Comprehensive risk management of reservoir landslide-tsunami hazard chains: a case study of the Liangshuijing landslide in the Three Gorges Reservoir area

Abstract

Landslide-induced tsunamis in reservoirs often pose greater risks than landslides themselves. Existing studies and mitigation practices have prioritized increasing landslide stability to meet safety standards, incurring high costs and lacking sustainability. More than 5000 landslides have developed along the Three Gorges Reservoir banks in China, and some may trigger tsunamis. To effectively and sustainably manage risk of landslide-tsunami hazard chains (LTHC), we propose a new framework (based on quantitative risk analysis) involves decision-making based on risk characteristics and local economies, a strategy for selecting optimal risk control plan through cost–benefit analyses that consider long-term effectiveness and adverse effects, and dynamic management through iterative risk reassessment-recontrol cycles. The Liangshuijing landslide accelerated in 2009, posing a tsunami threat to the Yangtze River and coastal residents. Post-mitigation, the risks under four mitigation plans and combined scenarios were quantitatively evaluated. The mass removal plan reduces total risk by approximately 68%, less than the 80% reduction from the anti-slip pile plan, but with a 30-fold greater benefit–cost ratio (BCR). The surface drainage and monitoring network plans show limited long-term cost-effectiveness due to short measure lifetimes, however, their short-term BCRs exceed those of the mass removal plan due to lower direct costs. According to comprehensive long and short-term analyses, combined plans involving mass removal are the most cost-effective. Our results reveal how to select appropriate strategies for managing LTHC risk, how landslide mitigation controls tsunami risks, and how time-related parameters affect solution effectiveness. Our findings show that partially mitigating risks may provide more cost-effective and sustainable management of LTHCs than eliminating risks to negligible levels.

Introduction

Landslides are among the most common geohazards worldwide, and unstable reservoir landslides are especially dangerous due to the potential to trigger tsunamis (Sassa et al. 2016; Du et al. 2020; Karahan et al. 2020). Notable historical incidents, such as the Vajont landslide (Guzzetti 2000), Jipazi landslide (Wen et al. 2004), and Baige landslide (Fan et al. 2020), demonstrate the catastrophic consequences of landslide-tsunami hazard chains (LTHCs). Preventing similar events requires significant investments to enhance slope stability and meet safety standards. In the Three Gorges Reservoir area (TGRA), more than 5000 landslides were recorded along the riverbanks by 2018 (Li et al. 2019), prompting China to invest more than 12 billion RMB in geohazard prevention between 2001 and 2009; however, the local needs exceed hundreds of billions. For instance, the mitigation efforts for the 1999 Houzishi landslide (volume: 5 × 10⁶ m³, average thickness: ~ 37m) spanned almost a decade. The project, which involved the excavation of tunnels and shafts and the replacement of sliding soil with reinforced concrete to form anti-slip structures and enhance slope stability, cost more than 150 million RMB (Zheng et al. 2016). The mitigation of the Shijiapo landslide (10 × 10⁶ m³) required investments in anti-slip piles, lattice-anchored structures, retaining walls and drainage systems, amounting to 46 million RMB, which were reduced due to budget constraints (Zhang and Wang 2016). The sustainable management of LTHCs depends on cost-effective and long-term mitigation strategies (Glade and Nadim 2014; Hostettler et al. 2019; Sassa et al. 2022; Casagli et al. 2023).

Losses due to LTHCs in the TGRA mainly result from landslide-induced tsunamis, as observed in events, such as the Qianjiangping landslide (Yin et al. 2015), Hongyanzi landslide(Xiao et al. 2018), and Gongjiafang landslide (Huang et al. 2012). Landslide-induced tsunamis may have broader impacts and more severe consequences than landslides themselves. Therefore, prevention and mitigation strategies for reservoir landslides should place greater emphasis and proactive consideration on reducing the threat posed by landslide-induced tsunamis. The current slow-moving landslides in reservoir areas offer a unique opportunity for mitigation. However, during the decision-making stage, secondary tsunamis, which are less visible than primary landslides, may be overlooked by decision-makers due to their potential occurrence.

Risk studies enable a comprehensive understanding of LTHCs and provide cost-effective solutions, addressing uncertainties in the evolution of hazards (Morgenstern 1997; Løvholt et al. 2020) and the prediction of potential losses for elements at risk (Dai et al. 2002; Vranken et al. 2015; Chen et al. 2023). Possible hazard consequences, often overlooked in stability enhancement strategies, provide important insights for decision-makers who are usually unconcerned about hazards in uninhabited mountain areas (Lacasse et al. 2012; Liang et al. 2022; Yang et al. 2022). Globally recognized frameworks for the risk management of landslides, tsunamis, and multiple hazards have been developed (Crozier and Glade 2005; Fell et al. 2008; Macciotta and Lefsrud 2018). Risk control strategies have been proven effective in mitigating geohazards. For instance, the implementation of the Slope Safety System has reduced landslide casualties in Hong Kong by more than 75% (Ho and Ko 2009; Cheung 2021).

However, few studies have explored specific workflows for managing large-scale or individual hazards/hazard chains based on risk analysis results (Bründl et al. 2009; Segoni et al. 2018). In general, risk decisions include risk acceptance, risk avoidance, risk reduction, and risk transfer (Popescu and Sasahara 2009; Martínez et al. 2020). Common risk zoning studies can guide local land use planning (Huang et al. 2020; Liu et al. 2021; Zhou et al. 2022; Miao et al. 2023; Xiao et al. 2023), which falls under the category of preemptive risk avoidance. However, the process for implementing risk-reduction-oriented mitigation is not yet clear or specific. Currently, risk reduction is the most dominant decision in the TGRA, given the presence of built elements (i.e., structures on slopes) within possible hazard-affected areas (Guo et al. 2020; Zeng et al. 2023) or the presence of fixed and unalterable elements (i.e., navigation channels and passing vessels) (Huang et al. 2019; Du et al. 2020). Appropriate strategies are crucial for effective risk control.

Existing studies on reservoir hazard chains have often prioritized "immediate" hazards and neglected "potential" hazards. Mitigation measures for both landslides and tsunamis have been well developed (Tang et al. 2019; Sultana and Tan 2021; Wang et al. 2021), and the economic reasonability of a mitigation plan is usually evaluated through a cost–benefit analysis (CBA) (Galve et al. 2016; Mechler 2016). In geotechnical engineering, hazard mitigations are designed based on technology-driven security, while in environmental and administrative contexts, utility-based criteria are often followed (Strouth and McDougall 2022). Insufficient understanding of the importance of landslide-induced tsunamis and unclear risk distributions of LTHCs may result in over mitigation or inadequate risk control, leading to a notable imbalance between benefits and costs.

Some studies have considered the time-effectiveness (i.e., lifetime of measure) of mitigation measures (Kong 2002; Bischiniotis et al. 2020), indicating the persistent nature of risk and the long-term commitment to mitigation efforts (Lan et al. 2022; Di Napoli et al. 2023). In practice, due to the uncertainties in the entire lifecycle of mitigation measures, including varying construction durations, significant lifetime differences, and possible ongoing impacts beyond lifetime, the resulting risk is not a static value, but a dynamic function that evolves over time.

