Risk-based approach to Factor of Safety selection

Introduction & Summary

NZGS is currently preparing a Slope Stability Guidance Series. At the time of writing (September 2024), Unit 3 – titled Slope Stability Analysis – has a completed draft and has been sent to the peer reviewers. 

One of the new things to be presented in Unit 3 is the selection of the target Factor of Safety (FoS) based on the uncertainty involved and the consequence of slope movement. Unit 3 will present only a broad description of the methodology of the derivation of the target FoS. Presented in this paper is a detailed description of the methodology.

Some key points regarding this work:

• In some situations, target FoS may be prescribed by a Crown entity, stakeholder, or local authority, such as NZSOLD (2023) for dams or NZTA Waka Kotahi (2022) for highway slopes. If a clear authority is present, then the recommendations of those authorities should be followed. We suggest that the Unit 3 recommendations (and those herein) are appropriate for slopes where there is no clear other authority present. 

• The target FoS presented are for Long-term Static and High Ground Water conditions only. Seismic analysis is not covered in this paper but will be covered in Unit 3.

• These values are for new slopes and new developments. Assessment of existing slopes (including those with existing landslides) is not covered in this paper but will be covered in Unit 3.

Recommended minimum factors of safety for new slopes under Long-term Static conditions are presented in Table 1.

Recommended FoS for the High Ground Water case are shown in Table 2.

Details of the derivations of these values, and the definitions of the Consequence Categories and Levels of Engineering, are presented below. Advice on which of the (up to) three values presented in each cell of these (and subsequent) tables is provided in Unit 3.

1. A Problem with Factor of Safety

Factor of Safety (FoS) is the most common quantitative measure of a slope’s stability. The most widely used definition for slope stability FoS is that it is the ratio of the shear strength of the soil to the shear stress required for equilibrium (Duncan et al, 2014).

Terzaghi, in his 1943 “Theoretical Soil Mechanics”, presents a target FoS of 1.5 for slope stability, without a detailed discussion of why this value was selected (Schnaid et al, 2020). Subsequently, geotechnical professionals and authorities have adopted minimum FoS for slope stability for various loading conditions. Frequently, the minimum FoS under static, long-term loading conditions selected by authorities and geotechnical professionals is still 1.5, as presented by Terzaghi. 

Common target values are periodically revised based on experience, particularly after large slope failures have occurred (Schnaid et al, 2020). Table 3 presents a list of some commonly used target FoS values.

While the adoption of typical minimum FoS based on experience is logical, use of the same value across a wide range of conditions is not (Duncan, 2000). It does not account for the varying degrees of uncertainty in the stability assessment, or the consequences that would ensue from failure. In other words, the use of the same FoS target across a range of situations does not reflect the varying degrees of risk. In New Zealand this issue was highlighted by Crawford & Millar (1998, 1999) who drew on results of a questionnaire to Councils and geotechnical consultants throughout New Zealand and emphasized the need for explanation and qualification of applicable design conditions and level of risk when using typical FoS targets.  

The importance of considering the uncertainty of the analysis and consequence of failure in selection of minimum FoS for slope stability has been recognised by many authors (Duncan, 2000; Fell et al, 2000; Schnaid et al, 2020; Adams, 2015) and has, to varying degrees, been incorporated into some standards and guidance (GEO, 2000; Read & Stacey, 2009). However, our research has not found an author or authority that provides a mathematical basis for their selections of minimum FoS. Even when considering risk elements, such as consequence level and level of design confidence, Adams selected minimum FoS “by a process of interpolation and comparison against typical industry-standard recommendations”.

That is, new target FoS are just based on old targets, which are based on still older targets, admittedly with adjustments made over the years based on experience, but with no explicitly expressed mathematical basis, except perhaps for the notion that the FoS should be more than 1 but not too much more than 1.

It is possible to quantitatively assess the risk of slope instability in which the probability of failure is estimated through either historic data or a probabilistic slope stability analysis. These assessments can, however, require a great deal of analysis and judgement and can be time-consuming and costly. Therefore, it remains common practice for routine projects to assess adequate stability by way of limit equilibrium methods and achieving minimum factors of safety. But what are defensible factors of safety that appropriately account for risk?

2. Purpose and Approach

The purpose of this paper is to describe our approach to selection of minimum FoS that accounts for the level of risk that slope instability poses. The approach presented is intended to be applicable across a range of low to medium risk “routine” projects. High risk projects may require specific quantitative estimation of the probability and consequence of failure. We have targeted risk levels associated with new developments and new slopes. When assessing stability associated with existing developments and slopes and when assessing stability of existing landslides and their mitigation, there is often acceptance of higher levels of risk. As such, lower values of FoS than those presented here may be suitable; however, these would need to be justified on a case-by-case basis. 

We have undertaken the following steps, outlined in further detail in this paper, to develop FoS recommendations:

(1) Utilised research completed by others that relates FoS to a slope’s probability of failure for various levels of uncertainty (defined by “Levels of Engineering” (LoE)). 

(2) Developed generalised maximum acceptable probabilities of failure for several consequence levels using a range of risk frameworks used in New Zealand. 

(3) For the threshold probability of failure at each consequence level developed in Step 2, the corresponding FoS from relationships in Step 1 was determined for each level of uncertainty.

(4) The resulting FoS for each level of uncertainty and consequence level were reviewed and compared against typical values. These results were used to develop generalised guidance for geoprofessionals to aid the project team and stakeholders in determining minimum FoS for slope stability assessments. 

3. Relating Probability of Failure to FoS

The research of Silva et al (2008) provides relationships between a slope’s annual probability of failure and its FoS, dependent on the Level of Engineering (LoE) as shown in Figure 1. These relationships are a culmination of years of development and experience and combine the quantification of expert judgment with consideration of probability theory. The data was developed from “over 75 projects spanning over 4 decades” including “zoned and homogenous earth dams, tailings dams, natural and cut slopes, and some earth retaining structures”. Silva et al selected engineering projects with well-known design, construction, and operation characteristics from their practice. Stability analyses assessed FoS, using the “best estimate of strength acting in the field and not necessarily the average strength or a conservative value of strength”. 

