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Suggested Citation:"6. Scour Management Case Studies." National Academies of Sciences, Engineering, and Medicine. 2007. Risk-Based Management Guidelines for Scour at Bridges with Unknown Foundations. Washington, DC: The National Academies Press. doi: 10.17226/23243.
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Suggested Citation:"6. Scour Management Case Studies." National Academies of Sciences, Engineering, and Medicine. 2007. Risk-Based Management Guidelines for Scour at Bridges with Unknown Foundations. Washington, DC: The National Academies Press. doi: 10.17226/23243.
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Suggested Citation:"6. Scour Management Case Studies." National Academies of Sciences, Engineering, and Medicine. 2007. Risk-Based Management Guidelines for Scour at Bridges with Unknown Foundations. Washington, DC: The National Academies Press. doi: 10.17226/23243.
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Suggested Citation:"6. Scour Management Case Studies." National Academies of Sciences, Engineering, and Medicine. 2007. Risk-Based Management Guidelines for Scour at Bridges with Unknown Foundations. Washington, DC: The National Academies Press. doi: 10.17226/23243.
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Suggested Citation:"6. Scour Management Case Studies." National Academies of Sciences, Engineering, and Medicine. 2007. Risk-Based Management Guidelines for Scour at Bridges with Unknown Foundations. Washington, DC: The National Academies Press. doi: 10.17226/23243.
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Suggested Citation:"6. Scour Management Case Studies." National Academies of Sciences, Engineering, and Medicine. 2007. Risk-Based Management Guidelines for Scour at Bridges with Unknown Foundations. Washington, DC: The National Academies Press. doi: 10.17226/23243.
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Suggested Citation:"6. Scour Management Case Studies." National Academies of Sciences, Engineering, and Medicine. 2007. Risk-Based Management Guidelines for Scour at Bridges with Unknown Foundations. Washington, DC: The National Academies Press. doi: 10.17226/23243.
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Suggested Citation:"6. Scour Management Case Studies." National Academies of Sciences, Engineering, and Medicine. 2007. Risk-Based Management Guidelines for Scour at Bridges with Unknown Foundations. Washington, DC: The National Academies Press. doi: 10.17226/23243.
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Suggested Citation:"6. Scour Management Case Studies." National Academies of Sciences, Engineering, and Medicine. 2007. Risk-Based Management Guidelines for Scour at Bridges with Unknown Foundations. Washington, DC: The National Academies Press. doi: 10.17226/23243.
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Suggested Citation:"6. Scour Management Case Studies." National Academies of Sciences, Engineering, and Medicine. 2007. Risk-Based Management Guidelines for Scour at Bridges with Unknown Foundations. Washington, DC: The National Academies Press. doi: 10.17226/23243.
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Suggested Citation:"6. Scour Management Case Studies." National Academies of Sciences, Engineering, and Medicine. 2007. Risk-Based Management Guidelines for Scour at Bridges with Unknown Foundations. Washington, DC: The National Academies Press. doi: 10.17226/23243.
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Suggested Citation:"6. Scour Management Case Studies." National Academies of Sciences, Engineering, and Medicine. 2007. Risk-Based Management Guidelines for Scour at Bridges with Unknown Foundations. Washington, DC: The National Academies Press. doi: 10.17226/23243.
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NCHRP 24-25 Page 69 Phase II Final Report 6. SCOUR MANAGEMENT CASE STUDIES This section offers a few examples of how the scour guidelines in the previous section may be used to evaluate bridges with unknown foundations and select a management plan. The examples given here are based on 60 case studies obtained from a recent survey of bridges in six States (see Appendix F). 6.1. Information Search and Preliminary Screens The first step in applying the scour guidelines to bridges with unknown foundations is to collect the pertinent data for each bridge. The first step in this data collection should be to search harder for any records that might be used to determine or infer the foundation. If foundation records are located and the bridge engineer is confident that these records are sufficient for inferring the foundation, then they should follow the advice given in the “Are there any Foundation Records?” subsection of the scour management guidelines. If foundation records can not be found, the next step is to see if the bridge is considered a high priority structure. The “Is the Bridge a High Priority Structure?” subsection of the scour risk management guidelines gives the definition of a high priority structure, and outlines the course of action for any high priority structures. Once the foundation has been satisfactorily determined or inferred, the bridge can be evaluated as a known foundation using FHWA HEC-18 (2). All remaining bridges with unknown foundations should be evaluated using data that is easy to collect or obtain. The bridge survey form (see Appendix F) can be used to collect the pertinent data for evaluating these bridges using the scour risk management guidelines. Table 28 summarizes all of the data that the screening analysis may require. The first step in the “Perform Screening Analysis” subsection of the guidelines, however, only requires four of the NBI items in this table – namely, items 26, 60, 61, and 71.