The Liangshuijing landslide in the TGRA, which is considered a relatively successful case in risk management, is investigated in this paper. It has a submerged toe in the Yangtze River (with a main channel width of approximately 600 m). The landslide underwent two accelerations in November 2008 and April 2009. This event caused great concern to authorities due to the potential risk of landslide-induced tsunamis which threatened residential areas, navigation, and passengers both upstream and downstream of the Yangtze River, with significant economic and social consequences. Conventional mitigation practices typically involve implementing measures to increase the factor of safety (F_s) margin to meet the local standard of 1.15, aiming to rigorously control the probability of landslide occurrence, thereby reducing associated risks to a negligible level. However, the high cost of the initially proposed solution, which involved multirow anti-slip piles and drainage projects due to the sliding body thickness exceeding 40 m, caused hesitancy among decision-makers. The author Professor Kunlong Yin suggested a risk management strategy emphasizing cost-effective control through landslide mass removal. This approach aims to reduce the probability of landslide failure potential and the intensity of landslide-induced tsunamis (expressed in terms of wave height), thereby partially mitigating the risk of the hazard chain (Yin et al. 2016). Local authorities have finally implemented this strategy on an experimental basis, resulting in nearly tenfold savings compared to the initial budget (Li et al. 2021a). Recent monitoring data presented an immediate and sustained deceleration in landslide velocity, indicating successful mitigation. We aim to distill these experiences into a practical, step-by-step guide as an alternative cost-effective solution, to enhance the confidence of decision-makers when addressing reservoir LTHCs via a risk management approach.

In this paper, we propose a workflow for LTHC risk control, involving four steps: risk decision, risk control strategy, optimal plan selection, and monitoring and reciprocal feedback. This workflow integrates with the risk analysis workflow described in our prior study (Li et al. 2021a), thereby establishing a comprehensive risk management framework for LTHC. In the case study of the Liangshuijing LTHC, four mitigation plans, including anti-slip piles, mass removal, surface drainage, and monitoring network plans, were proposed based on the risk characteristics. To identify the most cost-effective plan, we suggest a principle based on CBA, with a focus on the economic risks of LTHCs and the monetary costs of mitigation measures. Additionally, we introduce time-related parameters to capture evolving risk trends over measure lifetimes, ensuring that the selected plans possess long-term effectiveness. The results suggest that the combined plans involving the mass removal measure are the most cost-effective in comprehensive long and short-term analyses. The benefit–cost ratio of the mass removal plan that partially reduced the risk, was 30 times greater than that of the anti-slip pile plan which was designed to reduce risk to a negligible level. Additionally, both the drainage and monitoring plan had higher short-term benefit–cost ratios than did the other two plans. Our findings provide new insights for the mitigation and management of LTHCs and sustainable development in riverbank areas.

Risk management of a landslide-tsunami hazard chain

The comprehensive risk management framework for LTHCs (Fig. 1) is proposed based on the foundational structure of landslide risk management frameworks from Crozier and Glade (2005) and Fell et al. (2008) and our studies and practical experience concerning LTHCs for more than two decades. This section sequentially describes each step of the risk management process.

Fig. 1

Flowchart for risk management of a landslide-tsunami hazard chain, emphasizing the risk control component

Risk analysis

Based on the classical frameworks of Varnes (1984) and Fell et al. (2008) and the improved equation given in Eq. (1) from Yin et al. (2016), we have proposed a quantitative risk analysis framework for an LTHC (Li et al. 2021a). As shown in Eq. (2), hazard (H) is characterized by the occurrence probability of a hazard. Given the assumption that rapid landslide movement into a body of water invariably leads to tsunami generation, the occurrence probability or hazard of secondary tsunamis (H_lt) is considered numerically equivalent to the occurrence probability or hazard of primary landslides (H_l). The elements at risk (typically, piers and vessels in reservoir areas) are identified and classified (E_l, E_lt) based on their characteristics and relative positions to hazard sources. The vulnerability (V_l, V_lt) analysis incorporates the assessment of damage severity to these elements at risk, considering both the intensity of the hazards impacting on the elements (e.g., tsunami wave height) and the resilience of the exposed elements themselves. The specific calculation methodology can be found in a prior study (Li et al. 2021a) and is not further elaborated here.

$$R = H \cdot V \cdot E + R_{\sec }$$

(1)

$$R_{t} = R_{l} + R_{lt} = H_{l} \cdot V_{l} \cdot E_{l} + H_{lt} \cdot V_{lt} \cdot E_{lt}$$

(2)

where R refers to risk; H refers to the hazard of a landslide; V and E refer to vulnerability and the quantity or value of elements at risk, respectively; R_sec refers to the risk of secondary hazard; and R_t, R_l, and R_lt refer to total risk, landslide risk, and landslide-induced tsunami risk, respectively.

Here, we recommend using economic risk rather than population risk as the risk quantification indicator. As human life should not be simply measured in monetary terms, when using population risk as the assessment indicator, it is challenging to determine whether the measures used to mitigate the loss of life resulting from hazard chains are cost-effective.

Risk evaluation

Risk evaluation involves a comparison of the risk values estimated in the previous risk analysis step with risk criteria or local economic considerations to conduct value judgments or even assessments of the acceptability/tolerability of risk if available. It serves as the foundation for subsequent risk decision-making. The existing risk criteria generally address individual or societal risk acceptance for a population (i.e., F-N curve and ALARP methods) to examine the need for risk mitigation options (Düzgün and Lacasse 2005; Sim et al. 2022). Some tolerance criteria have been developed based on hazard probability (Hungr et al. 2016). F-N charts are constructed considering hazard-induced losses rather than fatality numbers (Isaza-Restrepo et al. 2016). Few existing studies have provided available economic risk criteria for reference landslide or tsunami hazards. This may be due to the significant differences in economic levels among different regions, as well as in hazard awareness levels among local governments and residents (Koler 2005).

Effective criteria making is complex in practice and requires wide agreement among geo-scientists, government decision-makers, and the community (Maes et al. 2019). Moreover, geohazard risk management often falls short of the stated goal of “reducing risk to a tolerable level” due to challenges, such as physical constraints, resource scarcity, competing objectives, and competing hazard types. Therefore, a more pragmatic goal is needed, such as “minimizing risk with available resources” (Strouth and McDougall 2021). The quantification of economic risk provides a more intuitive understanding of the level of hazards (generally measured in monetary terms). This facilitates the evaluation of different risk mitigation measures (Dai et al. 2002). The costs of mitigation measures are expressed in terms of economic investments, while the benefits of implementing these measures are expressed in terms of the difference in economic risk levels before and after their implementation. The congruity in measurement between the costs and benefits allows for the feasibility of conducting CBAs regarding mitigation measures. As a result, these results can in turn assist in making risk decisions and selecting optimal risk control strategies. In addition, no specific economic risk tolerance thresholds are set in this study, ensuring that all strategies explored in this study are applicable to the case; thus, a comprehensive discussion of the characteristics of various measures and their comparisons can be conducted.

Risk decision and risk control strategy

LTHC risk decisions generally involve risk acceptance, avoidance, hazard occurrence probability reduction, consequence reduction, risk transfer, and decision postponement (Fell et al. 2008; Leventhal and Withycombe 2009; Australian Geomechanics Society 2020; Rafliana et al. 2022; Matti et al. 2023), elaborated in the following subsections.

Risk acceptance

This decision requires that the total risk of hazard chain is acceptable or tolerable (low economic losses and no casualties) (Porter et al. 2017). This does not imply doing nothing; however, contingency plans should be developed, and local capacity to respond to hazards should be built.

Risk avoidance

This decision requires proactive measures before geohazard occurrence, generally involving land-use planning based on geohazard investigations and risk identification, to ensure that human settlements and vital infrastructures are situated outside high-risk areas (Dominey-Howes and Goff 2013).

Reduction in the occurrence probability of landslides and catastrophic tsunamis

If the LTHC occurrence probability is significant (e.g., > 50%, highly unstable according to Melchiorre and Frattini 2012), decision-making should include reducing the probability of landslide failure and potential tsunamis. Risk control strategies include structural and nonstructural measures (Zhang et al. 2021). Mitigation efforts on slopes may change the failure mechanisms, thereby reducing mass volume and velocity to lower the occurrence probability of catastrophic tsunamis.

Structural measures

• 1. Slope retaining structures, such as retaining walls, piles, and caissons for soil slopes, while retention nets, rock trap ditches, and fences for rock slopes (Choi and Cheung 2013). These measures can improve landslide stability by enhancing slip resistance and limiting mass movement to reduce the probability of landslide and tsunami occurrence. Slopes with challenging geometric modifications and small-medium volumes are suitable.