The Level of Engineering is described by categories, with LoE I being the “best” and features, amongst many other things, continuous sampling during investigations, laboratory testing on undisturbed specimens, a peer review of analysis, full-time engineering supervision during construction, and operations and maintenance after construction. 

In contrast, LoE IV, “poor”, features no investigations or laboratory testing, approximate analyses using assumed parameters, no engineering construction supervision, and only occasional post-construction inspections by a non-qualified person. LoE Categories II and III fall in between, with Category II being “above average” and Category III being “average”. 

As expected, for a given FoS, Category I gives the lowest probability of failure and Category IV the highest probability of failure, with Categories II and III in between. This reflects the generally accepted concept that a larger FoS does not necessarily mean lower probability of failure, because it depends on the uncertainties in the assessment. LoE provides an index of that degree of uncertainty. We have provided a description of each LoE provided in Silva et al (2008) in Appendix 1. 

Armed with Silva et al’s work, if one knows the engineering category, and one knows the maximum acceptable annual probability of failure, then the appropriate factor of safety can be found. 

4. Reviewed Risk Thresholds

Arguably the most critical and difficult step in our approach is in developing threshold probabilities of failure for a range of consequence levels that broadly reflects generally accepted levels of slope stability risk within New Zealand. New Zealand has no regulatory framework setting out acceptable or tolerable risk, so we have turned to published guidance on risk acceptance used within New Zealand to develop risk thresholds. Defining acceptable or tolerable risk is a complex, context-specific task and as such, the applicability of the risk thresholds selected here should be considered on a project-by-project basis. 

“Tolerable” and “Acceptable” risks have been defined by AGS (2007), amongst others. Several risk thresholds have been reviewed to develop ranges of generally accepted values of “acceptable” risk for a variety of consequence categories as summarised in Table 4. 

5. Consequence categories

The risk assessment systems described above each use different descriptions of consequence. To allow comparison of risk thresholds summarised in Table 4 we have created a new set of consequence categories and descriptions that is similar to those used by AGS (2007), Saunders et al. (2013), Justice et al. (2006), and Saunders & Glassey (2007). We provide a consequence description at each level related to life risk, damage to buildings/property, and damage to roads. 

To allow a description of the number of damaged houses that matches the life risk for those categories that include fatalities, it is necessary to estimate the ratio of deaths to destroyed houses in landslides. We have reviewed several sources to establish a reasonable ratio of fatalities to destroyed houses and this review is described in Appendix 3. Owing to the high uncertainty in estimates of the ratio of deaths to destroyed houses and the paucity of research in this area we have allowed for the ratio to vary between 0.05 and 0.5.

Recommended consequence levels and their associated descriptions are presented in Table 5.

6. Comparison of Risk Thresholds across Consequence Categories

We mapped the consequence descriptors from reviewed publications summarised in Table 4 onto our proposed descriptors (Table 5) and provided the selected AEP range for each category as follows: 

An oddity of the AGS classification can be seen in Table 8 – the same implied AEP for both Medium and Minor (AGS terms). This is because the Low/Moderate risk threshold lies at the unlikely/possible boundary for both Medium and Minor (AGS terms), as shown in Appendix 2. Had AGS assigned Possible-Minor as Low Risk rather than Moderate Risk, as would appear more intuitive, then this oddity would not have occurred (and one of the few obvious outliers in Table 12 would not have occurred).

The measures of consequence under Saunders et al’s framework appear targeted toward area-wide assessments, not assessment of individual properties. Particularly, the level of risk associated with consequences that involve multiple fatalities is higher and not consistent with other reviewed frameworks. The AEP for the Catastrophic category from this framework appears unconservative and has been omitted. The AEPs in Table 6 to Table 11 were combined in Table 12.

The Geometric mean values can be thought of as the mean value of the log (1/AEP) – the values in italics – and then converted back to AEP. The following outliers were disregarded in the calculation: (1) The AEP from Saunders et al associated with the Catastrophic consequence category (2) the AEP from AGS associated with the Low consequence category (3) AEP from NZS1170 associated with Major consequence related to snow loading.

A summary of the AEP ranges and means are presented below with the implied return period for easy comparison:

7. Factors of Safety for AEP Values

The values in Table 13 were compared to Figure 1 from Silva et al (2008) to determine the associated minimum FoS for each AEP and each Level of Engineering (LoE). The results are presented in Table 14. These values are associated with the static, long term loading condition. 

Several important concepts are reflected in Table 14:

• The required minimum FoS should be larger where there has been less investigative effort and oversight (i.e. where the Level of Engineering Category is higher), reflecting the higher uncertainty, and should reduce with increasing certainty in analysis results. 

• Lower FoS can be adopted where consequences of the instability are low, and there is adequate certainty in analysis results (area shaded green in Table 14). 

• At higher levels of consequence, it becomes necessary to achieve a particular level of certainty in the performance (i.e. LoE category). Situations where this has not been achieved are marked as N/A* in Table 14. Increasing the required minimum FoS in these cases has diminishing returns as slope failure often occurs because of unforeseen conditions that are not incorporated into the model (Silva et al 2008). Instead, more investigation and/or oversight is needed to increase the certainty in results. 

• Where the LoE is commensurate with the consequence (i.e. “better” engineering where the consequence is high), the indicated minimum FoS are broadly consistent with the typical value of 1.5 often adopted for the long-term static load case (the condition to which this table refers). This region is shaded blue in Table 14. This is a useful finding from our exercise as one goal was to determine the situations in which typical values are applicable. This trend indicates that if geoprofessionals match the level of investigation, design and oversight to the potential consequence of failure, the typical minimum FoS value of 1.5 likely reflects broadly accepted levels of risk. It appears that many geoprofessionals probably do this, as the value of 1.5 minimum FoS has been vetted, to a degree, through experience of the industry over time, and that experienced geoprofessionals instinctively match level of investigation to consequence.

