Infrastructure Risk Assessment refers to the systematic identification, analysis, and evaluation of hazards that can affect infrastructure systems, considering both the likelihood of occurrence and the severity of potential consequences [20] . Resilience is the capacity of infrastructure systems to absorb disturbances, adapt to changing conditions, and rapidly recover functionality after a disruption [21] . Resilience includes pre-disaster preparedness, adaptive responses, and post-event recovery capacity. Grey Engineering comprises conventional, human-engineered infrastructure solutions such as concrete drainage systems, asphalt pavements, and reinforced embankments, designed primarily for structural protection and service continuity [22] . Green Engineering (or nature-based solutions) involves the use of ecological processes and natural systems, such as vegetative buffers, permeable pavements, bioswales, and green roofs, to provide hazard mitigation while delivering environmental and social co-benefits [23] . Hybrid Infrastructure (Grey-Green) integrates structural grey engineering with ecological green systems to enhance adaptive capacity, sustainability, and multiple co-benefits [24] . Adaptation Pathways are phased, flexible planning approaches that allow sequential interventions over time in response to evolving hazards, climatic changes, and socio-economic conditions.

This study is grounded in Engineering Resilience Theory, which originates from Holling [25] socio-ecological resilience framework but has been adapted for infrastructure systems [26] . While socio-ecological resilience emphasizes a system’s capacity to absorb disturbances without shifting into an alternative state, engineering resilience focuses on the stability of performance and the speed of recovery following a disruptive event. It is particularly suited for infrastructure analysis because it quantifies how quickly a system can return to an acceptable level of functionality after a hazard, thereby providing a practical basis for risk assessment and adaptation planning. [27] describe engineering resilience as encompassing three interrelated capacities: absorptive capacity, which is the ability of a system to buffer, absorb, or contain the effects of hazards without significant degradation in service delivery; adaptive capacity, which reflects the ability to make operational or structural adjustments when absorptive limits are exceeded; and restorative capacity, which is the ability to restore and potentially enhance functionality after disruption.

Within the context of Kangundo Road, the framework guides risk characterization by identifying points at which absorptive and adaptive limits are likely to be exceeded under conditions such as flooding, erosion, and poor drainage performance. It also directs the evaluation of adaptation measures that can strengthen restorative capacity, thereby reducing downtime and enhancing long-term performance. Integrating hybrid grey-green engineering designs within this framework aligns with its emphasis on minimizing service loss while enabling rapid recovery [28] . Grey infrastructure elements, such as reinforced culverts and durable asphalt surfacing, provide immediate structural stability, while green infrastructure components, including vegetated swales, bioswales, and permeable pavements, enhance adaptability and deliver environmental co-benefits [12] [29] . These approaches embody the principles of engineering resilience by ensuring that Kangundo Road can withstand disturbances, adapt to changing conditions, and recover quickly while maintaining environmental sustainability.

Contemporary infrastructure planning has increasingly shifted away from reliance on purely grey engineering solutions toward the adoption of integrated hybrid systems [30] . Within this paradigm, resilience is understood as a dynamic and adaptive process rather than a fixed attribute, requiring infrastructure to adjust and evolve in response to emerging hazards and changing conditions [27] . International studies on urban drainage and transport networks consistently demonstrate that the incorporation of green elements, such as permeable pavements, vegetated swales, and green roofs, can significantly reduce peak flood flows, enhance water quality, and contribute to urban cooling [31] . The adaptation pathways approach further strengthens this integration by enabling phased, flexible interventions that can be adjusted to accommodate climatic variability and socio-economic change over time [1] . Beyond their hydrological and structural benefits, nature-based solutions also deliver important socio-economic gains, including improvements in public health, enhancement of biodiversity, and stimulation of local economies. Despite these advantages, empirical evidence from African high-traffic road corridors remains scarce. Most existing hybrid infrastructure frameworks have been developed and tested in coastal or urban drainage contexts, with limited application to major inland transport routes where traffic demands, climatic stresses, and budget constraints present unique resilience challenges.

Irankunda [32] developed the NIRAC and RIRA frameworks for multi-scenario road infrastructure resilience assessment, applied to rain-damaged roads in Burundi. Findings confirmed their value in guiding sustainable recovery, though testing was limited to one region. Applicability to hybrid grey-green systems remains unexplored.