• 2. Slope reinforcement structures, such as soil nails, geocell confinement systems, and stone or lime/cement columns, for soil slopes, as well as rock bolts, anchors, and shotcrete for rock slopes (Kumar et al. 2021). These measures can enhance slip resistance and address slope stress and erosion. The applicable conditions are the same as those described above.

• 3. Drainage systems, such as surface collecting ditches and pipes, that divert water flow away from slopes; horizontal/sub-horizontal and vertical/subvertical boreholes with pumping or self-draining; and drainage tunnels or galleries (Sun et al. 2010; Yan et al. 2019). Riverbank slopes are generally hydraulically connected to rivers; thus, effective drainage is a crucial mitigation measure. This involves discharging groundwater, controlling infiltration, and reducing pore water pressure to enhance slope slip resistance.

Nonstructural measures

• 1. Slope geometry modifications, such as mass removal from the head, mass addition at the toe, and slope angle reduction (Siddique et al. 2020), offer a cost-effective way to improve slope stability, especially for deep-seated landslides. However, careful consideration of site-specific conditions, such as fixed vulnerable exposures or limited construction space, is needed. These measures reduce mass volume and velocity to mitigate tsunami probability.

• 2. Internal slope improvement, such as grouting, heat treatment, or chemical treatment (Wang and Huang 2022). These measures can enhance slope slip resistance, but challenges in construction control and effect testing have made them less widely adopted.

• 3. Bioengineering techniques, such as vegetation stabilization (Galve et al. 2015). These measures increase soil shear strength through root-binding, benefiting shallow landslides. Plant absorption and canopy interception of rainfall may help reduce peak pore water pressure, benefiting both shallow and thick landslides. However, vegetation roots may adversely impact landslides by penetrating ground cracks and jointed rock.

Reduction in hazard intensity

If landslides/tsunamis have considerable volumes/wave heights and velocities, which may cause catastrophic consequences, decision-making should include reducing hazard intensity. For landslides, structural and nonstructural measures help mitigate hazard intensity by changing failure mechanism or preventing part of the sliding materials to reduce sliding volume and velocity. For hazard chains, decreased landslide energy reduces energy transfer to water body, thus lowering the wave heights and speeds to weaken the tsunami intensity. For tsunamis, hazard intensity can be mitigated by the following measures:

• 1. Wave slowing and decay measures, such as forest barriers and floating structures (i.e., floating tanks and boards) (Thuy et al. 2018). These measures limit wave propagation by enhancing dissipation to reduce the amount of wave energy reaching elements at risk.

• 2. Wave bearing structures near important exposures (i.e., ferry terminals and coastal towns), such as breakwaters and seawalls (Oetjen et al. 2022). These structures withstand waves, preventing run-ups and reducing tsunami intensity. They also mitigate wave erosion and scouring on the shore, similar to protective structures, such as T-shaped dams, gabions, and stone walls.

Consequence reduction

If numerous high-value elements are at risk, then consequence reduction decisions should be prioritized. Corresponding measures to enhance the resilience of the elements at risk are described as follows:

• 1. Monitoring and timely warning. In LTHCs, landslide development may span a significant period, while the propagation of induced tsunamis can take only minutes. Therefore, monitoring landslide deformation is more cost-effective than preemptively monitoring tsunamis. Instruments on slopes and critical elements at potential risk enable timely warning signals for alerts or relocation (Pecoraro et al. 2019).

• 2. Relocation of the elements at risk. For movable elements at risk (e.g., people, vehicles, vessels), measures, such as evacuation, sheltering, and relocation, can be implemented in emergencies (Rafliana et al. 2022).

• 3. Administrative restrictions. In emergencies, authorities can issue alerts and navigation prohibitions to restrict vessel and human entry into hazardous areas, thereby minimizing LHTC consequences (Zhou et al. 2016).

• 4. Public awareness and education. Educating residents on risks, evacuation procedures, and safety measures enhances preparedness and responsiveness during hazard events, proactively controlling consequences (Dominey-Howes and Goff 2013).

Risk transfer

This decision involves the transfer or dispersion of LTHC risks from affected parties to capable entities, aiming to ease the burden on local governments. Noteworthy measures include insurance, reinsurance, catastrophe bonds, government assistance, and social donations (Sarmiento and Torres-Muñoz 2020).

Decision postponement

When the LTHC risk is not imminent (no signs of accelerated deformation) and the available data are insufficient for a thorough analysis, it is advisable to postpone risk decision-making and further investigation and monitoring are required.

In summary, comprehensive LTHC risk management can prioritize landslide mitigation, as it is generally more feasible than tsunami mitigation. The chain can be weakened by improving landslide-prone conditions (e.g., slope geometry modification) and controlling triggering factors (e.g., drainage). Intervening and blocking chain nodes help prevent hazard spread and risk amplification. Additionally, developing future scenarios to assess LTHC evolution is necessary to guide the sustainable risk management under environmental changes (Nadim and Lacasse 2008).

In this study, to ensure the compliance of mitigation with local requirements and the reasonableness of post-mitigation risk reassessment, the design of mitigation plans adheres to relevant standards, such as the Code for the Design of Landslide Stabilization [GB/T 38509–2020], and the Design Code for Hydraulic Concrete Structures [SL191-2008]. Both standards are specifically applicable to landslide stabilization in the TGRA. The former mainly includes aspects such as the landslide design factor of safety, anti-slip pile engineering, drainage engineering, other stabilization engineering, and engineering monitoring. The latter primarily addresses the design, calculation, and regulations governing reinforced concrete structural components.

Risk reanalysis and optimal plan selection based on CBA

When dealing with indecision among multiple risk decisions and mitigation strategies, a comparative analysis and prioritization of alternative mitigation plans can be performed using CBA.

Benefit assessment of implementing a risk control plan

The benefit of a risk control plan is the reduction in the total risk of LTHC after mitigation (i.e., residual risk, R_r) compared to that before mitigation. It can be quantified in monetary terms when only economic risk is considered. To assess R_r, scenario-specific risk reanalysis is necessary. Hazard (H) updates are crucial if the measure alters the failure mechanism and failure probability (P_f) of landslides. After mitigation, landslides may retain a low probability of failure (P_f_m) due to the spatial variabilities in sliding material properties. Effective mitigation measure may shift the limit failure mechanism to a local slip, creating a new slip surface:

$${H}_{l\_f}={P}_{f\_m}$$

(3)

$$H_{l\_s} = (1 - P_{f\_m} ) \cdot P_{fs}$$

(4)

where H_{l_f} and H_{l_s} denote the hazards of a landslide with failed and successful mitigation, respectively; P_{f_m} refers to the landslide failure probability after mitigation; P_fs refers to the landslide failure probability after successful mitigation with a new failure mechanism. In risk reanalysis, H_lt is still assumed to be equal to H_l. V × E also needs to be reassessed.

The total risk of the LTHC post-mitigation is the sum of the failure and success scenarios:

$$R_{r0} = H_{l\_f} \times \sum {(V_{fi} \times E_{fi} } ) + H_{l\_s} \times \sum {(V_{si} \times E_{si} )}$$

(5)

where R_r0 refers to the residual risk just after the completion of mitigation implementation; V_fi, E_fi, V_si, and E_si denote the vulnerability and economic value of an element at risk of LTHC with failed and successful mitigation, respectively.

Mitigation measures show time-dependent effectiveness. Measures with long construction periods are inadequate for imminent crises (i.e., impending landslides), and may endanger construction workers. The construction period (T_c), indicating the time from measure initiation to completion and full effectiveness (reducing the risk to R_r0), is introduced in the benefit assessment.

