient notation to reflect factored loads. When applying these guidelines, designers should replace <math>\~~boldsymbol~~\gamma Q</math> with load combinations and load factors that are appropriate for the structure and limit state being considered.		Throughout EPG 751.38, factored loads are denoted as <math>\mathbf\gamma Q</math>. This notation should not be taken to suggest inclusion or exclusion of specific load effects, but rather is simply intended as a convenient notation to reflect factored loads. When applying these guidelines, designers should replace <math>\mathbf\gamma Q</math> with load combinations and load factors that are appropriate for the structure and limit state being considered.

	Design procedures within this subarticle are categorized according to material type, including methods for design of spread footings founded upon “rock”, “weak rock”, “cohesive soil” and “cohesionless soil”. While these categories serve to logically separate the guidelines according to design method, complexities present at some sites may lead to cases where multiple methods could potentially be used. In such cases, designers should utilize the method that is most appropriate for the conditions encountered, rather than selecting the method that produces the smallest or largest footing dimensions.		Design procedures within this subarticle are categorized according to material type, including methods for design of spread footings founded upon “rock”, “weak rock”, “cohesive soil” and “cohesionless soil”. While these categories serve to logically separate the guidelines according to design method, complexities present at some sites may lead to cases where multiple methods could potentially be used. In such cases, designers should utilize the method that is most appropriate for the conditions encountered, rather than selecting the method that produces the smallest or largest footing dimensions.
Line 1,048:		Line 1,048:
	EPG 751.38.4.3 and EPG 751.38.4.4 are intended for use with cohesive and cohesionless soils, respectively.		EPG 751.38.4.3 and EPG 751.38.4.4 are intended for use with cohesive and cohesionless soils, respectively.

	Throughout EPG 751.38, factored loads are denoted as <math>\~~boldsymbol~~\gamma Q</math>. This notation should not be taken to suggest inclusion or exclusion of specific load effects, but rather is simply intended as a convenient notation to reflect factored loads. When applying these guidelines, designers should replace <math>\~~boldsymbol~~\gamma Q</math> with load combinations and load factors that are appropriate for the structure and limit state being considered.		Throughout EPG 751.38, factored loads are denoted as <math>\mathbf\gamma Q</math>. This notation should not be taken to suggest inclusion or exclusion of specific load effects, but rather is simply intended as a convenient notation to reflect factored loads. When applying these guidelines, designers should replace <math>\mathbf\gamma Q</math> with load combinations and load factors that are appropriate for the structure and limit state being considered.

	====Commentary on [[#751.38.4.1 Settlement of Spread Footings on Rock (qu ≥ 100 ksf)\|EPG 751.38.4.1 Settlement of Spread Footings on Rock (''q<sub>u</sub> ≥ 100 ksf'')]]====		====Commentary on [[#751.38.4.1 Settlement of Spread Footings on Rock (qu ≥ 100 ksf)\|EPG 751.38.4.1 Settlement of Spread Footings on Rock (''q<sub>u</sub> ≥ 100 ksf'')]]====

← Older revision		Revision as of 13:10, 28 June 2021
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	Resistance factors (<math>\boldsymbol \phi_b</math>) to be applied to the nominal resistance values (''q<sub>n</sub>'') determined according to the provisions of this article shall be established from Figure 751.38.3.1 based on the coefficient of variation of the mean uniaxial compressive strength, <math>COV_{\overline{q_u}}</math>. Values for ''q<sub>u</sub>'' and <math>COV_{\overline{q_u}}</math> shall be determined in accordance with methods described in [[321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation\|EPG 321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation]] for the site and location in question. Values for design parameters ''q<sub>u</sub>'', ''m'' and ''s'' shall be taken as mean values for the rock between the base of the footing and a depth of ''B'' below the base of the footing. Values for <math>COV_{\overline{q_u}}</math> should similarly reflect the variability of the mean uniaxial compressive strength for the rock over the same depth range.		Resistance factors (<math>\boldsymbol \phi_b</math>) to be applied to the nominal resistance values (''q<sub>n</sub>'') determined according to the provisions of this article shall be established from Figure 751.38.3.1 based on the coefficient of variation of the mean uniaxial compressive strength, <math>COV_{\overline{q_u}}</math>. Values for ''q<sub>u</sub>'' and <math>COV_{\overline{q_u}}</math> shall be determined in accordance with methods described in [[321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation\|EPG 321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation]] for the site and location in question. Values for design parameters ''q<sub>u</sub>'', ''m'' and ''s'' shall be taken as mean values for the rock between the base of the footing and a depth of ''B'' below the base of the footing. Values for <math>COV_{\overline{q_u}}</math> should similarly reflect the variability of the mean uniaxial compressive strength for the rock over the same depth range.