Joyce [33] coupled flood risk assessment with resilience metrics in a coastal drainage system in Florida using copula-based modeling. Results showed multi-criteria evaluation improves decision-making. The study has limited application to inland road networks; co-benefits of green measures are underrepresented.

Dong [34] proposed a resilience formula incorporating social, environmental, and technological severity, comparing green and grey drainage strategies in Kunming, China. Green measures proved cost-effective under climate uncertainty. The study methodology was not tailored to road transport infrastructure.

Kapetas [22] applied adaptation pathways to evaluate grey and blue-green flood solutions in London. Monetizing co-benefits shifted preferences to hybrid solutions. The study lacks application to African road corridors with budget constraints; maintenance feasibility is underassessed.

Staddon [35] reviewed green infrastructure’s role in urban resilience, identifying five key implementation challenges. Advocated hybrid socio-technical systems. Gap: scarce empirical data on road corridor performance in developing contexts. Table 1 outlines existing gaps in the study.

Table 1 indicates that the reviewed literature emphasizes the potential of hybrid grey-green infrastructure for enhancing resilience but also reveals critical gaps relevant to Kangundo Road. Existing frameworks such as NIRAC, RIRA, and adaptation pathways offer strong foundations but lack contextual testing in African high-use road corridors. Studies on drainage systems show the efficiency of green infrastructure under climate change, yet few address road-specific hazards and performance metrics. Key gaps motivating this research include: Lack of empirical testing of hybrid solutions for African road infrastructure. Absence of integrated frameworks linking risk characterization, resilience assessment, and adaptation option evaluation for transport corridors. Limited valuation of co-benefits to support decision-making and investment in road resilience. This study will address these gaps by assessing the risks and resilience of Kangundo Road and evaluating hybrid grey-green engineering designs for their technical feasibility, cost-effectiveness, and environmental co-benefits, thereby contributing a localized, evidence-based framework for climate-resilient road infrastructure planning in Kenya.

This study will contribute to the growing body of knowledge on climate-resilient infrastructure by providing the first detailed, empirical assessment of risks and resilience for the Kangundo Road corridor in Kenya. While previous research has established the increasing vulnerability of road infrastructure to climate change and highlighted the potential benefits of integrating grey and green engineering solutions, there remains a lack of localized, data-driven frameworks for their practical application in high-use transport corridors within the Kenyan context. By systematically characterizing the specific climatic, environmental, and socio-economic risks affecting Kangundo Road, this research will generate a comprehensive risk profile that can guide targeted adaptation planning. Furthermore, the study will evaluate hybrid grey-green engineering design options, assessing their technical feasibility, cost-effectiveness, and potential co-benefits. The resulting framework will provide policymakers, engineers, and infrastructure planners with actionable strategies for integrating hybrid resilience measures into road infrastructure projects, ultimately enhancing service continuity, reducing maintenance costs, and contributing to sustainable urban and regional development.

Kangundo Road, as presented in Figure 1 , lies in a low-elevation zone that naturally functions as a catchment for runoff from surrounding highlands.

Figure 1 indicates that Kangundo road is the lowest point in its vicinity, making it highly susceptible to flooding during heavy rainfall. The adjacent regions, Kiambu, Ngong, and Machakos, are situated at significantly higher altitudes, with Ngong representing the highest elevation. Rainfall in these upland areas produces considerable runoff that flows downhill towards the Kangundo-Kamulu stretch. The gradient from Kiambu to Kangundo further accelerates this flow, directing large volumes of water into flood-prone sections of the road. Machakos, as another high-altitude area, contributes additional runoff during intense rainfall events, compounding the flood risk. The combination of topography and hydrological patterns frequently overwhelms the road’s drainage systems, resulting in water pooling, flash floods, and damage to the infrastructure. These conditions make Kangundo Road an appropriate case study for climate-resilient infrastructure research, particularly in the design of effective drainage systems, the use of flood-resistant construction materials, and the integration of predictive flood management systems to mitigate risks in similar low-lying, flood-prone areas.