Some studies have highlighted the diminished efficacy of these measures without proper maintenance (Holcombe et al. 2012), suggesting a consideration of maintenance costs. However, we believe that introducing the attenuation of measure effects as an alternative to this cost is more practical and feasible, due to the challenges in patrolling and restoring measures in mountainous areas. The measure lifetime comprises full and diminishing effectiveness phases, with the decay rate denoted by i (%/year). Given the significant deterioration of materials and structures near their limit states, the decay process is modeled as exponential decay. Additionally, measures that are difficult to demolish or do not entirely fail post-lifetime may retain some mitigative effects, necessitating consideration in estimating post-lifetime residual risk (R_r1). In summary, R_r can be estimated by the following equation:

$$R_{r} (t) = \left\{ \begin{gathered} R_{t} -t/T_{c} \cdot (R_{t} - R_{r0} ) \, ,t \le T_{c} \hfill \\ R_{r0} \, ,T_{c} < t \le (T_{c} + T_{le} ) \hfill \\ R_{r0} \cdot (1 + i)^{t} \, ,(T_{c} + T_{le} ) < t \le (T_{c} + T_{l} ) \hfill \\ R_{r1} \, ,t \ge (T_{c} + T_{l} ) \hfill \\ \end{gathered} \right.$$

(6)

where R_r0 refers to the residual risk just after the completion of mitigation implementation; R_r1 denotes the LTHC residual risk beyond the measure lifetime; R_t denotes the total risk of the LTHC; t denotes the time since mitigation execution; T_l denotes the lifetime of the measure; T_c denotes the time of the construction period; T_le denotes the time when mitigation measures take full effect; and i denotes the attenuation rate of the mitigation effect.

Cost assessment of a risk control plan

Plan costs include direct and indirect considerations. Direct costs involve resource expenses (e.g., labor, materials, equipment) used in engineering (e.g., project budget) and non-engineering measures (e.g., personnel transfer and public education). While indirect costs reflect productivity losses during mitigation, including specific losses, such as cargo delays and productivity losses (Galve et al. 2016). Indirect losses, often lagged or hidden, however may exceed direct losses. It is recommended that environmental losses be included in the indirect costs of LTHC comprehensive risk management. Therefore, the temporal evolution of indirect costs can be quantified by the ecological recovery period (T_e). The total cost of a plan (C) is

$$C={C}_{d}+{C}_{i}={C}_{d}+\left({C}_{p}+{C}_{e}\right)$$

(7)

where C_d and C_i denote direct and indirect costs, respectively; C_p denotes productivity loss; and C_e denotes ecological environment loss.

Ecological mitigation plans generally involve engineering measures (e.g., shotcrete and grouting). Surface-level measures (e.g., mass removal, drainage, GNSS station) allow gradual ecological recovery post-construction or post-lifetime. Eco-friendly measures (e.g., vegetation planting) contribute to restoration, offsetting environmental losses. In contrast, large-scale structures (e.g., piles and seawalls) have lasting impacts, resulting in residual ecological losses post-lifetime (C_er). The actual ecological restoration process is complicated and influenced by numerous factors; however, for simplicity, the process is modeled as a linear gradient to gain insights into the trend of indirect costs over time:

$$C_{e} (t) = \left\{ \begin{gathered} C_{ei} ,{ 0} \le t{ < (}T_{c} + T_{l} ) \hfill \\ C_{ei} - (C_{ei} - C_{er} )/T_{e} \cdot (t - T_{c} - T_{l} ),{ (}T_{c} + T_{l} ) \le t < (T_{c} + T_{l} + T_{e} ) \hfill \\ C_{er} \, ,t \ge (T_{c} + T_{l} + T_{e} ) \hfill \\ \end{gathered} \right.$$

(8)

where C_ei and C_er denote the initial and residual losses, respectively, of the ecological environment; t denotes the time since mitigation execution; T_l denotes the lifetime of the measure; T_c denotes the time of the construction period; and T_e denotes the duration of the ecological recovery period.

Optimal mitigation selection strategy

The benefit–cost ratio (BCR), an indicator used to evaluate the economic feasibility of a plan, is calculated as the ratio of total benefits to total costs. Other parameters, such as measure lifetime, are often considered in existing studies (Table 1). The BCR formula is:

$$\begin{gathered} BCR = B/C \hfill \\ \, = \sum {[R_{t} - R_{r} (t)]} /\sum {[C_{d} + C_{p} (t) + C_{e} (t)]} \hfill \\ \end{gathered}$$

(9)

where B and C denote the benefit and cost of a mitigation plan, respectively; R_t denotes the total risk of the LTHC; R_r(t) denotes the residual risk of the LTHC over time; C_d, C_p, and C_e denote direct costs, productivity loss, and ecological environment loss, respectively, in the implementation of a mitigation plan.

Table 1 Formulas for CBA of hazard mitigation measures in existing literature

When comparing plans, the one with the highest BCR is optimal. A plan is considered reasonable if the reduction in risk exceeds the cost; otherwise, adjustments or supplementary explanations are required for insufficient benefits compared to the investments.

PLL denotes the probability of loss of life; Δ denotes the reduction in related parameters; R denotes the risk of a specific geohazard; R_r denotes the residual risk after mitigation; r denotes the currency discount rate; I denotes the measure investment; P denotes the occurrence probability of a geohazard of a certain intensity during a specific period.

Monitoring and reciprocal feedback

Continuous monitoring after mitigation is necessary due to the uncertainties in hazard chain evolution and exposure vulnerabilities. Real-time monitoring, manual inspection, and remote sensing are important for identifying significant changes of landslides, facilitating timely risk reassessment and decision adjustment. The reciprocal influence between mitigation and risk is noteworthy. Dynamic risk management for LTHCs ensures long-term, effective, and sustainable mitigation.

Case study: the Liangshuijing landslide

General description and displacement history

The Liangshuijing landslide, located in Guling town, Yunyang County, TGRA (Fig. 2), on the right bank of the Yangtze River, has an elevation ranging from 100 to 320 m above sea level (asl), with an average slope angle of 26° (Fig. 3a). It is composed of Quaternary silty clay with breccia and rock debris and sits atop interbedded sedimentary sandstones and mudstones of the Jurassic Shaximiao Formation. Geological drilling yields a maximum sliding body thickness of approximately 44 m and an average of 22 m (Fig. 3b). The landslide body has a volume of 2.63 × 10⁶ m³, with 38% submerged when the reservoir reaches its peak at 175 m asl. The study area is subject to a sub-tropical monsoon climate.

Fig. 2

a Map showing the location of the study area. b 3D satellite model showing the location of the Liangshuijing landslide and possible elements at risk (piers A and B, boat groups A and B) along the Yangtze River. c Oblique photograph showing the Liangshuijing landslide post-mitigation from the Yangtze River

Fig. 3

a Topographic map of the Liangshuijing landslide with locations of displacement measurements (G01-G24) and the designed mitigation layout. b Geological cross-section of the Liangshuijing landslide; global/simulated local slip surface after implementing Plan A in cross-Sect. 1–1′. c Landslide mass removal area and the global failure mechanism after implementing Plan B; simulated local failure after implementing combined Plan A + B in cross-Sect. 1–1′

The available surface displacement data (measured at 24 GPS reflector stations G01-G24, as shown in Figs. 3a and 4) indicate that between April 5, 2009, and May 12, 2014, the landslide exhibited an average velocity of approximately 0.7 mm/day, peaking at 75.2 mm/day on June 3, 2009, with a maximum cumulative displacement exceeding 1700 mm (Fig. 4). The correlation analysis between displacement and reservoir level (Li et al. 2021b) along with the simulations of landslide stability in response to reservoir level fluctuations (Li et al. 2021a) suggests that as the reservoir water level decreases, the landslide stability decreases, leading to an increased probability of a landslide-tsunami event.