We have compared our findings in Table 14 to other similar efforts including: 

• Adams (2015) – Opencast Mine Design

• Schnaid et al (2020) – Tailings Dams

• Hong Kong Highway Slope Manual (GEO, 2000) 

The comparison found that the minimum FoS values presented in this document (Table 14) are typically higher than those recommended in Adams (2015) and Schnaid (2020). This likely reflects the higher risk acceptance of the mining industry relative to the more generic thresholds for new slopes and developments. This highlights a key point: the values of risk thresholds used for this assessment may not reflect the risk tolerance for a specific project. Some industries and situations may be more risk tolerant (e.g. mining) and others less. Defining acceptable risk needs to be done on a project-by-project basis and needs to account for local regulation and input from the project stakeholders. 

Further detailed discussion on the comparison of FoS values from this study with those by others, including discussion on considering high groundwater cases, is included in Appendix 4. 

Although our work demonstrated that there is a mathematically defensible argument to support using FoS of around 1.0 or 1.1, we acknowledge that there is likely to be concern in the geotechnical community about using such low values. Some of this concern is because values of 1.0 or 1.1 are close to failure and that incipient slope movement might occur at these values. Also, low values of FoS mean that there is little margin for mistakes, by either the designer or contractor, that do occasionally occur no matter what LoE has been achieved. It was therefore concluded that it would be prudent to have FoS values no lower than 1.2 for Medium (and worse) consequence situations. Table 14 was thus adjusted, with the following Table 15 (a duplication of Table 1, except for the colours and AEP) used for Unit 3. This resulted in only one change, with the Medium-LoE I changed from “1.0 to 1.2 (1.1)” to “1.2”. The number in brackets in the Low-LoE I cell was also increased from 1.0 to 1.1, as this appeared more suitable.

The results of our assessment (summarised in Table 15) form the basis for conclusions and recommendations in the following Section. 

8. Conclusions and Recommendations

The FoS values developed in this study (Table 15, and in Table 19 for high GWT conditions) aim to reflect general levels of slope stability risk acceptance within New Zealand. An interesting and useful conclusion that can be drawn from these values is that where the level of investigation, design and oversight for slope stability assessment reflects the magnitude of the consequence (i.e. higher level of engineering where the consequence is higher, and lower where the consequences are low), the “typical” values of FoS that have been commonly used for decades generally achieve a broadly acceptable level of risk. While this conclusion is not unexpected, it provides confidence in the use of these values provided the appropriate level of investigation and oversight is carried out. In general, we consider that if the recommendations in IAEG Commission 25 (Baynes & Parry, 2022) on the level of ground model development relative to the project and geology complexity are followed (Figure 5.5 and 5.6 in the draft Unit 1 of the Slope Stability Guidance), “typical” values of FoS are appropriate to achieve broadly acceptable levels of slope stability risk in New Zealand. 

In practice, however, the authors’ experience is that it is common to use “typical” values without consideration of uncertainty and consequence. These values have been applied to situations where their use does not achieve an adequately low level of risk. To account for uncertainty and consequence, we recommend geoprofessionals follow the approach presented below. The aim of the approach is to encourage the geoprofessional to consider the elements of risk and communicate the risk to the project stakeholders. 

a. Are risk levels from this study appropriate? The first step should be to interrogate the threshold AEPs used in this study (Table 13) to confirm that the accepted level of risk from this study is appropriate for the project. As Table 13 was developed using a variety of sources, it is expected that the AEPs contained within it will be appropriate for most projects. However, in some circumstances, clients and/or authorities may have risk appetites different from those implied by Table 13 and where this is so, the geoprofessional should work with the project team and stakeholders to define acceptable AEPs. The Silva chart (Figure 1) can be used to determine project specific FoS values for the project specific AEPs. Once acceptable AEPs have been established, either using the values in Table 13, or otherwise, move on to Step b. 

b. Estimate the consequence. The geoprofessional should then estimate the consequence that could occur if the slope failed and select the corresponding consequence category (Table 5). Different failure surfaces/mechanisms could result in different consequences and multiple consequences may need to be assessed for the same slope. 

c. Determine LoE. We recommend the geoprofessional review this approach at the beginning of the project. Table 15 and Table 20 can be used in conjunction with Unit 1 of the Slope Stability Guidance to determine the appropriate level of investigation and oversight (Table 16) for the consequence of failure (Table 5). By targeting a Level of Engineering to be within the blue region of Table 15 and Table 20, typical FoS values can be used. Alternatively, if investigations have already been carried out and further investigations are not proposed, the LoE should be assessed using Table 16, and the geoprofessional should determine which region in Table 15 and Table 20 applies and proceed as indicated on the Tables. The orange region indicates that the consequence is too large for the level of investigation and that additional certainty in the ground model and slope stability results is required. This could be achieved through additional investigations or design work. Within the plum region, a higher than typical FoS should be targeted. Within the blue region, typical values can be adopted, and within the green region, it may be acceptable to adopt a lower than typical minimum FoS. 

The geoprofessional shall provide, in their design report, an appropriately detailed evaluation of the consequence selected, the LoE selected, and hence the selected minimum FoS. Where the minimum FoS is lower than typical values, territorial authorities (and others) may be wary, and hence the justifications in the design report should be especially clear and prominent.

9. Additional Information

9.1 Soil Strength 

To be consistent with Silva et al, from whose work the recommendations in this study are derived, it is recommended that soil and rock “strength determination corresponds to the best estimate of the strength acting in the field and not necessarily the average strength or a “conservative” value of strength”. 

What is the “best” estimate of soil strength? If the investigation has provided many measurements of soil strength, then the best estimate may be the mean value, if the anticipated failure surface is long, and hence a large amount of soil will be mobilised. But if the anticipated failure surface is short, the best estimate may be the lower quartile or possibly even the lowest value. If the investigation has yielded few measurements of soil strength, then usually the best value would be the lowest value or one near the low end of the range measured. The consequence of failure need not be considered in the selection of soil strength when using recommendations in this study, because it has already been considered in the selection of the minimum FoS.