	[[image:751.38.3.1.jpg\|center\|775px\|thumb\|<center>'''Fig. 751.38.3.1 Resistance factors for bearing resistance of spread footings on rock.'''</center>]]		[[image:751.38.3.1 2021.jpg\|center\|775px\|thumb\|<center>'''Fig. 751.38.3.1 Resistance factors for bearing resistance of spread footings on rock.'''</center>]]

	Values for ''C<sub>f1</sub>'' shall be taken from Table 751.38.3.1.1. Values for the rock mass parameters ''m'' and ''s'' can be established as:		Values for ''C<sub>f1</sub>'' shall be taken from Table 751.38.3.1.1. Values for the rock mass parameters ''m'' and ''s'' can be established as:
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	Resistance factors (<math>\boldsymbol \phi_b</math>) to be applied to the nominal resistance values (''q<sub>n</sub>'') determined according to the provisions of this subarticle shall be established from Figure 751.38.3.2 based on the coefficient of variation of the mean uniaxial compressive strength <math>COV_{\overline{q_u}}</math>. Values for <math>\overline{q_u}</math> and <math>COV_{\overline{q_u}}</math> shall be determined in accordance with methods described in [[321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation\|EPG 321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation]] for the site and location in question. Values for design parameter ''q<sub>u</sub>'' shall be taken as the mean value of the parameter for the rock between the base of the footing and a depth of ''B'' below the base of the footing. Values for <math>COV_{\overline{q_u}}</math> shall similarly reflect the variability of the mean uniaxial compressive strength over the same depth range.		Resistance factors (<math>\boldsymbol \phi_b</math>) to be applied to the nominal resistance values (''q<sub>n</sub>'') determined according to the provisions of this subarticle shall be established from Figure 751.38.3.2 based on the coefficient of variation of the mean uniaxial compressive strength <math>COV_{\overline{q_u}}</math>. Values for <math>\overline{q_u}</math> and <math>COV_{\overline{q_u}}</math> shall be determined in accordance with methods described in [[321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation\|EPG 321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation]] for the site and location in question. Values for design parameter ''q<sub>u</sub>'' shall be taken as the mean value of the parameter for the rock between the base of the footing and a depth of ''B'' below the base of the footing. Values for <math>COV_{\overline{q_u}}</math> shall similarly reflect the variability of the mean uniaxial compressive strength over the same depth range.

	[[image:751.38.3.2.jpg\|center\|thumb\|700px\|<center>'''Fig. 751.38.3.2 Resistance factors for bearing resistance for spread footings on weak rock.'''</center>]]		[[image:751.38.3.2 2021.jpg\|center\|thumb\|700px\|<center>'''Fig. 751.38.3.2 Resistance factors for bearing resistance for spread footings on weak rock.'''</center>]]

	The value of ''N<sub>c</sub>'' shall be taken as 5.0. The respective correction factors for footing shape and depth and for load inclination shall be computed as		The value of ''N<sub>c</sub>'' shall be taken as 5.0. The respective correction factors for footing shape and depth and for load inclination shall be computed as
Line 272:		Line 272:


	[[image:table 751.38.3.3.jpg\|center\|775px\|thumb\|<center>'''Fig. 751.38.3.3 Resistance factors for bearing resistance for spread footings on cohesive soils.'''</center>]]		[[image:table 751.38.3.3 2021.jpg\|center\|775px\|thumb\|<center>'''Fig. 751.38.3.3 Resistance factors for bearing resistance for spread footings on cohesive soils.'''</center>]]