Fig. 4

Cumulative displacement of 24 GPS reflector stations from April 2009 to May 2014, from February 2015 to June 2016 (post-mitigation, 13 stations left), and from July 2019 to August 2021 (9 stations left). Displacements are illustrated on the left axis with reservoir level and rainfall shown on the right axis

Risk analysis of the Liangshuijing LTHC

Our previous study (Li et al. 2021a) revealed that the landslide-induced tsunamis pose greater and more widespread risks than the Liangshuijing landslide itself. During the annual water level decrease from 159 to 145 m asl (≈ 0.6 m/day), the F_s is at a minimum of 0.981, with a P_f of 58.8%. The potential peak run-up is 17.0 m. The maximum propagating wave reaches approximately 18.7 m downstream and 12.3 m upstream, impacting piers A and B, boat groups A and B, and moving vessels within 5 km of the landslide (Fig. 2b). The elements at risk on the landslide body include a 500 m country road at 200 m asl and a woodland area of approximately 7.5 × 10⁴ m² (Fig. 3a). The direct and indirect consequences resulting from the landslide and potential tsunamis are 2.35 and 32.74 million RMB, respectively. This results in the direct economic risk (R_l) from the landslide being only one-tenth of the indirect risk (R_lt) resulting from potential landslide-induced tsunamis.

Model and parameters

To ensure continuity with the previous study (risk analysis results before mitigation, Li et al. 2021a), the model was constructed in a consistent manner. A two-dimensional geological model is established based on cross-Sect. 1–1′ in GeoStudio software and comprises 2693 elements and 2862 nodes (Fig. 3b–c). The P_f of the landslide is determined using the Morgenstern-Price limit equilibrium method within the Monte-Carlo framework. The cohesion of the sliding belt follows a log-normal distribution, while the friction angle follows a normal distribution (Table 2). The initial water tables were determined from the borehole groundwater data. A three-dimensional model, covering a 5 km radius upstream and downstream of the landslide, is established in Tsunami Squares software to simulate landslide motion, as well as the propagation and run-up of landslide-induced tsunamis. It comprises 1063 × 472 topographic grids with a 10-m resolution. The dynamic friction coefficients for landslide movement in air and water were set at 0.01 and 0.25, respectively, based on inverse analysis of similar landslide-tsunami events (Xiao et al. 2018; Wang et al. 2019). The basal friction coefficient is 0.2cos(θ), the time step is 0.1 s, and the drag-along coefficient is 0.11.

Table 2 Physical and mechanical properties of the Liangshuijing landslide

The simulation and analysis in this study only focused on the most adverse scenario, characterized by the reservoir water rapid drawdown phase (from 159 to 145 m, 0.6 m/day), coupled with extreme precipitation. Using 55 years of daily rainfall data (1960–2014) from Yunyang County from the Chongqing Geological and Environmental Monitoring Station, statistical analysis was conducted for single maximum rainfall events during the accelerated descent phase of the reservoir water level from 159 to 145 m asl. A Pearson type III distribution was used to fit the observed rainfall and obtain a frequency curve (Fig. 5). 5 consecutive days of rainfall is the highest frequency event, accounting for 18% of the total events. The extreme accumulation for a single rainfall event with a 100-year return period is 217.05 mm. Therefore, the rainfall scenario is set at an intensity of 43.41 mm/day for 5 consecutive days.

Fig. 5

Rainfall statistics of Yunyang County: a Cumulative rainfall and corresponding consecutive rainy days of annual maximum rainfall events from 1960 to 2015; b Rainfall frequency analysis using the Pearson type III distribution

Results

Risk decision based on risk analysis results

Based on our previous risk analysis (Li et al. 2021a), considering additional extreme rainfall conditions, the F_s and P_f of the Liangshuijing landslide before mitigation are 0.975 and 63.7%, respectively. According to Eq. (2), the total risk (R_t) is 22.35 million RMB. Potential landslide deposits on riverbeds will not block the river (deposit thickness < 10% of the river depth).

Ongoing visible landslide deformation and temporarily invisible tsunami threats to the main busy channel require prompt mitigation. Since P_f exceeds 50% and risk concentrated along the river, risk decisions involving reducing occurrence probability, hazard intensity, and consequences are selected. Risk transfer can be implemented by promoting relevant life and property insurance for ships, crews, and riverside residents. In emergency situations, risk avoidance can be executed by temporarily closing navigation.

Risk reanalysis based on the implementation of an independent mitigation plan

The decision to reduce risks is examined in detail in this paper, focusing solely on landslide mitigation due to challenges in implementing wave dissipation and protection measures in the busy Yangtze River Channel. Four common mitigation measures investigated were: (1) Plan A—anti-slip pile project involving a structural measure enhancing slip resistance and changing the failure mechanism; (2) Plan B—mass removal project involving a nonstructural measure reducing slip force and changing the failure mechanism (both Plans A and B mitigate the occurrence probability and hazard intensity); (3) Plan C—surface drainage project involving a structural measure lowering hazard occurrence by reducing surface water infiltration and pore water pressure within the slope; and (4) Plan D—monitoring network construction project, aiming to minimize consequences by real-time monitoring of landslide movement and issuing timely warnings for elements at risk. The risk reanalysis process for the four mitigation plans and the quantification of the residual risks after their implementation are described in the following subsections.

Plan A: anti-slip pile project

The intact bedrock of the Liangshuijing landslide allows for the construction of anti-slip piles. The anti-slip pile design should follow the TGRA standards, targeting a post-mitigation F_s of 1.15. The proposal by the Chongqing Gaoxin Engineering Survey and Design Institute (CGESDI) (Li et al. 2021a) outlined a mitigation plan including 5 rows of piles at elevations range from 210 to 260 m asl (Fig. 3b and Table 3). The piles had a cross-section of 2.5 × 4.0 m and were spaced 4 m apart. The anti-slip piles are implemented as reinforcement loads on the slope. Coupled calculations are performed using the Seep/W and Slope/W modules in GeoStudio, yielding a post-mitigation P_f result of 3.6% (following global failure). This indicates a significant reduction of 94% in the occurrence probability of the landslide compared to the pre-mitigation value of 63.7%.

Table 3 The designed top elevation and length of the anti-slip piles

• 1. The post-mitigation probability of global failure (P_{f_m}) was 3.6%, indicating that even after implementing the anti-slip pile project, there remains a 3.6% probability of landslide instability. Therefore, if the landslide occurs with this small probability, the project can be considered to have failed. Conservatively assuming that the piles are not impeded to allow full release of the sliding body, the direct and indirect consequences (2.35 and 32.74 million RMB) of the LTHC are equal to those before mitigation (Li et al. 2021a).

• 2. Upon full reinforcement by piles, the landslide may transform into a local failure (auto-searched head elevation in GeoStudio software: 183 m asl; Fig. 3b) with a P_f of 26.7% (P_fs). Based on this transformation, the numerical landslide model in TS software is modified. The landslide motion process is re-simulated with the same friction parameters as those before mitigation (Fig. 6a-b). Compared with those of pre-mitigation global failure pre, the local landslide experiences a 58% reduction in maximum velocity (from 8.6 to 3.6 m/s) and a 57% reduction in volume (from 2.63×10⁶ to 1.12×10⁶ m³). Maximum downstream and upstream wave heights decreased by 62% to 6.4 m and 4.3 m, respectively (17.2 m and 11.0 m before mitigation). The run-ups did not threaten coastal towns, similar to pre-mitigation levels (Fig. 6c). The local failure impacts 5000 m² of woodland (175-183 m asl) at a direct consequence of 0.15 million RMB. The landslide-induced tsunamis impact the piers and vessels, resulting in an indirect consequence 13.03 million RMB (Table 4). The post-mitigation residual risk is 4.65 (1.26+3.39) million RMB (Table 5), which is 80% lower than that before mitigation.