It is therefore understood that strength parameters may, in the field, be lower than those chosen for design, and that is one of the reasons why, in most cases, the required factor of safety exceeds 1.0. To consider the possibility that field values of strength might be significantly lower than those assumed in analysis, sensitivity studies should be carried out.

9.2 Applicability

Limitations to the applicability of recommendations in this study are described below:
Hierarchy of authority: In some cases, a target FoS will be prescribed by a Crown entity, stakeholder, or local authority, such as NZSOLD (2023) for dams or NZTA (2022) for highway slopes. If a clear authority is present, then the target FoS of those authorities should be followed. We suggest that the recommendations in this paper are appropriate only where there is no clear authority present. 

Existing Slopes/Developments: There is generally a higher risk tolerance (around an order of magnitude higher AEP thresholds) for slope hazards for existing developments. For existing slopes and developments, the concepts and general approach outlined in this study can be applied once the appropriate level of risk has been determined by the project team and stakeholders. If possible, it is more suitable to assess the stability of existing slopes by visual assessment, historical photographs, and other field-based methods (Unit 1, Part 3) than by computer modelling. If the slope has been stable for more than about 20 years, and is not part of a recognisable landslide, it is reasonable to assume that it is stable under static and high ground water conditions, without having to undertake numeric analyses. However, limit equilibrium analysis (or risk assessment) should be carried out on existing slopes whose failure could affect new developments, if a substantive change in risk is proposed, such as (but not limited to):
– The slope is to be altered in a way that increases the probability of failure (such as cutting the slope’s toe, or de-vegetation). 
– A substantial new load (for instance, from a new structure or railway line) is being added above an existing slope.

If new structures are to be placed near existing slopes, such that there is a significant change to the consequence of failure (but no change to the likelihood of failure) then a sound engineering geological appraisal of existing and past slope performance (including investigations as required) should be carried out, followed by a risk assessment.

Retaining wall design: When undertaking slope stability analysis during retaining wall design, practitioners should use the appropriate target factors of safety indicated in existing design guidance (examples include FHWA, 2009 and FHWA, 2015) where the slope analysis includes structural elements (ground anchors, synthetic reinforcement, piles, etc.). This is because the strength parameters of the structural elements used in the slope stability assessment/programme should have due regard to the recommendations of the retaining wall guidance documents, and hence the target FoS should also be in accordance with that guidance. However, when considering deep-seated failures that either don’t include the structural elements or only include those structural elements to a minor degree (for instance, the critical failure surface intercepts only the last metre of a 10-metre-long ground anchor) then the FoS values provided in this document are appropriate.

Existing Landslides: Where assessment is being undertaken for mitigation of an existing landslide, the “typical” targets are often not achievable. It is common practice to adopt lower FoS targets or target marginal stabilization where an incremental increase of FoS over the existing conditions is targeted. 

High Risk Projects: For higher risk projects (generally those with higher consequences of failure), a more thorough site-specific quantitative risk analysis may be required. This may involve an investigation and laboratory programme extensive enough to characterise the distribution of soil strength parameters to allow for a probabilistic slope stability analysis to be undertaken.

9.3 Estimating Consequence

Assessing the consequence of a failure can be a difficult exercise. It involves estimating the likely velocity of the failure and runout distance as well as considering the elements (structures, infrastructure, people) that are within that runout distance or could be undermined.

The likelihood of fatalities is dependent on the location of the landslide relative to structures and people. A landslide (including rock fall and debris flows) that descends on structures and people from above is more likely to result in fatalities than a similar sized landslide that occurs below structures and people. Catastrophic and Disastrous consequences are most likely to arise from landslides impacting buildings from above, and those with the highest velocities are the most likely to cause fatalities. Landslides that undermine structures are, typically, less likely to result in fatalities, with the prominent exception of cliff collapse, where fatalities are more likely. 

Appendix 2: Determining Acceptable AEP

An example of the process for determining an acceptable AEP for each consequence is shown below. Under the AGS (2007) system, Low and Very Low Risk are acceptable, and Moderate, High and Very High Risks are not acceptable. So, for instance, for a Catastrophic consequence, the threshold AEP is between 10^-5 and 10^-6, and hence is set at 5 x 10^-6. A similar process is carried out for each consequence category. This was also carried out for Saunders & Glassey, Justice et al, and Saunders et al. 

Appendix 3: Ratio of Fatalities to Destroyed Houses

Four methods were used to estimate this ratio, as follows.

A3.1 Select Recent Major Landslides in New Zealand

In recent major landslide and rockfall events in New Zealand, the number of fatalities was substantially lower than the number of buildings damaged or destroyed. Examples of rapid landslides for which suitable information was readily available are listed below:

Summing the examples in the table, the ratio of Fatalities / damaged houses = 9/464 = 0.02. 

It is possible that these examples are not representative, and that recent examples have been unusually non-lethal. If we imagine that a disaster like the 1997 Thredbo disaster in Australia, where 18 people died when two ski lodges were destroyed by a landslide², were to happen in New Zealand tomorrow, then the ratio would become 27 / 466 = 0.06.

A3.2 From Estimates of Total Fatalities and Total Landslide costs in New Zealand

Between 1843 and 2016, there were at least 600 fatalities from landslides in New Zealand and a lower estimate of the national annual cost associated with landslides is NZ $250–$300 M/year (Rosser et al, 2017).

Fatalities per year from landslides > 600 / (2016-1843) = 3.47 fatalities per year

Cost per year = $250 – $300 million 

To estimate the number of damaged houses from the total cost, we obtained information from large disasters with published total cost estimates and damaged houses estimates. 