The climate datasets used in this study were sourced from the Kenya Meteorological Department and the World Bank Climate Knowledge Portal. To ensure their suitability for modelling within the Fisher Climate framework, a systematic data-processing workflow was applied: Temporal Range: Historical precipitation and temperature records spanning several decades were extracted to capture both long-term variability and the frequency of extreme events affecting the Kangundo Road corridor. Quality Control: Raw data were screened for errors and inconsistencies, including the removal of statistical outliers, verification of station-level continuity, and cross-checking against regional climatological norms. This step ensured that anomalies reflected genuine climatic extremes rather than measurement errors. Gap-Filling Methods: Where gaps existed in the Kenya Meteorological Department records, complementary data from the World Bank portal were used. Interpolation techniques were applied for short, isolated gaps, while longer discontinuities were supplemented through cross-station substitution and trend-based estimation. The cleaned and harmonized datasets were then normalized and parameterized to generate the climate variable weights (α values) that support the Fisher Climate Model’s scenario simulations.

The Fisher Climate Model was applied to generate future scenarios using hydrological data on river flows, groundwater levels, and soil moisture to map hazard exposure along Kangundo Road. Its integration of hydrological, geotechnical, and thermal processes within a single framework enables multi-hazard interactions such as drainage deterioration, flooding, and thermal expansion to be analyzed simultaneously, making it particularly suitable for road-scale risk assessment where rainfall variability and drainage efficiency are dominant drivers [34] . Sensitivity assessments considered susceptibility to flooding, thermal stress, and material degradation, while adaptive capacity was evaluated through drainage efficiency, material resilience, and maintenance practices. Engineering interventions, such as elevated roadbeds, upgraded culverts, and heat-resistant asphalt, were modelled alongside nature-based solutions, including vegetative buffers, wetland restoration, and bioswales, to enhance resilience. Key hydraulic, geotechnical, and thermal processes were simulated using literature-based equations, including Manning’s equation for drainage, thermal expansion for heat, and limit equilibrium for slope stability. A combined resilience model, incorporating SSP4.5 and SSP8.5 climate scenarios, evaluated performance under moderate and extreme conditions, with resilience scores computed using weighted factors for material quality, design, adaptability, and projected climate impacts. Cost-benefit analysis and life-cycle evaluation guided prioritization of adaptation measures, with recommendations integrated into updated engineering standards and broader transport planning to ensure long-term climate resilience of Kangundo Road.

Historical climate data on temperature, precipitation, and extreme events were sourced from the Kenya Meteorological Department. The section presents equations that were used in modelling the infrastructure based on a literature review.

Manning’s Equation for open channel flow:

$Q_{\text{flow}}=\left(1/n\right)A{R}^{\frac{2}{3}}{S}^{\frac{1}{2}}$ (1)

Thermal Expansion Equation for extreme heat:

$\text{Δ}L=\alpha L_0\text{Δ}T$ (2)

Frost-Heave Equation for heavy snow ice:

$h_f=C_f\text{Δ}T/d$ (3)

Limit Equilibrium Equation for landslide:

$FS=\left(c\cdot L+W\cdot \text{cos}\left(\theta \right)\cdot \text{tan}\left(\varphi \right)\right)/\left(W\cdot \text{sin}\left(\theta \right)\right)$ (4)

Bruun Rule for predicting shoreline retreat based on sea-level rise:

$R=S/\left(\text{tan}\left(\beta \right)\right)$ (5)

The combined model equation for climate-resilient infrastructure, considering the relative importance of each factor, was given by:

$\text{Resilience Score}=w_1{Q}_{\text{flow}}+w_2\text{Δ}L+w_3{h}_f+w_{4}FS+w_{5}R$ (6)

where $w_1,w_2,w_3,w_4$, and $w_5$ are weights representing the relative importance of each factor. The model incorporated climate scenarios SSP 4.5 (conservative) and SSP 8.5 (worst-case) to evaluate the resilience of infrastructure under different climate change conditions. SSP 4.5 represented a moderate climate change scenario with some mitigation, while SSP 8.5 represented a scenario of higher emissions and greater climate impacts. The model calculates the resilience score (R) of infrastructure considering these scenarios and other critical factors influencing infrastructure performance. Thus, $R$ in Equation (6) becomes