Fig. 6

Movement status when local sliding body a reaches the peak velocity and b stops on the riverbed. The yellow box displays the movement time, V (landslide volume), A (landslide area), M (average thickness), v_s (mean velocity of sliding body), and v_p (maximum velocity of computing squares), in that order. c Peak wave heights and run-ups of landslide-induced tsunamis along the Yangtze River

Table 4 Potential tsunami consequences post-mitigation. h_max: maximum wave height at elements of risk; I: tsunami intensity on elements at risk. The calculations of I and V_lt are based on the results of the previous study (Li et al. 2021a)

Table 5 Residual risk (R_r0) of the LTHC after implementing different risk control plans

Plan B: mass removal project

This project was designed to remove material from the steep upper landslide (~ 35°) within the elevation range of 210–280 m asl (Fig. 3c), resulting in a volume reduction at the landslide head of about 3.6 × 10⁵ m³; thus, the landslide volume after the removal project is 2.27 × 10⁶ m³. The numerical model in both GeoStudio and TS software is modified to re-perform landslide stability analysis and motion simulation. The post-mitigation F_s is 1.051 with a P_f of 25.1% (about 60% lower than the pre-mitigation value of 63.7%). Compared with pre-mitigation values, the global failure of the treated slope along the bedrock results in a 15% lower peak velocity (7.3 m/s, Fig. 7a); the landslide volume decreases by approximately 14% (Fig. 7b); the maximum run-up decreases to 13.1 m; the maximum downstream and upstream wave heights decrease by approximately 26% to 12.5 m and 8.1 m, respectively (Fig. 7c). The landslide consequences included the destruction of the country road and 3.4 × 10⁴ m² of woodland, totaling 1.28 million RMB. Potential tsunamis losses amounted to 27.32 million RMB (Table 4). Therefore, according to Eq. (2), the residual risk decreased by about 68% to 7.18 million RMB (Table 5) after mitigation.

Fig. 7

Movement status when the sliding body (after implementing Plan B) a reaches the peak velocity and b stops on the riverbed. c Peak wave heights and run-ups. The wave height at the locations of the elements at risk versus time: d pier A, pier B and boat group A; e boat group B

Plan C: surface drainage project

Two drainage ditches were designed following the existing gullies (total of ~ 700 m), and an interceptor ditch was designed along the landslide boundaries (~ 650 m, Fig. 3a).

P_f equaled to that of the pre-mitigation scenario with no rainfall, at 58%. It is considered that the surface drainage project reduced rainfall effect on the seepage field inside the slope; thus, the potential consequences were numerically equal to those of the pre-mitigation scenario without rainfall (Table 5). After drainage implementation, the residual risk decreased to 20.63 million RMB, indicating only an 8% reduction compared to that before mitigation. This may be due to the low sensitivity of thick landslides to rainfall. Given the heightened sensitivity of landslide stability to reservoir level fluctuations, effective risk control requires the implementation of subsurface drainage projects.

Plan D: monitoring network project

To comprehensively track the landslide deformation in real-time, a monitoring network is designed (Fig. 3a): (1) GNSS surface displacement monitoring stations: three benchmarks outside the landslide and 3 GNSS stations along each of 5 control lines, totaling 18 stations. (2) Surface crack gauges: 3 gauges at the crown and 2 on each side, totaling 7 gauges. (3) Deep inclinometers: 2 installed along cross-Sect. 1–1′ and 1 each along the control lines (except for the right side second column with minor deformation), totaling 5 inclinometers. (4) Groundwater level loggers: 3 loggers positioned on cross-Sect. 1–1′. (5) Rain gauge: 1 gauge outside but near the landslide.

In the conservative scenario, the implementation of the monitoring network will not influence the failure mechanism and stability of landslide. P_f equaled 63.7% of the pre-mitigation level. As neither Plans C nor D alter the landslide intensity, the distribution and values of landslide-induced tsunamis are the same as those pre-mitigation. It is assumed that the monitoring system functions effectively and detects abnormal signals promptly, authorities can issue landslide warnings and implement emergency measures, such as navigation closures. A near-slip warning helps prevent indirect loss by keeping mobile elements at risk from entering the affected area. While, fixed elements at risk may still be impacted by the hazard chain. After mitigation, the direct and indirect consequences were 2.35 and 13.39 million RMB, respectively (including losses from piers A and B, and boat groups A and B). The residual risk decreases by approximately 55% from the pre-mitigation level (Table 5), highlighting the notable impact of early warnings on LTHC risk control.

Risk control plan selection

The benefit assessment, cost assessment, and BCRs for the four independent plans are discussed in the following subsections. The four time-related parameters involved, namely, the construction period (T_c), lifetime (T_l), fully effective period of measure (T_le), and ecological recovery period (T_e), for Plans A-D are identified (Tables 6, 7) based on related standards and literature, comparisons with similar projects, and scenario estimations. To analyze the long-term cost-effectiveness beyond the measure lifetime, the study period is assumed to be 100 years.

Table 6 Time-related parameters, residual risk, and benefit analysis for each risk control plan

Table 7 Direct cost (C_d) of each mitigation plan, estimated based on the workload and main engineering expenses

Cost–benefit analysis for Plan A

• 1. Benefit assessment

  Parameter determination: (a) T_c is estimated by the engineering action duration and average local construction speed for the respective projects. The designed anti-slip pile project takes approximately 1 year (involving vertical excavation, pile construction, etc.) (b) The T_l for an anti-slip pile project is 50 years according to local technical requirements. (c) The T_le is conservatively assumed to be 30 years. This is due to the potential degradation of concrete caused by reservoir water and corrosion, leading to a gradual weakening of its strength. The mutual support effect of multiple rows of piles can mitigate this drawback.

  Residual risk beyond measure lifetime (R_r1): Complicated pile failures after the end of pile lifetime may lead to unpredictable landslide failure mechanisms, increasing the difficulty in residual risk estimation. Therefore, a reduction coefficient (rc) is introduced to describe the decline in the effectiveness of mitigation measures beyond their lifetime. As long as the piles are not artificially removed post-lifetime, they still provide a certain degree of slip resistance. Therefore, with rc taken to be 0.7, R_r1 is 9.96 million RMB (Table 6).

  Benefit assessment: The short-term benefit (B′) of implementing Plan A is the difference between the total risk of the Liangshuijing LTHC (R_t) and the residual risk just after the completion of the mitigation measure (R_r0), denoted as B′ = R_t – R_r0, which is 17.70 million RMB (Tables 5–6). The long-term benefit (B) is the difference between R_t and the residual risk over 100 years according to Eq. (6), as shown in Table 6.

• 2. Cost assessment

  Direct cost (C_d): C_d for an engineering measure represents its main construction expenses, estimated based on relevant regulations (i.e., Ministry of Water Resources [2017]116), similar cases, and local price levels (Table 7). Due to the thick sliding body, the anti-slip pile project involved multiple rows of piles, resulting in a direct cost of approximately 126.93 million RMB, which is much greater than that of the other plans (Table 8).

  Indirect cost (C_e): As all plans are designed to be executed within the landslide area, C_e is estimated by the loss of woodland due to construction. The anti-slip piles, set within the range of 210–259 m asl, traverse the soil mass and anchor into the bedrock, affecting the seepage field inside the slope below the pile elevation. The piles are considered to disrupt the woodlands below 259 m asl (area ~ 4.3 × 10⁵ m²), leading to an initial ecological loss (C_ei) of approximately 1.28 million RMB. The piles will continue to affect the local ecosystem and recovery if not artificially removed. Therefore, the time required for ecosystem restoration (T_e) after the implementation of Plan A can be considered equivalent to the measure lifetime (T_l), and the residual ecological loss beyond the measure lifetime (C_er) is set at 90% of C_ei.

Table 8 Estimation of the benefit–cost ratio for individual plans

Indirect cost (C_e): As all plans are designed to be executed within the landslide area, C_e is estimated by the loss of woodland due to construction. The anti-slip piles, set within the range of 210–259 m asl, traverse the soil mass and anchor into the bedrock, affecting the seepage field inside the slope below the pile elevation. The piles are considered to disrupt the woodlands below 259 m asl (area ~ 4.3 × 10⁵ m²), leading to an initial ecological loss (C_ei) of approximately 1.28 million RMB. The piles will continue to affect the local ecosystem and recovery if not artificially removed. Therefore, the time required for ecosystem restoration (T_e) after the implementation of Plan A can be considered equivalent to the measure lifetime (T_l), and the residual ecological loss beyond the measure lifetime (C_er) is set at 90% of C_ei.