The 2011 Christchurch earthquakes were estimated to cost more than NZ$40 billion¹³, with one source reporting that about 7500 homes were demolished because of land damage or rockfall risk¹⁴ and another that about 10,000 buildings needed to be demolished¹⁵. Although not all damage in an earthquake (or landslide) would be due to damaged houses, it is still useful to understand the ratio of total disaster cost / number of damaged houses = $40 billion / 10,000 = $4 million. A similar process for US disasters suggests that this ratio may be too high (see below) but for our purposes here it is conservative for it to be high, so we will use it. If we assume that the Christchurch earthquake cost/damaged houses ratio is representative of typical landslide events (admittedly a big assumption), then the estimated number of damaged houses per year in NZ from landslides may be $300 million / $4 million = 75 houses per year. From only the landslides listed in Table 17, the number of damaged houses since 2005 is 464, or 24 houses per year. As it is our expectation that those landslides listed in the table form just a fraction of the total damaging landslides since 2005, a total value of 75 houses per year seems plausible.

Thus, the ratio of fatalities / damaged houses could be 3.47 / 75 = 0.046.

If instead we use a lower total disaster cost / damaged houses ratio of US$1.25 million (see below), which is NZ$2.07 million, then the ratio of fatalities / damaged houses reduces to 3.47 / 145 = 0.024.

A3.3 From Estimates of Total Fatalities and Total Landslide costs in USA

An average of 25-50 people are killed by landslides each year in the United States¹⁶. The U.S. Geological Survey estimated annual losses to be between $2 billion and $4 billion per year¹⁷ but no estimate of the total number of houses damaged by landslides each year appears to be available. As in the previous calculation, we used large disasters with published total cost and total damaged house numbers to attempt to infer the yearly count of houses damaged in landslides.

The Loma Prieta (1989) earthquake caused an estimated US$6 billion (equivalent to US$15 billion today) in property damage, with some 12,000 homes and 2,600 businesses damaged¹⁸. The ratio of total cost / houses damaged = US$1.25 million in today’s money.

Hurricane Katrina is the costliest U.S hurricane, with estimated damage over $81 billion and costs over US$160 billion (2005 US dollars). More than 800,000 housing units were destroyed or damaged in the storm¹⁹. Another source indicated that the hurricane displaced, destroyed, or severely damaged 217,000 homes along the Gulf Coast²⁰. 

Using the lower estimate of houses damaged, this is US$160 billion / 217,000 = US$737,000 per house in 2005 dollars (US$1.17 million in 2024 money), giving good agreement with the Loma Prieta estimate.

So, if landslide costs in the USA are $2 to $4 billion, and it’s $1.25 million / house, that is 1600 to 3200 homes. Hence the fatalities / damaged houses ratio is (25 to 50) / (1600 to 3200) = 0.008 to 0.031.

A3.4 From Damage State classification

Work of Massey – presented in Figure 6.5 in the draft of Unit 1 (NZGS, 2023) – provides typical photographs of various damage states for landslide-induced damage to buildings. From examination of the photographs, fatalities are unlikely in buildings with damage states under 0.6 and likely with a damage state of 1.0. From Massey’s work reproduced in Figure 9.14 of the draft of Unit 1 (18 houses have damage state 1.0, 15 above 0.6 but less than 1.0, 31 below 0.6) suggest that perhaps 30% (18 / (18 + 15 + 31)) of the landslides analysed by Massey might have caused fatalities, were people present in the houses. We imagine that Massey would have included houses which might have been categorised Major, Disastrous and Catastrophic under the system developed in this study, although he might also have included some Mediums. Data on the likelihood of people being present in houses at any given time are scarce, but Iceland suggests a temporal spatial probability of 0.75 for residential (de Vilder et al 2024, page 35). The average household size in New Zealand is 2.7 people²¹. 

Putting these together E (fatalities | damage) = 30% x 0.75 x 2.7 = 0.6, and this assumes that everyone present in each house with damage state 1.0 died, and that everyone is present 75% of the time, which are both worst-case assumptions unlikely to be true.

A3.5 All estimates

The death/damaged house ratio from each of the above methods is listed in Table 18. 

The damage state method appears to be an outlier, with agreement between the other methods being quite good, and the inference is that the ratio is about 0.05, or less. 

There is doubt about what constitutes a “damaged house” in the estimates above. It may be that some of the estimates include houses that had only moderate damage, and hence the ratios calculated are fatalities / moderately (or worse) damaged house, and that the fatalities / extensively (or worse) damaged house ratio would be higher. 

Therefore, because of this uncertainty, the paucity of research in this area, and because fatality rates appear to vary widely, we have allowed for the ratio to vary between 0.05 and 0.5 when matching “Life risk” to “Expected damage to building and property” in Table 5.

¹ Massey et al (2012)

³ https://nzhistory.govt.nz/page/christchurch-earthquake-kills-185, retrieved 31 March 2024

³ https://en.wikipedia.org/wiki/2023_Auckland_Anniversary_Weekend_floods, retrieved 31 March 2024

⁴ https://en.wikipedia.org/wiki/Cyclone_Gabrielle, retrieved 31 March 2024

⁵ https://teara.govt.nz/en/landslides/page-5, retrieved 31 March 2024

⁶ https://www.nzgs.org/libraries/nzgs20_dellow2/, retrieved 5 April 2024

⁷ Justice et al (2022).

⁸ https://www.nzherald.co.nz/nz/rain-brings-more-misery-to-nelson/X5NE2AKHIIBOOZGFGM4HRQXQQI/, retrieved 5 April 2024

⁹ https://www.theprow.org.nz/events/nelson-and-tasman-floods/, retrieved 5 April 2024

¹⁰ Page, M. J. (2013)

¹¹ https://en.wikipedia.org/wiki/1997_Thredbo_landslide, retrieved 31 March 2023. This scenario is easily imaginable somewhere in Wellington, for example.

¹³ https://www.icnz.org.nz/industry/canterbury-earthquakes/, retrieved 5 April 2024

¹⁴ https://www.stuff.co.nz/the-press/news/300411398/end-of-the-earthquake-era-the-last-redzone-house-in-christchurch-is-demolished, retrieved 31 March 2024.