$R=w_1{X}_1+w_2{X}_2+\cdots +w_n{X}_n+{\beta }_{1}SS{P}_{4.5}+{\beta }_{2}SS{P}_{8.5}$ (7)

where $w_1,w_2,\cdots ,w_n$ are the weights representing the importance of various factors influencing infrastructure resilience, $x_1,x_2,\cdots ,x_n$ are the factors representing material quality, design, adaptability and ${\beta }_1$ and ${\beta }_2$ are coefficients representing the impact of climate scenarios SSP 4.5 and SSP 8.5, respectively. $SS{P}_{4.5}$ and $SS{P}_{8.5}$ are variables representing projected climate impacts such as temperature, sea level rise under these scenarios. By incorporating both SSP 4.5 and SSP 8.5, the model evaluates the resilience of infrastructure under moderate and extreme climate change scenarios. The variables $SS{P}_{4.5}$ and $SS{P}_{8.5}$ represent expected changes in climate variables such as temperature, sea-level rise, or frequency of extreme weather events under these scenarios. The coefficients ${\beta }_1$ and ${\beta }_2$ adjust the overall resilience score based on the projected climate impact for each scenario. This approach ensures that the model accounts for a range of future climate conditions, helping decision-makers design infrastructure that can withstand both conservative and worst-case scenarios.

The SSP 4.5 (conservative) and SSP 8.5 (worst-case) climate change scenarios represent different future pathways for greenhouse gas (GHG) emissions, which affect temperature rise, sea-level rise, and extreme weather events. These scenarios can be represented through mathematical equations to model the impact of climate change on infrastructure resilience.

For temperature increase, $\text{Δ}T$ for SSP 4.5 and SSP 8.5, the temperature increase over time can be modeled as:

$\text{Δ}{S}_{SS{P}_{4.5}}\left(t\right)=0.3+0.005t+0.0002t^2$ (8)

$\text{Δ}{S}_{SS{P}_{8.5}}\left(t\right)=0.3+0.01t+0.0004t^2$ (9)

where $t$ is time in years, and the coefficients 0.02 and 0.04 represent the annual rate of temperature increase. For sea-level rise $\text{Δ}S$, Sea-level rise can be modeled as a quadratic function due to potential acceleration over time. However, since this case study area is not near the sea, sea-level rise is used as an analogy for the erosion of road structures caused by poor drainage design:

$\text{Δ}{S}_{SS{P}_{4.5}}\left(t\right)=0.3+0.05t+0.0002t^2$ (10)

$\text{Δ}{S}_{SS{P}_{8.5}}\left(t\right)=0.3+0.01t+0.0004t^2$ (11)

where $t$ is time in years, and the quadratic terms represent the potential acceleration in sea-level rise. The frequency or intensity of extreme weather events can be modeled as follows:

$E_{SS{P}_{4.5}}=1+0.01t$ (12)

$E_{SS{P}_{8.5}}=1+0.02{\text{e}}^{0.03t}$ (13)

where the exponential term in the SSP 8.5 equation reflects the accelerated increase in extreme weather events. To evaluate the overall effect of the SSP 4.5 and SSP 8.5 scenarios on infrastructure resilience, the combined effect of temperature increase, sea-level rise, and extreme weather events can be represented as:

$SS{P}_{4.5}\left(t\right)={\alpha }_1\Delta T_{SS{P}_{4.5}}\left(t\right)+{\alpha }_2\Delta S_{SS{P}_{4.5}}\left(t\right)+{\alpha }_3{E}_{SS{P}_{4.5}}\left(t\right)$ (14)

$SS{P}_{8.5}\left(t\right)={\alpha }_1\Delta T_{SS{P}_{8.5}}\left(t\right)+{\alpha }_2\Delta S_{SS{P}_{8.5}}\left(t\right)+{\alpha }_3{E}_{SS{P}_{8.5}}\left(t\right)$ (15)

where ${\alpha }_1,{\alpha }_2$, and ${\alpha }_3$ are the weights representing the relative importance of temperature, sea-level rise, and extreme weather events.

The data was collected from https://climateknowledgeportal.worldbank.org/country/kenya/climate-data-historical . A summary of the data is presented in Table 2 .