NCHRP 24-25 Page 70 Phase II Final Report Table 28 Summary of Required Data Required Data Value Source Required Data Value Source Detour length (miles) NBI item 19 Truck running cost ($/mi) Planning, C3* Functional classification NBI item 26 Duration of detour (days) Planning, d* Average daily traffic NBI item 29 Value of time, cars ($/mi) Planning, C4* Structure length (feet) NBI item 49 Avg car occupancy Planning, O* Deck Width (feet) NBI item 52 Value of time, trucks ($/mi) Planning, C5* Substructure condition NBI item 60 Avg detour speed (mph) Planning, S* Channel protection NBI item 61 No. deaths from failure Planning, X* Waterway adequacy NBI item 71 Cost for each lost life ($) Planning, C6* Avg daily truck traffic (%) NBI item 109 Cost of automated scour monitoring ($) Hydraulics† Span length (> 100 ft?) Inspections Cost of scour countermeasures ($) Hydraulics† Remaining life (years) Design/Planning Cost of foundation reconnaissance ($) Geotechnical† Car running cost ($/mi) Planning, C2* Cost of scour evaluation ($) Hydraulics† *Estimate using local data or the default values as defined in Equation 2. †Estimate from past experience based on similar structures and streams. 6.2. The Minimum Performance Level Criterion The first step in the screening analysis involves comparing the estimated annual probability of failure for a bridge to its minimum performance level. Consider two examples from the case studies. The first example is bridge number 57-0072 in San Diego County, CA, which was built in 1938 and supports state route 76 – a rural minor arterial road – over Pala Creek. This bridge has five spans supported by concrete piles of known length, and has an NBI item 113 rating of “3” (scour critical and unstable). This known foundation was used to test the guidelines. The minimum performance level for a rural minor arterial class bridge according to Table 27 is 0.0005 – the threshold probability of failure that this bridge must outperform. The first step in evaluating this bridge is to estimate the overtopping frequency and scour vulnerability of this bridge, as in the Table 29 below, and then the annual probability of failure.

NCHRP 24-25 Page 71 Phase II Final Report Table 29 Annual Probability of Failure, Example 1 Data/Parameter (source) Value Interpretation NBI item 26 (bridge survey) 6 Rural minor collector NBI item 71 (bridge survey) 7 Waterway exceeds the minimum criteria ∴Overtopping Frequency (Table 13) S Slight (once in 11-100 years) NBI item 60 (bridge survey) 5 Foundation is in fair condition NBI item 61 (bridge survey) 3 Banks are failing and threaten the bridge ∴Scour Vulnerability (Table 14) 4 Analysis: stable; Survey: foundation is exposed ∴Annual probability of failure (Table 12) 0.0005 A 1 in 2,000 chance of failure in any given year This bridge has a known foundation that probably requires action. Furthermore, this bridge does not meet the minimum performance level for bridges with unknown foundations because the estimated annual probability of failure is not less than 0.0005. Thus, if this bridge had an unknown foundation the guidelines would have recommended the following three step strategy to ensure the safety of this bridge. 1. Perform field reconnaissance to determine foundation type and depth. If the foundation is a spread footing, drill through the footing to determine elevation of the footing bottom. If the foundation is piles, use foundation reconnaissance to determine depth of piles. The parallel seismic test is generally the most effective reconnaissance method. Assume that the foundation information from the field evaluation is accurate. If field reconnaissance is unsuccessful (no access for testing, poor signal from NDT, etc.), assume a foundation depth. For piles, assume a 10 foot depth or use local knowledge. This should be a conservative assumption. Spread footing depths are easily discovered and an assumption should not be necessary for this type of foundation. In other words, continue as if the foundation is known. 2. Evaluate scour using FHWA HEC-18 (2).