¹⁵ https://my.christchurchcitylibraries.com/canterbury-earthquake-2011-for-kids/#:~:text=Up%20to%20100%2C000%20buildings%20were,four%20zones%20after%20the%20earthquake, retrieved 31 March 2024.

¹⁶ https://www.usgs.gov/faqs/how-many-deaths-result-landslides-each-year#:~:text=An%20average%20of%2025%2D50,landslides%20is%20in%20the%20thousands., retrieved 31 March 2024

¹⁷ https://www.americangeosciences.org/critical-issues/faq/how-much-do-landslides-cost-terms-monetary-losses#google_vignette, retrieved 31 March 2024

¹⁸ https://en.wikipedia.org/wiki/1989_Loma_Prieta_earthquake, retrieved 5 April 2024.

¹⁹ https://hurricanescience.org/history/studies/katrinacase/impacts/, retrieved 5 April 2024.

²⁰ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2777735/, retrieved31 March 2024.

²¹ https://www.arcgis.com/home, retrieved 31 March 2024.

Appendix 4: Comparison of Study Results with Similar Efforts and Handling of High Ground Water Scenarios 

A4.1 Compared to Adams (2015) Table 5

Adams’ values are presented as “an example FoS-PoF Selection Matrix” noting that “specific values in each have been developed by a process of interpolation and comparison against typical industry-standard recommendations.” We compared Adams’ consequence categories with those adopted for this study, considering Adams’ “Insignificant to Minor” equivalent to this study’s “Minor-Low”, Adams’ “Moderate” equivalent to this study’s “Medium”, and Adams’ “Major-Catastrophic” equivalent to this study’s “Major-Disastrous”. Adams defines three levels of design confidence – high, medium, and low with no guidance on how to choose a confidence level except that “the basis of selected confidence level should be recorded to develop consistency” – the intention being that the system could evolve, perhaps for each particular mine, and this is consistent with Adams’ description of Table 5 as just an example. 

Adams presents target FoS for permanent, interim, temporary and “excavation for immediate backfill” cases. We used the permanent cases only for comparison.

Adams’ target FoS values are typically lower than this study, perhaps reflecting the higher risk acceptance in mining. For example, a Major-Catastrophic event with low design confidence has a target factor of safety in Adams of only 1.6, whereas in this study, it would not be acceptable to proceed with a Major-Catastrophic event with low design confidence – more information and/or analyses would need to be carried out. 

In another example, for a Moderate consequence, medium confidence event in Adams’ parlance, the target FoS is 1.4. This would map to a Medium consequence, LoE III in this study, which has a target FoS (geometric mean) of 1.6 (see Table 15).

A4.2 Compared to Schnaid et al (2020) Table 23

Schnaid et al describe three engineering levels in their Table 21, with their Category 1 mapping well onto Silva et al’s LoE I, and Category 2 mapping well onto LoE II. Category 3 varies between Silva’s LoE II and IV but is assessed as LoE III on average. 

Schnaid et al describe three consequence categories, their Category A having no deaths, but significant disruption to business and livelihoods, and is assessed as equivalent to “Major” in this study’s terms. Category B has potential loss of life of 1 to 50, so is assessed as equivalent to “Catastrophic” in this study’s terms. Category C has potential loss of life of greater than 50 so is beyond the intended scope of this study.

If the LoE is I or II, the required Factor of Safety in Schnaid et al’s Table 23 is 1.5 independent of the consequence. If the LoE is III, then the required Factors of Safety are 1.5 for Category A, 1.7 for Category B and 1.8 for Category C.

For LoE III, Schnaid’s target Factors of Safety are about 0.3 – 0.5 lower than the geometric mean values from this study. By comparison, results of this study would not allow analysis for Schnaid’s Consequence B or C with LoE III, whereas Schnaid would (with target FoS of 1.7 – 1.8).

For LoE I and II, Schnaid requires a somewhat higher FoS than this study at Major consequence (1.5 versus around 1.2 or 1.4).

For LoE I, Schnaid requires a slightly lower FoS than this study at Catastrophic consequence (1.5 vs mean of 1.6).

For LoE II, Schnaid requires a much lower FoS than this study at Catastrophic consequence (1.5 vs ~2.0).

Schnaid has a highest required FoS of 1.8 for an event that this study would classify as worse than Catastrophic (potentially more than 50 deaths), with LoE III. This study would not permit design for a Catastrophic event (let alone an event worse than Catastrophic) with LoE III.

Schnaid et al’s requirements have thus have some similarities to this study while having overall a higher acceptance of risk.

A4.3 Raised Ground Water Conditions

Analysis and design of slopes should consider the possibility of the ground water rising and/or surface soils saturating and the consequent detrimental effect on the stability of the slope. A raised ground water analysis could consider one or more of the following:

(a) The typical yearly high ground water condition – that is, the ground water condition that would typically occur each year in the wettest season of the year – usually in winter in New Zealand. It would be expected that this high ground water condition would last for 1 to 3 months.

(b) The ground water condition that is expected to occur during a severe storm. This may last for just a few days and occurs perhaps once every 5 or 10 years.

(c) The worst ground water condition expected to occur during the design life of the slope (or the structure to which it pertains). This is effectively a reasonable worst case (RWC) scenario, in which the designer estimates the worst plausible ground water condition, the typical duration of the scenario, and the expected frequency of the scenario.

The target factor of safety should be less than the target for Long-term Static conditions because the raised ground water scenario occurs less often.

Groundwater Case (a)

For case (a), the raised ground water condition occurs for 1 to 3 months out of 12 months, say 2 months on average, or 16% of the time. Therefore, calculation of FoS could be based on an AEP of 1/0.16 x Long-term Static conditions, which means that it occurs 0.5 – 1 orders of magnitude less often than Long-term Static conditions. Inspection of Figure 1 of Silva et al (2008) shows that a reduction in probability of half an order of magnitude results typically in a reduction of 0 – 0.2 in target FoS. 