Cost–benefit analysis for Plan B

• 1. Benefit assessment

  Parameter determination: (a) The T_c of the mass removing (involving open excavation and material transportation) takes 2–3 months. (b) Landslide mass removal is a near-permanent topographic modification, with an ideally indefinite T_l duration in geological terms. Thus, the T_l is considered 100 years. (c) The T_le is also set as 100 years.

  Residual risk beyond measure lifetime (R_r1): Slope geometry modification is considered effective indefinitely. Therefore, the rc of Plan B is taken to be 1.0, and R_r1 equals R_r0, which is still 7.18 million RMB (Tables 5, 6).

  Benefit assessment (B′ and B): The B′ of Plan B is 15.18 million RMB, approximately 14% lower than that of Plan A. While, Plan B yields the highest long-term cumulative benefit (B in Table 6), approximately 4% greater than that of Plan A.

• 2. Cost assessment

  Direct cost (C_d): The C_d of Plan B is approximately 5.65 million RMB (Table 7), which is less than one-tenth that of Plan A.

  Indirect cost (C_e): The removal of ground soil within the range of 210–280 m asl leads to the loss of woodland covering an area of about 6.1 × 10⁵ m², resulting in a C_ei of approximately 1.84 million RMB. Since there are no structural measures affecting vegetation recovery, natural recovery of the localized ecology is anticipated within approximately 3 years (i.e., T_e = 3), resulting in a C_er of 0. Therefore, according to Eq. (8), the C_e of Plan B is 3.07 million RMB.

Cost–benefit analysis for Plan C

• 1. Benefit assessment

  Parameter determination: (a) The T_c of the surface drainage project takes approximately 1 month (involving surface soil removal and simple installation). (b) The T_l is taken as 30 years according to the Code for Rational Service Life and Durability Design of Water Resources and Hydropower Projects [SL 654–2014]. (c) The T_le is 7 years, as drainage remains fully effective without maintenance for approximately 7 years (Holcombe et al. 2012).

  Residual risk beyond measure lifetime (R_r1): Drainage ditches may crack beyond the measure lifetime, affecting water discharge. Conservatively, at this stage, Plan C would lose its mitigation effect (i.e., rc = 0), resulting in an R_r1 of 22.35 million RMB in both plans.

  Benefit assessment (B′ and B): Plan C has the lowest benefit (both B′ and B) among the four plans, indicating the limited effectiveness of surface drainage in mitigating thick landslides.

• 2. Cost assessment

  Direct cost (C_d): The surface drainage project totals approximately 0.4 million RMB, which is the lowest cost, among the four plans.

  Indirect cost (C_e): Surface drainage projects obstruct parts of the ground surface, affecting the hydrological conditions of the slope area. Cemented ground ditches, if not removed, prevent localized ecosystem restoration; thus, the T_e is considered equal to the T_l (i.e., 30 years). The ditches cover about 0.3 × 10⁵ m² of woodland and yields a C_er of about 0.08 million RMB. Surface concrete structures have a minor regional impact on regional ecology; thus, the C_er is set at 20% of the C_ei.

Cost–benefit analysis for Plan D

• 1. Benefit assessment

  Parameter determination: (a) T_c of the monitoring network construction takes approximately 1 month. (b) The typical lifetime of monitoring instrument ranges from 3 to 10 years, contingent upon usage. The T_l has an average duration of 5 years. (c) The T_le is conservatively estimated at 1 year, excluding cross-checking possibilities between instruments, as high-precision devices need regular maintenance.

  Residual risk beyond measure lifetime (R_r1): Monitoring instruments may malfunction or be scrapped due to unreliability beyond their lifetime. Conservatively, at this stage, Plan D would lose its mitigation effect (i.e., rc = 0), resulting in an R_r1 of 22.35 million RMB.

  Benefit assessment (B′ and B): The short-term benefit of Plan D is approximately 20% lower than that of Plan B. Plans A and B yield 45 times greater long-term benefits than Plans C and D.

• 2. Cost assessment

  Direct cost (C_d): The monitoring network construction totals approximately 0.77 million RMB.

  Indirect cost (C_p and C_e): (a) C_p is considered the economic loss due to navigation closures, since the productivity of potentially affected areas is dependent on shipping. C_p was estimated only in Plan D, as the early warning systems in Plan D may prompt authorities to close navigation. As a result of the navigation closure, 3 large, 6 medium, and 1 small vessels passing are affected hourly (Li et al. 2021a). Estimated losses, based on cargo value assessments, amount to approximately 7.55 million RMB per hour (Table 8). Early warnings are generally issued 2–4 h before a landslide occurs; thus, the estimated cost of navigation closure measures is 15.10 million RMB in this case. (b) Similar to Plan C, Plan D involves installing instruments and occupying small areas of woodland. With each station taking up 1 m², the total woodland loss is 34 m², relatively minor. Fixed inclinometers and groundwater level loggers, although placed underground, have minimal ecological impacts due to their sparse distribution. Therefore, the C_e is nearly 0 (Table 9).

Table 9 Estimation of cargo capacity for vessels sailing on the Yangtze River

Optimal plan identification based on BCR comparison

In practice, natural hazard mitigation and management should be based on long-term considerations (Fig. 8a). Plan B emerges as the optimal risk control strategy for the Liangshuijing LTHC, with 25 times higher long-term BCR (B/C) than other plans, due to its notable cumulative benefits and moderate costs. Excluding navigation closure costs (C_p), Plan D closely follows. Additionally, Plan D also has the highest the short-term BCR (B′/C_d), about 6 times that of Plan B. Both Plans B and C provide cost-effective short-term risk control, making them suitable supplementary measures. However, when C_p is included, the short-term BCR of Plan D drops 95%, indicating an unreasonable imbalance between benefits and costs, emphasizing the importance of cautious decision-making in evacuation scenarios. For Plan A, the challenge of managing the thick sliding body leads to considerable engineering costs. Therefore, although Plan A shows a comparable long-term BCR to Plan C (more than twice that of Plan D), its short-term BCR is notably lower (only 0.1 compared to 4.3 of Plan C), which indicates its unsuitability as a standalone mitigation measure for thick landslides in reservoir areas.

Fig. 8

a Evolution of the Liangshuijing LTHC over time after the implementation of the different mitigation plans. The shaded area represents long-term risk benefits. The original total risk (R_t), residual risk (R_r0 and R_r1), and time-related parameters of Plan A are illustrated by dashed lines, which serve as examples. b Cost, benefit, and BCR of different combined plans

Discussion

According to the risk management analysis above, mass removal is the most cost-effective solution for the Liangshuijing LTHC, although it does not eliminate the risk to a negligible level. Further insights include the following:

• 1. Mitigation measures applied to landslides also have notable risk control effects on landslide-induced tsunamis. Compared to that before mitigation, Plans A–C demonstrate reductions of 94%, 60%, and 8%, respectively, in the occurrence probability of tsunamis. Plans A and B lead to 83–89% and 24–27% reductions in the maximum wave height, respectively, when impacting the four elements at risk (Fig. 7d–e). Plan A costs approximately 1.46 million RMB to reduce the maximum wave height at the elements by 1%, while Plan B costs only a tenth of that. Additionally, Plans A-D reduce the potential tsunami risk by approximately 79%, 68%, 8%, and 59%, respectively. Without considering cumulative effects, the BCRs of Plans A-D for tsunami risk control are 0.1, 2.7, 4.3, and 16.0, respectively, which are very close to the BCRs for hazard chain risk control in Table 8 (B′/C_d), as secondary tsunami risk dominates the total risk of reservoir LTHCs (Li et al. 2021a). However, the consequent predictions rely on statistics from similar events and assumed extreme scenarios, which are unverified because the Liangshuijing landslide was mitigated in time and no tsunami event actually occurred. Therefore, the results are only an indication of what might apply.