NCHRP 24-25 Page 72 Phase II Final Report 3. If scour analysis indicates that countermeasures are warranted, countermeasures should be designed using FHWA HEC-23 (8) – or consider replacing or closing the bridge. The second example is bridge number 091470064302038 in Limestone County, TX, which was built in 1977 and supports FM-39 – a rural major collector road – over Sanders Creek. This bridge has pre-stressed concrete box girders on multiple concrete drilled shafts, and has an NBI item 113 rating of “3” (scour-critical and unstable). This known foundation was also used to test the guidelines. The minimum performance level for an urban-local class bridge according to Table 27 is 0.0005 – the threshold probability of failure that this bridge must outperform. The first step in evaluating this bridge is to estimate the overtopping frequency and scour vulnerability of this bridge, as in the Table 30 below, and then the annual probability of failure. Table 30 Annual Probability of Failure, Example 2 Data/Parameter (source) Value Interpretation NBI item 26 (bridge survey) 7 Rural major collector NBI item 71 (bridge survey) 6 Waterway meets the minimum criteria ∴Overtopping Frequency (Table 13) S Slight (once in 11-100 years) NBI item 60 (bridge survey) 7 Foundation is in good condition NBI item 61 (bridge survey) 7 Channel has some minor drift and damage ∴Scour Vulnerability (Table 14) 7 Countermeasures now make it stable ∴Annual probability of failure (Table 12) 0.00025 A 1 in 4,000 chance of failure in any given year This bridge meets the minimum performance level because the estimated annual probability of failure is less than 0.0005. However, because the foundation is assumed to be unknown, this probability of failure should be used to calculate the lifetime risk of failure in order to select a management plan. 6.3. Scour Risk Assessment The bridge in the second example has a safe 29-year track record so far, and the Texas Department of Transportation (TXDOT) originally designed this bridge to last 47

NCHRP 24-25 Page 73 Phase II Final Report more years. This example will be evaluated as an unknown foundation even thought the foundation is known to be scour-critical and therefore unstable. The “Lifetime Risk of Scour Failure” section provides a way to estimate the risk of failure that can be used to select a reasonable management plan. The first step in calculating the risk of failure for this bridge is to calculate the lifetime probability of failure using Equations 6 and 7. The lifetime probability of failure for this bridge can be computed from the annual probability of failure and its tentative remaining life as follows: 1-(1-0.00025)47, or about 0.012. In other words, this annual probability of failure (0.00025) suggests that there is approximately a 1 in 83 (0.012) chance that this bridge will fail in the next 47 years. The next step in computing the risk of failure is to calculate the approximate cost of failure using Equation 2. Given that this bridge has an average daily traffic load of 2,700 motorists per day, if this bridge were to fail Table 11 estimates that two lives might be lost in the event of bridge failure. If each lost life is valued at $500,000, the lifetime cost of death is calculated as follows: 000,000,1$)2()/000,500($ 6 =⋅= ⋅= peopleperson XCCdeath TXDOT estimates that a new bridge in this location will cost about $1,092,987, that the detour would be approximately 11 miles long, and that the daily truck traffic is approximately 10 percent of the average daily traffic. Furthermore, if the running cost is $0.45/mi/car and $1.30/mi/truck, the duration of the detour is about 365 days (see Table 3), then the car and truck running cost associated with the detour for this bridge is computed as follows:

NCHRP 24-25 Page 74 Phase II Final Report 668,799,5$ )365()/700,2()11( 100 10/30.1$ 100 101/45.0$ 100100 1 32 = ⋅⋅⋅⎥⎦ ⎤⎢⎣ ⎡ ⋅+⎟⎠ ⎞⎜⎝ ⎛ −⋅= ⋅⋅⋅⎥⎦ ⎤⎢⎣ ⎡ ⋅+⎟⎠ ⎞⎜⎝ ⎛ −⋅= daysdaymimimi dADTCTCCrunning If the average wage of each car occupant is $6.96 (see Table 8), the average occupancy per car is 1.63 people, and the average cost of truck time is about $22.01, then the cost of lost time is computed as follows: 623,363,3$ /40 )365()/700,2()11( 100 10)/01.22($ 100 101)63.1()96.6($ 100100 1 54 = ⋅⋅⋅⎥⎦ ⎤⎢⎣ ⎡ ⋅+⎟⎠ ⎞⎜⎝ ⎛ −⋅⋅= ⋅⋅⋅⎥⎦ ⎤⎢⎣ ⎡ ⋅+⎟⎠ ⎞⎜⎝ ⎛ −⋅⋅= hrmi daysdaymitruck S dADTCTOCCwages Thus, the total cost of bridge failure is approximately $11,256,277. The risk adjustment factor (i.e. K in “Lifetime Risk of Scour Failure”) for this bridge is equal to one (i.e. no adjustment) because this bridge has spans that are less than 100 feet long. The risk of a scour-induced failure over the remaining life of the bridge is just the product of the lifetime probability of failure, the total cost of failure, and the risk adjustment factor; in other words about $131,504 (i.e. 1.2% of the total cost of failure). 6.4. Management Alternatives At this point the “Scour Risk Management Guidelines” stipulate that the lifetime risk of failure (above) should be compared to the cost of three different mitigating actions for the bridge in Limestone County, TX. The first alternative (see Figure 4) is to consider automated scour monitoring. Since the cost of automated scour monitoring was estimated to be $20,000 and the risk of death is approximately $11,069 (i.e. PL*Cdeath*K = 0.012*$1,000,000*1.0), automated scour monitoring is probably not warranted.

NCHRP 24-25 Page 75 Phase II Final Report Next, scour countermeasures are considered warranted if the lifetime risk of failure is greater than the estimated cost of scour countermeasures, which TXDOT estimates to be about $50,000. In this case, scour countermeasures are probably warranted because the lifetime risk of failure ($131,500) is more than twice the estimated cost of countermeasures ($50,000). Thus, even though this bridge (i.e. example 2 in Table 30) passed the minimum performance level, the estimated risk associated with this bridge is greater than the cost of installing protective countermeasures. At this point, the bridge owner must now decide if a full scour analysis using foundation reconnaissance and FHWA HEC-18 (2) is warranted before installing countermeasures. In this case, TXDOT estimated that a scour evaluation would cost $5,000. The cost of foundation reconnaissance was unknown, but it is probably less than $10,000. In other words, the total cost of field analysis ($15,000) is only 30% of the estimated cost of installing countermeasures. Thus, field reconnaissance (i.e. foundation reconnaissance followed by scour analysis) is probably warranted because the total cost of field analysis is less than half the estimated cost of countermeasures. Thus, if this bridge had an unknown foundation, the guidelines would have recommended the following steps to ensure the safety of this bridge: 1. Perform field reconnaissance to determine foundation type and depth. If the foundation is a spread footing, drill through the footing to determine elevation of the footing bottom. If the foundation is piles, use foundation reconnaissance to determine depth of piles. The parallel seismic test is generally the most effective reconnaissance method. Assume that the foundation information from the field evaluation is accurate. If field reconnaissance is unsuccessful (no access for testing, poor signal from NDT, etc.), assume a foundation depth. For piles, assume a 10 foot depth or use local knowledge. This should be a conservative

NCHRP 24-25 Page 76 Phase II Final Report assumption. Spread footing depths are easily discovered and an assumption should not be necessary for this type of foundation. In other words, continue as if the foundation is known. 2. Evaluate scour using FHWA HEC-18 (2). 3. If scour analysis indicates that countermeasures are warranted, countermeasures should be designed using FHWA HEC-23 (8) – or consider replacing or closing the bridge. Since this bridge has a known foundation that was found to be scour-critical, this management plan – for an unknown foundation – would probably reveal that this bridge in fact needs corrective action. Table 31 shows a tally of the scour management decisions for 59 of the 60 case studies (see Appendix F for the survey data) versus functional classification and priority. This table shows that 30 case studies are considered high priority, which means that their economic value is difficult to quantify but is probably more than sufficient to justify foundation reconnaissance and standard scour analysis using FHWA HEC-18. Of the remaining 29 case studies that are not high priority structures, the scour guidelines found that 9 of these warrant foundation reconnaissance and standard scour analysis. It should be recognized that while performing a scour analysis may not ultimately change the management plan of any of these bridges, the benefit of an informed management decision is assumed to be greater than the risk associated with the existing management decision. Finally, risk analysis suggests that the remaining 20 bridges only warrant developing a bridge closure plan that includes monitoring the bed elevation during biennial inspections. Thus, this table shows that the scour guidelines are conservative in that they recommended foundation reconnaissance for 39 of the 59 case studies evaluated. However, this is partly due to the fact that 36% (21 bridges) of the case studies involved a principal arterial (i.e.