However, these numbers are so close to Long-term Static conditions that there may be little benefit in recommending them to practitioners. Furthermore, a seasonal variation, occurring 1 to 3 months out of every 12, is so frequent that it probably should be considered “Long-term Static conditions” and may have been considered as such by Silva et al, and hence a reduction in factor of safety for such regular rises in ground water is not warranted. Another way of looking at it is to consider the meaning of the phrase “annual probability of failure” used in Silva et al. Anything that is expected to happen every year must be included and hence a typical seasonal high water table must be considered “Long-term Static”. 

Therefore, case (a) is excluded from this study.

Groundwater Case (b) and Comparison with the HK Manual

To estimate AEP values associated with groundwater conditions that occur every 5 to 10 years, we suggest considering that ground water conditions approach, but don’t reach, the 5 to 10 year storm level perhaps two or three times per year, for a total duration of about one week per year, thus they approximate 5-10 year storm levels about 1/50^th of the time (1 week each year / 52 weeks). It follows that the acceptable probability of failure (were those conditions to occur all the time) should be 50 times higher, and using that reasoning, the following FoS table 19 is calculated:

The Hong Kong Highway Slope Manual (GEO, 2000 – herein called the HK Manual) presents minimum FoS values for slopes adjacent to highways in Hong Kong when considering a 10-year return period rainfall event (HK Manual Table 4.4). We would expect that the risk appetite regarding slopes adjacent to highways in Hong Kong would be broadly similar to highways in New Zealand. 

The HK Manual lists minimum FoS based on Consequence-to-life categories 1 to 3 and economic consequence categories A to C. There is no explicit uncertainty consideration in the table. It is, we infer, assumed that the other recommendations within the HK Manual are followed. Although the HK Manual provides commentary on the level and type of Investigation, Testing, Analyses & Documentation, Construction, and Operation & Monitoring (the aspects considered by Silva et al), often these recommendations are themselves based on the consequences. For instance, Section 8.2 of the HK Manual says, “In determining the frequency of routine maintenance inspections for highway slopes, consideration should be given to the potential consequence-to-life and the seriousness of the socio-economic consequence … in the event of a slope failure”. This is, of course, sensible, but makes a comparison with the proposed approach in this study awkward. However, what seems to be true is that the HK Manual expects at worst LoE II and sometimes LoE I. 

The recommendations in the HK Manual relate to a 10-year return period rainfall, so are most comparable with case (b) in the Raised Ground Water Conditions. We have compared the values recommended in the HK Manual with the underlined values in Table 19. 

We assessed HK Manual’s Category A and 1 as being “Catastrophic” to “Disastrous” in this study’s terms, with the HK Manual providing a minimum FoS of 1.4 in a 10-year storm. Noting that the HK Manual appears to recommend LoE I to II, but that it would probably recommend LoE I for “Catastrophic” to “Disastrous”, then the equivalent target FoS in Table 19 is 1.1 to 1.4. 

We assessed Category B as being “Major” to “Disastrous” and 2 as being “Medium” to “Major” (therefore “Major” on average) in this study’s terms, with the intercept of B and 2 in the HK Manual providing a minimum FoS of 1.2 in a 10-year storm. Noting that the HK Manual appears to recommend LoE I to II, then the equivalent target FoS in Table 19 is 1.0 – 1.2. 

We assessed Category C as being “Low” to “Medium” and 3 as being “Low” to “Major” (therefore “Medium” on average) in this study’s terms, with the intercept of C and 3 in the HK Manual providing a minimum FoS of 1.0 in a 10-year storm. Noting that the HK Manual appears to recommend LoE I to II, but that it would probably recommend LoE II for “Medium” then the equivalent target FoS in Table 19 is 1.0. 

Therefore, the numbers in Table 19 match the HK Manual reasonably well, although the lower part of our calculated range was lower than the HK Manual in some cases. 

Groundwater Case (c)

We consider that a reasonable worst case (RWC) scenario might be analogous to a 50-year return period ground water condition. Similar to the reasoning for Case (b), an RWC ground water condition will not typically be the condition that is reached for a few days in 50 years. Rather, it would be approached but not exceeded, perhaps every 5 or 10 years, for a few days on each occasion. Hence the RWC condition may occur perhaps 10 times every 50 years, on each occasion for perhaps a week. This means it occurs (10 weeks) / (50 x 52 weeks) = 0.0038 of the time (1/260), which would justify a reduction of 2.4 orders of magnitude below the AEPs adopted for the static long term load case. We have checked the FoS from Silva et al (2008) for these reduced return periods. The results indicate slight decreases in FoS from those in Table 19 (about 0.1 to 0.2) and follow the same trend. The FoS values in the blue shaded cells are around 1.0 to 1.3 for the RWC groundwater scenario. The HK Manual does not provide FoS values for the RWC groundwater table but does note that for Consequence to Life Category 1 (similar to Disastrous to Catastrophic Categories in this Study, and likely LoE I) a FoS of at least 1.1 should be achieved under predicted worst credible groundwater conditions. This is similar to the range of values we calculated. 

For the purposes of this study, we considered that it would be relatively rare for designers to know or be able to accurately estimate the 50 year return period event for routine low to medium risk projects, and that therefore there is little use in providing a table for it. For most cases, if designers can identify a design RWC, then they are likely to apply it as the 5 to 10-year storm (case b). Where a 50 year return period groundwater table can be assessed, a minimum FoS of 1.1 seems reasonable. 

Conclusion for High Ground Water Case

It was concluded that the 5 – 10 year case (case b) was the appropriate case to use for the High Ground Water analysis. 

As for the Long-term Static Conditions case, it was considered prudent to have FoS values no lower than 1.2 for Medium (and worse) consequence situations. Table 19 was thus adjusted, with the following Table 20 used for Unit 3 (and is a duplicate of Table 2 in this paper, but with colours and AEP). 