	===751.38.3.4 Bearing Resistance for Spread Footings on Cohesionless Soils===		===751.38.3.4 Bearing Resistance for Spread Footings on Cohesionless Soils===
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	For cases where the footing is underlain by practically homogeneous rock masses, ''H'' can be assumed to be equal to the footing dimension, ''B'' and values for <math>\overline{q_u}</math>, <math>COV_{\overline{q_u}}</math>, ''v'' and GSI shall be taken as the mean values of these parameters for the rock mass between the base of the footing and a depth of 2∙''H'' below the base of the footing. For cases where the rock beneath the footing is stratified, the value for ''H'' can be assumed to be the cumulative thickness of the more compressible strata within a depth of 2∙''B'' beneath the base of the footing. In such cases, values for <math>\overline{q_u}</math>, <math>COV_{\overline{q_u}}</math>, ''v'' and GSI shall be taken as the mean values of these parameters over the thickness of the more compressible strata.		For cases where the footing is underlain by practically homogeneous rock masses, ''H'' can be assumed to be equal to the footing dimension, ''B'' and values for <math>\overline{q_u}</math>, <math>COV_{\overline{q_u}}</math>, ''v'' and GSI shall be taken as the mean values of these parameters for the rock mass between the base of the footing and a depth of 2∙''H'' below the base of the footing. For cases where the rock beneath the footing is stratified, the value for ''H'' can be assumed to be the cumulative thickness of the more compressible strata within a depth of 2∙''B'' beneath the base of the footing. In such cases, values for <math>\overline{q_u}</math>, <math>COV_{\overline{q_u}}</math>, ''v'' and GSI shall be taken as the mean values of these parameters over the thickness of the more compressible strata.

	[[image:751.38.4.1.jpg\|center\|700px\|thumb\|<center>'''Fig. 751.38.4.1 Resistance factors for settlement of spread footings on rock.'''</center>]]		[[image:751.38.4.1 2021.jpg\|center\|700px\|thumb\|<center>'''Fig. 751.38.4.1 Resistance factors for settlement of spread footings on rock.'''</center>]]

	====<center>''Table 751.38.4.1 Poisson’s Ratio values for intact rock (modified after Kulhawy, 1978''</center>====		====<center>''Table 751.38.4.1 Poisson’s Ratio values for intact rock (modified after Kulhawy, 1978''</center>====
Line 406:		Line 406:
	Values for ''Φ<sub>S</sub>'' shall be established from Figure 751.38.4.2 based on the coefficient of variation of the mean uniaxial compressive strength, <math>COV_{\overline{q_u}}</math>, determined in accordance with methods described in [[321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation\|EPG 321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation]] for the site and location in question. Values for ''v'' can be estimated from Table 751.38.4.1.		Values for ''Φ<sub>S</sub>'' shall be established from Figure 751.38.4.2 based on the coefficient of variation of the mean uniaxial compressive strength, <math>COV_{\overline{q_u}}</math>, determined in accordance with methods described in [[321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation\|EPG 321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation]] for the site and location in question. Values for ''v'' can be estimated from Table 751.38.4.1.

	[[image:751.38.4.3.jpg\|center\|700px\|\|thumb\|<Center>'''Fig. 751.38.4.2 Resistance factors for settlement of spread footings on weak rock.'''</center>]]		[[image:751.38.4.2 2021.jpg\|center\|700px\|\|thumb\|<Center>'''Fig. 751.38.4.2 Resistance factors for settlement of spread footings on weak rock.'''</center>]]

	For cases where the footing is underlain by practically homogeneous rock masses, ''H'' can be assumed to be equal to the footing dimension, ''B'' and values for <math>\overline{q_u}</math>, <math>COV_{\overline{q_u}}</math> and ''v'' shall be taken as the mean values of these parameters for the rock mass between the base of the footing and a depth of 2∙''H'' below the base of the footing. For cases where the rock beneath the footing is stratified, the value for ''H'' can be assumed to be the cumulative thickness of the more compressible strata within a depth of 2∙''B'' beneath the base of the footing. In such cases, values for <math>\overline{q_u}</math>, <math>COV_{\overline{q_u}}</math> and ''v'' shall be taken as the mean values of these parameters over the thickness of the more compressible strata.		For cases where the footing is underlain by practically homogeneous rock masses, ''H'' can be assumed to be equal to the footing dimension, ''B'' and values for <math>\overline{q_u}</math>, <math>COV_{\overline{q_u}}</math> and ''v'' shall be taken as the mean values of these parameters for the rock mass between the base of the footing and a depth of 2∙''H'' below the base of the footing. For cases where the rock beneath the footing is stratified, the value for ''H'' can be assumed to be the cumulative thickness of the more compressible strata within a depth of 2∙''B'' beneath the base of the footing. In such cases, values for <math>\overline{q_u}</math>, <math>COV_{\overline{q_u}}</math> and ''v'' shall be taken as the mean values of these parameters over the thickness of the more compressible strata.
Line 495:		Line 495:
	Values for ''Φ<sub>c</sub>'' and ''Φ<sub>r</sub>'' shall be established from Figure 751.38.4.3.1 based on the coefficient of variation of the mean compression index (<math>COV_{\overline{c_c}}</math>) and mean recompression index (<math>COV_{\overline{c_r}}</math>), respectively. Similarly, values for ''Φ<sub>p</sub>'' shall be established from Figure 751.38.4.3.2 based on the coefficient of variation of the mean maximum past vertical effective stress (<math>COV_{\overline{\sigma^'_p}}</math>). Coefficients of variation for each of these parameters shall be determined in accordance with methods described in [[321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation\|EPG 321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation]].		Values for ''Φ<sub>c</sub>'' and ''Φ<sub>r</sub>'' shall be established from Figure 751.38.4.3.1 based on the coefficient of variation of the mean compression index (<math>COV_{\overline{c_c}}</math>) and mean recompression index (<math>COV_{\overline{c_r}}</math>), respectively. Similarly, values for ''Φ<sub>p</sub>'' shall be established from Figure 751.38.4.3.2 based on the coefficient of variation of the mean maximum past vertical effective stress (<math>COV_{\overline{\sigma^'_p}}</math>). Coefficients of variation for each of these parameters shall be determined in accordance with methods described in [[321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation\|EPG 321.3 Procedures for Estimation of Geotechnical Parameter Values and Coefficients of Variation]].