• 2. A comprehensive risk control strategy, rather than solely focusing on landslide stability enhancement, may be more suitable for managing large reservoir LTHCs. In general, landslide mitigation in the TGRA has prioritized improving stability to meet F_s requirements in the standard (generally 1.15–1.20), resulting in high costs, low socioeconomic benefits, and challenges in widespread implementation. In this study, Plan A, which represents the traditional strategy, showed the most significant improvement in landslide stability (F_s = 1.144), with an average direct cost of 0.75 million RMB for each 0.001 increase in F_s. However, Plan B (representing the risk control strategy) and Plan C cost 0.07 million RMB for each 0.001 increase in F_s, which is only a tenth of Plan A’s cost. Although Plan B is lower than Plan A in terms of stability enhancement, it significantly reduces hazard intensity and consequences. Plans A and B reduce risk by 79% and 68%, respectively, with an 11% difference in immediate effectiveness (R_t − R_r0). However, their construction periods differ by four times, and their direct costs vary by 22 times. Plan D, while not enhancing landslide stability, can effectively mitigate the consequences, especially concerning population risk (if considered). Furthermore, Plan B, which causes permanent modification of slope morphology unless significant human activities or tectonic movements occur, is presumed to continuously and effectively control potential risk; thus, implementing Plan B has considerable long-term benefits.

• 3. In practice, a combination of measures is typically employed to achieve cost control while comprehensively enhancing mitigation effectiveness. For instance, in the combination of Plans A and B, anti-slip piles are placed after the removal of landslide mass. Two rows of 60 m piles are positioned at elevations of 188 m and 180 m asl (Fig. 3c). The implementation of this combined plan results in a 4.9% probability of global landslide failure. If piles successfully resist sliding, the Liangshuijing landslide may experience local failure, with a P_f of 9.6%. The sliding volume is 5.05 × 10⁵ m³, generating waves at heights of 0.04 m, 0.11 m, 0.01 m, and 0.06 m at piers A and B and boat groups A and B, respectively. The direct cost is 72.61 million RMB. For other combinations involving anti-slip piles, the pile arrangement is consistent with the design in the “Cost–benefit analysis for Plan A” section. For the T_e of combined plans, the implementation sequence and feasibility of overlapping timelines for each measure were key considerations. The T_le and T_l for each measure in combination do not influence one another. The cost is the sum of the costs of individual measures. Ecological impact assessments prioritize the more persistent measure in overlapping ranges, with separate calculations when there is no overlap, summed in the final assessment.

  The combined plans effectively enhance the risk control of the Liangshuijing LTHC (Table 10). When only drainage projects are combined (i.e., Plans A + C, B + C, and C + D), the improvement is limited (a 1%-8% risk reduction) due to the restricted performance of surface ditches on thick landslides. The other combinations showed more than 30% immediate risk reduction. For instance, Plan A + B reduces R_r0 by 52% and 69%, outperforming individual Plans A and B, respectively. When combined with Plan A or B, R_r0 is reduced by more than 60% compared to that of Plan C or D alone. Furthermore, combining short- and long-lifetime measures yields substantial long-term cumulative benefits that are at least 30 times greater. This study provides only indicative trends based on rough cost estimates. In practice, precise engineering accounting should be conducted to ensure accurate evaluation.

  Table 10 Estimation of the benefit–cost ratio for combined plans

  Plan B + D (mass removal and monitoring) is the most cost-effective strategy for the Liangshuijing LTHC, followed by Plan B + C + D. The addition of Plan A significantly reduces cost-effectiveness due to its high cost. Excluding navigation closure due to early warning from the costs, long-term BCRs, B/(C_d + C_e), for each plan, ranked B > B + D > B + C > B + C + D, while short-term BCRs, B′/C_d, ranked D > C + D > C > B + D > B + C + D > B > B + C (Fig. 8b). The BCRs for the other combinations are significantly lower than these. Therefore, the comprehensive optimal solution is Plan B + D, followed by Plan B + C + D. This finding reaffirms the imbalance between the benefits and costs of anti-slip pile projects. Considering the widespread need for LTHC mitigation in reservoir areas, a CBA from a risk management perspective may be valuable.

• 4. In the long-term, global warming may increase the frequency and intensity of tropical cyclones, causing elevated precipitation. Future climate and socioeconomic changes, including rapid urbanization and land use alterations, may heighten uncertainties in the evolution of geohazards (Almeida et al. 2017). Subsequent studies should account for sustainable management under extreme climate conditions (Dhyani et al. 2020). For instance, the “8.31” event occurred in the TGRA (Li et al. 2022), and recent heavy rainfall occurred in July 2023 in Wanzhou County (maximum > 260 mm/day).

Practical application

In fact, the landslide mass removal strategy has effectively mitigated the Liangshuijing LTHC. The mitigation measures were implemented between May 2014 and January 2015. According to the available surface displacement data, between Feb 2, 2015, and May 31, 2016, post-mitigation landslide average velocity decreased to 0.11 mm/day—an approximately 86% reduction compared to pre-mitigation—with an average cumulative displacement of approximately 52 mm (Fig. 4). From June 22, 2019, to August 2, 2021, the average velocity decreased to below 0.05 mm/day, presenting an approximately 93% reduction. This indicates effective control of landslide speed and intensity, further demonstrating a notable reduction in the total risk of the hazard chain. The chosen strategy derived in this paper aligns with that implemented and validated to be effective in practice, which affirms the reliability and practicality of the proposed framework.

Reservoir landslides in the TGRA are generally thick and thus have a high potential tsunami intensity, which poses challenges in meeting safety standards and eliminating risks to negligible levels. Moreover, traditional mitigation strategies may lead to excessive governance, causing a significant imbalance between benefits and costs. For small/shallow/nonchain-forming inland landslides, a low-cost factor of safety approach may be cost-effective.

Conclusions

• We have proposed a risk control workflow to develop and complete the risk management framework for reservoir LTHCs, ensuring that risk studies extend beyond analysis results and can be applied to guide mitigation practices. The workflow includes risk decisions, risk control strategies, optimal plan selection, and monitoring and reciprocal feedback. The Liangshuijing LTHC case, which was successfully mitigated through a partial risk control strategy determined by the authorities, was investigated in-depth. We hope that this quantitative framework can supplement LTHC mitigation practices from a cost-effectiveness perspective, breaking through the traditional criterion of evaluating mitigation effectiveness solely for landslide stability. These findings may at least enhance the confidence of authorities in applying sustainable risk management strategies as alternative mitigation solutions, especially when the costs and benefits of conventional stabilization measures are extremely imbalanced.

• We recommend mitigating reservoir LTHCs through risk management rather than solely focusing on reducing the probability of hazard occurrence. The large number of reservoir landslides and their costly mitigation measures make it challenging for authorities to decide on the widespread adoption of traditional strategies that provide a large margin in slope stabilization. Estimating potential losses before and after mitigation provides a comprehensive understanding of the overall effectiveness of measures. This will facilitate more informed decision-making among various departments, including those responsible for natural hazard management and mitigation, land resource planning, emergency management, public safety, and maritime operations.

• The mitigation of geohazards (LTHCs in particular) requires a long-term perspective. An optimal risk control plan can be selected through a cost–benefit analysis considering time-effect parameters. The cost is the sum of the project investment, production materials, and ecological losses. The benefit is the reduction in risks post-mitigation. When introducing the construction period, fully effective period, lifetime, and ecological recovery period, the benefit–cost ratio changes from a fixed value to a dynamic function over time. This approach maximizes the advantages of uncertainty-based comprehensive risk management and helps decision-makers select effective and sustainable mitigation strategies.