With these changes, the Unit 3 recommended values are more closely aligned with those from the HK Manual:

10. References

Adams, B.M. (2015). Slope stability acceptance criteria for opencast mine design. Proc. 12^th Australia New Zealand Conference on Geomechanics, Wellington, February 2015.

Australian Geomechanics Society (AGS) (2007). Practice Note Guidelines for Landslide Risk Management. Australian Geomechanics Vol 42 No 1 March 2007.

Baynes, F. J. and Parry, S. (2022). Guidelines for the Development and Application of Engineering Geological Models on Projects. IAEG Commission 25 Publication No. 1.

de Vilder, S. J., Kelly, S. D., Buxton, R.B., Allan, S., and Glassey, P. J. (2024). Landslide planning guidance: reducing landslide risk through land-use planning. Lower Hutt (NZ): GNS Science. 77p. (GNS Science miscellaneous series; 144). 

Crawford, S.A. & Millar, P. J. (1998). The Design of Permanent Slopes for Residual Building Development. EQC Research Foundation Project 95/183 prepared by Tonkin & Taylor Ltd. Republished in NZ Geomechanics News, June 1998.

Crawford, S.A. & Millar, P. J. (1999). The Design of Permanent Slopes for Residual Building Development. Distilled technical paper version of the EQC report 95/183, 8th Australia New Zealand Conference on Geomechanics, ISBN 1864450029

Duncan, M. (2000). Factors of Safety and Reliability in Geotechnical Engineering. Journal of Geotechnical and Geoenvironmental Engineering, 126(4), 307–316. 

Duncan M.J., Wright S.G, Brandon T.L. (2014). Soil Strength and Slope Stability 2nd Edition.  John Wiley & Sons, Inc. 

Federal Highway Administration (FHWA) (2009). Design and Construction of Mechanically Stabilized Earth Walls and Reinforced Soil Slopes – Volume I. Publication No FHWA-NHI-10-024. November 2009. 

Federal Highway Administration (FHWA) (2015). Geotechnical Engineering Circular No. 7: Soil Nail Walls – Reference Manual. Technical Report FHWA-NHI-14-007. February 2015.

Fell, R., Hungr, O., Leroueil, S, and Riemer, W. (2000). Geotechnical engineering of the stability of natural slopes, and cuts and fills in soil. 

[GEO] Geotechnical Engineering Office (1998). Landslides and boulder falls from natural terrain: interim risk guidelines. Hong Kong (CN): ERM-Hong Kong Ltd. 183p. GEO Report 75.

[GEO] Geotechnical Engineering Office (2000). Highway Slope Manual. The Government of Hong Kong. 115p.

Justice, T. R., Cole, R. G., and Singh, D. (2006). Slope Hazard Prioritisation for Wellington City. Proc NZ Geotechnical Soc Symp, Nelson, February 2006.

Justice, T. R., Gkeli, E., Scott, J. & Roberts, R. (2022). Proposed slope stability guidance modules. Geomechanics News, June 2022, p20-24.

Massey, C. I., McSaveney, M. J., Heron, D., & Lukovic, B. (2012). Canterbury Earthquakes 2010/11 Port Hills Slope Stability: Pilot study for assessing life-safety risk from rockfalls (boulder rolls). GNS Science Consultancy Report 2011/311.

Ministry of Business Innovation and Employment (MBIE) (2021). Earthquake geotechnical engineering practice – Module 6: Earthquake resistant retaining wall design. 

Ministry of Education (MoE) (2020). Designing Schools in New Zealand – Structural and Geotechnical Requirements. Version 3.0, October 2020.

New Zealand Geotechnical Society (NZGS) (2023). Slope Stability Geotechnical Guidance Series – Unit 1 – General Guidance. December 2023. Draft for Comment.

NZSOLD (2023). New Zealand Dam Safety Guidelines. New Zealand Society of Large Dams. 

New Zealand Transport Agency (NZTA) Waka Kotahi (2022). Bridge Manual SP/M/022. 3rd edition, Amendment 4 (BM3.4).

Page, M. J. (2013). Landslides and debris flows caused by the 15-17 June 2013 rain storm in the Marahau-Motueka area, and the fatal landslide at Otuwhero Inlet, GNS Science Report 2013/44. 35p.

Read, J. and Stacey, P. (editors) (2009). Guidelines for open pit slope design. CSIRO publishing, Collingwood, Australia.

Rosser, B., Dellow, S., Haubrock, S. and Glassey, P. (2017). New Zealand’s National Landslide Database. Landslides (2017) 14:1949-1959.

Saunders, W., and Glassey, P. (Compilers) (2007). Guidelines for assessing planning, policy and consent requirements for landslide-prone land, GNS Science Miscellaneous Series 7. 

Saunders, W. S. A., Beban, J. G., and Kilvington, M. (2013). Risk-based approach to land use planning, GNS Science Miscellaneous Series 67. 97p.

Schnaid, F., de Mello, L. G. F. S., and Dzialoszynski, B. S. (2020). Guidelines and recommendations on minimum factors of safety for slope stability of tailings dams. Soils and Rocks 43 (3): 369-395.

Silva, F., Lambe, T. W., and Marr, W. A. (2008). Probability and risk of slope failure. Journal of Geotechnical and Geoenvironmental Engineering. December 2008, 1691-1699.

Sim, K. B., Lee, M. L., & Wong, S. Y. (2022). A review of landslide acceptable risk and tolerable risk. Geoenvironmental Disasters. 9(1):3. doi:10.1186/s40677-022-00205-6

Standards NZ (2002). Structural Design Actions Part 0: General Principles, AS/NZS 1170.0:2002.

Standards NZ (2024). Structural Design Actions Part 5: Earthquake Actions – New Zealand, DZ TS 1170.5:2024 Public Consultation Draft.

U.S. Army Corps of Engineers (2003). Slope stability: Engineering and design (Engineer Manual No. EM 1110-2-1902)