751.38 Spread Footings - Revision history

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

Smithk at 14:24, 24 October 2019

2019-10-24T14:24:27Z

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	===751.38.8.3 Details===		===751.38.8.3 Details===

	====751.38.8.3.1 Reinforcement====		====751.38.8.3.1 Spread Footing Reinforcement====

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Smithk: /* 751.38.4.3 Settlement of Spread Footings on Cohesive Soils */

2019-02-19T19:07:46Z

751.38.4.3 Settlement of Spread Footings on Cohesive Soils

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	where:		where:

	:''S'' = length of shortest bridge span adjacent to footing (consistent units of length)		:''S'' = length of shortest bridge span adjacent to footing (consistent units of length).

	'''Factored total settlement'''		'''Factored total settlement'''

Smithk: /* 751.38.4.3 Settlement of Spread Footings on Cohesive Soils */

2019-02-19T19:06:02Z

751.38.4.3 Settlement of Spread Footings on Cohesive Soils

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	:''δ<sub>R</sub>'' = factored total settlement (consistent units of length) and		:''δ<sub>R</sub>'' = factored total settlement (consistent units of length) and

	:''δ<sub>tol</sub>'' = tolerable settlement (consistent units of length).		:''δ<sub>tol</sub>'' = tolerable settlement (consistent units of length),

	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.

Smithk: /* 751.38.4.2 Settlement of Spread Footings on Weak Rock (5 ksf ≤ qu ≤ 100 ksf) */

2019-02-19T19:04:21Z

751.38.4.2 Settlement of Spread Footings on Weak Rock (5 ksf ≤ qu ≤ 100 ksf)

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	[[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:751.38.4.3.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.

	===751.38.4.3 Settlement of Spread Footings on Cohesive Soils===		===751.38.4.3 Settlement of Spread Footings on Cohesive Soils===

Smithk: /* 751.38.4 Design for Axial Loading at Serviceability Limit States */

2019-02-19T19:00:53Z

751.38.4 Design for Axial Loading at Serviceability Limit States

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	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 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.

	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_u~~) greater than 100 ksf; EPG 751.38.4.2 shall be followed for footings founded in weaker rock with ~~q_u~~ 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.

	===751.38.4.1 Settlement of Spread Footings on Rock (''q<sub>u</sub> ≥ 100 ksf'')===		===751.38.4.1 Settlement of Spread Footings on Rock (''q<sub>u</sub> ≥ 100 ksf'')===

EPGsysop at 20:04, 7 April 2017

2017-04-07T20:04:44Z

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	Long, narrow footings supporting individual columns should be avoided unless space constraints or eccentric loading dictate otherwise, especially on foundation material of low capacity. In general, spread footings should be made as close to square as possible. The length to width ratio of footings supporting individual columns should not exceed 2.0, except on structures where the ratio of longitudinal to transverse loads or site constraints makes use of such a limit impractical.		Long, narrow footings supporting individual columns should be avoided unless space constraints or eccentric loading dictate otherwise, especially on foundation material of low capacity. In general, spread footings should be made as close to square as possible. The length to width ratio of footings supporting individual columns should not exceed 2.0, except on structures where the ratio of longitudinal to transverse loads or site constraints makes use of such a limit impractical.

	Footings located near to rock slopes (e.g. rock cuts, river bluffs, etc.) shall be located ~~such~~ that the footing is founded beyond a prohibited region established by a line inclined from the horizontal passing through the toe of the slope as shown in Figure 751.38.1.2. The boundary of the prohibited region shall be established by the Geotechnical Section. For the purposes of this provision, the toe of the slope shall be the point on the slope that produces the most severe location for the active zone. Exceptions to this provision shall only be made with specific approval of the Geotechnical Section and shall only be granted if overall stability can be demonstrated as provided in [[#751.38.7 Design for Overall Stability\|EPG 751.38.7]].		Footings located near to rock slopes (e.g. rock cuts, river bluffs, etc.) shall be located so that the footing is founded beyond a prohibited region established by a line inclined from the horizontal passing through the toe of the slope as shown in Figure 751.38.1.2. The boundary of the prohibited region shall be established by the Geotechnical Section. For the purposes of this provision, the toe of the slope shall be the point on the slope that produces the most severe location for the active zone. Exceptions to this provision shall only be made with specific approval of the Geotechnical Section and shall only be granted if overall stability can be demonstrated as provided in [[#751.38.7 Design for Overall Stability\|EPG 751.38.7]].

	[[image:751.38.1.2.jpg\|center\|775px\|thumb\|<center>'''Fig. 751.38.1.2 Prohibited region for spread footings placed near rock slopes unless exception is specifically approved by MoDOT Geotechnical Section.'''</center>]]		[[image:751.38.1.2.jpg\|center\|775px\|thumb\|<center>'''Fig. 751.38.1.2 Prohibited region for spread footings placed near rock slopes unless exception is specifically approved by MoDOT Geotechnical Section.'''</center>]]
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	\|align="center"\|'''[[#Commentary on EPG 751.38.3 Design for Axial Loading at Strength Limit States\|Commentary for EPG 751.38.3 Design for Axial Loading at Strength Limit States''']]		\|align="center"\|'''[[#Commentary on EPG 751.38.3 Design for Axial Loading at Strength Limit States\|Commentary for EPG 751.38.3 Design for Axial Loading at Strength Limit States''']]
	\|}		\|}
	In general, spread footings shall be sized for strength limit states ~~such~~ that the factored bearing resistance exceeds the factored loads for the strength limit state of interest. This shall be accomplished by determining the minimum footing dimensions, ''B'' and ''L'', ~~such~~ that the following condition is satisfied		In general, spread footings shall be sized for strength limit states so that the factored bearing resistance exceeds the factored loads for the strength limit state of interest. This shall be accomplished by determining the minimum footing dimensions, ''B'' and ''L'', so that the following condition is satisfied

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Smithk: Per Bridge, numerous minor edits

2012-02-28T18:23:00Z

Per Bridge, numerous minor edits

Show changes

Smithk at 19:16, 31 March 2011

2011-03-31T19:16:42Z

← Older revision		Revision as of 14:16, 31 March 2011
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	[[Category:751 LRFD ~~Manual General~~]]		[[Category:751 LRFD Bridge Design Guidelines]]

← 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
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	[[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>====
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	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.
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	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>]]