NCHRP 24-25 Page 77 Phase II Final Report 70% of the high priority case studies), whereas about 4 percent of the bridges nationwide with unknown foundations support principal arterials. Table 31 Case Study Management Decisions by Functional Classification Scour Management Decision Functional Classification (NBI item 26) Countermeasures without analysis* Countermeasures with analysis* Closure plan and stream bed monitoring High Priority Principal arterials (all) 21 All others 9 Non-High Priority Urban minor arterials 1 Urban collectors 1 Urban locals 1 1 Rural minor arterials 3 7 Rural major collectors 4 3 Rural minor collectors 4 Rural locals 4 Totals 0 39 20 *Analysis implies foundation reconnaissance followed by standard scour analysis, which may change the decision to install countermeasures (or close or replace the bridge). Table 32 provides a more detailed summary of the sixty case studies results. Note that 26 of these bridges have known foundations (NBI item 113 ≠ “U”), and that one did not have enough information to be properly evaluated (i.e. 480A0430001 in Tennessee). Of the 29 case studies that were not high priority structures, five of them did not meet the minimum performance level (MPL). Of the five case studies that did not meet the MPL, three of them had known foundations that were rated scour critical, and one (#45-0063 in California) had an unknown foundation that recently failed due to scour. Risk analysis ultimately found that four of the case studies that passed the MPL warranted foundation reconnaissance and standard scour analysis before considering scour countermeasures. This table shows that most of the twenty-nine case studies for which there are scour evaluations validate the management plan that the “Scour Risk Management Guidelines” suggested. There are only four case studies with known foundations in which the scour guidelines may not have selected an appropriate management plan. For example, the scour

NCHRP 24-25 Page 78 Phase II Final Report guidelines may not have recommended a sufficiently aggressive management plan for three of the case studies – specifically: #89S42900017 in Tennessee, #0670091 in North Carolina, and #091100041802028 in Texas – when the NBI item 113 code was scour critical and therefore unstable. Alternatively, there was one bridge – #160062 in Florida – for which the scour guidelines recommended foundation reconnaissance when the NBI item 113 code indicated that the foundation is stable with respect to scour. However, given the uncertainties associated with using the available data to predict scour vulnerability, a few mistakes are inevitable. This possibility for error is the primary reason why the minimum requirement in the scour guidelines is to develop a bridge closure plan, and to keep a detailed record of the stream bed’s elevation during biennial inspections. Monitoring the stream bed elevation every two years and reviewing/updating the bridge closure plan each time should help officials identify problems that may not have been apparent before this risk analysis.

NCHRP 24-25 Page 79 Phase II Final Report Table 32 Summary of Bridge Case Studies Mitigating Action Decisions State Structure No. (NBI item 8) Functional Classification (NBI item 26)* NBI item 113 Overtopping Frequency Scour Vulnerability High Priority Meet MPL Automated Scour Monitoring Scour Counter- measures Field, Scour Analysis CA 55-0621M 14 (U PA) U Slight 7 Yes No Yes CA 57-0043Z 6 (R MnA) U Slight 6 Yes No No No CA 57-0096 6 (R MnA) U Slight 7 Yes No No No CA 45-0019R 2 (R PA) U Slight 5 Yes Yes Yes CA 45-0063 6 (R MnA) U Slight 6 Yes No† Yes Yes CA 55-0228 11 (U I) 3 Slight 5 Yes Yes Yes CA 57-0072 6 (R MnA) 3 Slight 4 No Yes CA 41-0025 14 (U PA) 3 Slight 6 Yes No Yes CA 20-0038 6 (R MnA) U Slight 4 Failed No Yes CA 12-0073 2 (R PA) 2 Slight 6 Yes No Yes FL 030145 2 (R PA) U Slight 7 Yes No Yes FL 050018 6 (R MnA) U Slight 7 Yes Yes Yes FL 120160 14 (U PA) U Slight 7 Yes No Yes FL 120165 2 (R PA) 8 Slight 8 Yes Yes Yes FL 160063 16 (U MnA) 8 Slight 6 No Yes FL 100352 1 (R I) 7 Remote 7 Yes No Yes FL 100434 2 (RPA) 7 Slight 7 Yes No Yes FL 150107 11 (U I) U Slight 6 Yes No Yes FL 100039 2 (RPA) U Slight 7 Yes No Yes FL 100100 14 (U PA) U Slight 7 Yes No Yes NY 3330270 7 (R MjC) 3 Slight 4 No Yes NY 2268710 9 (R L) U Occasional 6 Yes Yes Yes NY 2268950 9 (R L) U Occasional 6 Yes Yes Yes NY 5017820 14 (U PA) U Slight 7 Yes No Yes NY 3300120 14 (U PA) U Occasional 7 Yes No Yes NY 3330150 17 (U C) U Occasional 5 Yes No No No NY 1092839 11 (U I) 8 Slight 7 Yes No Yes NY 5516290 12 (U F/E) 6 Slight 7 Yes No Yes NY 1024960 14 (U PA) 8 Occasional 4 Yes No Yes NY 3312460 9 (R L) 8 Occasional 4 Yes No No No NC 0550011 7 (R MjC) 3 Slight 3 Yes No Yes NC 1470038 14 (U PA) 7 Slight 2 Yes No Yes NC 0670091 8 (R MnC) 3 Slight 7 Yes No No No