	[[image:751.38.4.4.jpg\|center\|700px\|thumb\|<center>'''Fig. 751.38.4.3.1 Resistance factors for compression index and recompression index in calculation of settlement for spread footings on cohesive soils.'''</center>]]		[[image:751.38.4.3.1 2021.jpg\|center\|700px\|thumb\|<center>'''Fig. 751.38.4.3.1 Resistance factors for compression index and recompression index in calculation of settlement for spread footings on cohesive soils.'''</center>]]

	Where footings are underlain by compressible soils of substantial thickness, the soil beneath the footing shall be subdivided into several sublayers to account for potential changes in consolidation parameters and stress distribution beneath the footing. Compression of each of these sublayers shall be computed using Equation 751.38.4.5, 751.38.4.6 or 751.38.4.7, as appropriate, and the resulting values should be summed to arrive at the total settlement. For each sublayer, values for ''c<sub>c</sub>'', ''c<sub>r</sub>'' and ''e<sub>0</sub>'' shall be taken as the mean values of these parameters over the thickness of the sublayer. Values for ''H<sub>0</sub>'' shall be taken as the thickness of the respective sublayer. Values for ''σ'<sub>0</sub>'', ''σ'<sub>f</sub>'' and ''σ'<sub>p</sub>'' for each sublayer shall also be taken as the mean values over each sublayer, although this is often approximated by using values calculated for the center of the sublayer. Values used for <math>COV_{\overline{c_c}}</math> , <math>COV_{\overline{c_r}}</math> and <math>COV_{\overline{\sigma^'_p}}</math> shall be representative of the variability and uncertainty of the mean values for the respective parameters within each sublayer.		Where footings are underlain by compressible soils of substantial thickness, the soil beneath the footing shall be subdivided into several sublayers to account for potential changes in consolidation parameters and stress distribution beneath the footing. Compression of each of these sublayers shall be computed using Equation 751.38.4.5, 751.38.4.6 or 751.38.4.7, as appropriate, and the resulting values should be summed to arrive at the total settlement. For each sublayer, values for ''c<sub>c</sub>'', ''c<sub>r</sub>'' and ''e<sub>0</sub>'' shall be taken as the mean values of these parameters over the thickness of the sublayer. Values for ''H<sub>0</sub>'' shall be taken as the thickness of the respective sublayer. Values for ''σ'<sub>0</sub>'', ''σ'<sub>f</sub>'' and ''σ'<sub>p</sub>'' for each sublayer shall also be taken as the mean values over each sublayer, although this is often approximated by using values calculated for the center of the sublayer. Values used for <math>COV_{\overline{c_c}}</math> , <math>COV_{\overline{c_r}}</math> and <math>COV_{\overline{\sigma^'_p}}</math> shall be representative of the variability and uncertainty of the mean values for the respective parameters within each sublayer.

	[[image:751.38.4.5.jpg\|center\|700px\|thumb\|<center>'''Fig. 751.38.4.3.2 Resistance factors for maximum past vertical effective stress used for calculation of settlement for spread footings on cohesive soils.'''</center>]]		[[image:751.38.4.3.2 2021.jpg\|center\|700px\|thumb\|<center>'''Fig. 751.38.4.3.2 Resistance factors for maximum past vertical effective stress used for calculation of settlement for spread footings on cohesive soils.'''</center>]]