NCHRP 24-25 Page 80 Phase II Final Report Mitigating Action Decisions State Structure No. (NBI item 8) Functional Classification (NBI item 26)* NBI item 113 Overtopping Frequency Scour Vulnerability High Priority Meet MPL Automated Scour Monitoring Scour Counter- measures Field, Scour Analysis NC 0450113 9 (R L) U Occasional 6 Yes No No No NC 0130115 9 (R L) 8 Slight 7 Yes Yes Yes NC 0120101 9 (R L) U Occasional 7 Yes Yes Yes NC 0510042 8 (R MnC) U Slight 6 Yes Yes Yes NC 0890008 9 (R L) U Slight 6 Yes No No No NC 0710032 6 (R MnA) 8 Slight 7 Yes No No No NC 1250013 8 (R MnC) U Slight 7 Yes Yes Yes TN 480A0430001 9 (R L) 0 Closed 0 Failed ‡ ‡ TN 040A1360001 9 (R L) U Occasional 6 Yes No No No TN 09SR0770025 7 (R MjC) U Slight 6 Yes No Yes Yes TN 12SR2250005 7 (R MjC) U Slight 6 Yes No No No TN 19019430001 19 (U L) U Slight 7 Yes No Yes Yes TN 31021320001 8 (R MnC) U Occasional 5 Yes No No No TN 58SR0270007 8 (R MnC) 5 Slight 6 Yes No No No TN 81S61140007 7 (R MjC) 5 Slight 6 Yes No No No TN 89S42900017 8 (R MnC) 3 Occasional 5 Yes No No No TN 780B0720001 19 (U L) U Slight 5 Yes No No No TX 090180039801026 7 (R MjC) 3 Slight 4 No Yes TX 090740004904052 2 (R PA) 3 Slight 7 Yes No Yes TX 091100001423285 1 (R I) 3 Slight 7 Yes No Yes TX 091100041802028 7 (R MjC) 3 Slight 5 Yes No No No TX 091470064302038 7 (R MjC) 3 Slight 7 Yes No Yes Yes TX 090140AA0268002 6 (R MnA) U Occasional 6 Yes No No No TX 090740AA0128001 6 (R MnA) U Occasional 6 Yes No No No TX 091100AA0878002 6 (R MnA) U Occasional 6 Yes No No No TX 091470AA0173001 6 (R MnA) U Occasional 5 Yes Yes Yes TX 091470AA0327001 6 (R MnA) U Occasional 5 Yes No No No *Abbreviations: R = rural; U = urban; I = interstate; F/E = freeway or expressway; PA = principal arterial; A = arterial; Mn = minor; Mj = major; C = collector; L = local. †Automated scour monitoring would have been warranted if scour countermeasures were not warranted. ‡Tennessee did not have enough information about this bridge – before it failed – to evaluate it.

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TRB's National Cooperative Highway Research Program (NCHRP) Web-Only Document 107: Risk-Based Management Guidelines for Scour at Bridges with Unknown Foundations examines a risk-based approach to managing bridges in the absence of foundation information. A risk assessment tool and instructions are available online.

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