Table 2 indicates that the rainfall records show a mean of 77.761 mm with a standard deviation of 201.410 mm, indicating exceptionally high variability relative to the average. This large dispersion suggests that precipitation in the Kangundo Road catchment is highly irregular, with extreme wet periods interspersed with prolonged dry spells. Such variability aligns with the related literature on the increasing intensity and frequency of extreme weather events in sub-Saharan Africa, which elevates flood risk for low-lying infrastructure like Kangundo Road. This inconsistency in rainfall is a critical driver of the recurrent flooding and drainage overloads described in your study area section, reinforcing the need for resilient stormwater management interventions that can accommodate both extreme inflows and prolonged low-flow periods.

In contrast, the temperature data reveal a mean of 18.70˚C with a small standard deviation of 0.627˚C, reflecting a stable thermal regime over the study period. The low variability implies that thermal stress on materials is minimal compared to hydrological stress, meaning that temperature-related degradation, such as thermal expansion damage, is less likely to be a dominant hazard driver in this corridor. However, the article’s methodology section still appropriately considers thermal expansion effects in resilience modelling, since even small temperature shifts can affect material performance over long design lifespans.

These findings highlight that rainfall-driven hazards should be the primary focus of adaptation planning for Kangundo Road. The combination of high precipitation variability and the road’s low-lying topography creates recurrent and severe flood exposure. Hybrid grey-green engineering solutions, such as reinforced culverts integrated with vegetated swales and upstream wetland restoration. These approaches can increase absorptive capacity to handle extreme rainfall events while delivering ecological co-benefits, thereby directly addressing the hydrological variability revealed by the statistical analysis.

$\alpha$ values were calculated by normalizing statistical features of the temperature and precipitation data. $\alpha$ represents weights used to define the contribution of each climate variable to climate impact indices or scenario models. The $\alpha$ weights in Table 3 were derived through min-max normalization of the statistical features (mean and standard deviation) of the climate variables, ensuring that each parameter contributed proportionally to the overall risk index within the Fisher Climate Model. The normalization procedure rescales each variable $x_i$ to a 0 - 1 range according to:

${\alpha }_i=\left(x_i-x_{\min }\right)/\left(x_{\max }-x_{\min }\right)$ (16)

where $x_i$ is the observed feature value of the variable $i$ such as rainfall and temperature. $x_{\min }$ and $x_{\max }$ are the minimum and maximum values across all variables, and ${\alpha }_i$ is the resulting normalized weight. After normalization, the weights were rescaled so that ${\displaystyle \sum {\alpha }_i}=1$. This ensured comparability across climate drivers and allowed the Fisher Climate Model to emphasize the dominant stressor. The results are presented in Table 3 .

Table 3 shows that the very low ${\alpha }_{\text{Temperature}}$ aligns with the previously reported low temperature standard deviation (0.627˚C), confirming minimal variability and negligible thermal impact on road deterioration. This makes temperature mitigation measures less critical. In contrast, ${\alpha }_{\text{Sea level}}=0.9967$, a proxy for cumulative rainfall, dominates, underscoring precipitation as the primary climate risk. Sustained soil saturation and high pore pressures weaken subgrades, causing rutting, potholing, and erosion, highlighting the need for robust drainage systems. ${\alpha }_{\text{Extreme events}}=0.0060$, though modest, reflects occasional storm impacts that can overwhelm drainage. Resilience planning should prioritize water-related stressors in design and maintenance. The objective was to assess infrastructure risks and resilience for Kangundo Road under various climate stressors, including floods, extreme heat, landslides, and sea-level rise. Findings show flooding as the dominant hazard, driven by the road’s location in low-lying, poorly drained clay soils and compounded by inadequate drainage slopes, particularly between Umoja and Komarocks. These conditions cause runoff accumulation and long-term saturation during heavy rains. While Nairobi lacks snowfall, climate models suggest potential frost-heave impacts from future temperature volatility, worsening siltation and drainage inefficiency. Steep slopes further increase landslide risk, and limited stormwater infrastructure heightens the road’s vulnerability to water-related hazards.

In this study, the resilience score is defined as a composite vulnerability index, where higher values indicate greater cumulative climate-induced stress such as lower resilience, while lower values reflect stronger resilience and adaptive capacity. The simulation results presented in Figure 2 are based on resilience score in Equation (3).

Figure 2 illustrates the temporal trends of four key parameters, Q_flow, thermal expansion (ΔL), factor of safety (FS), and shoreline retreat (R), central to assessing road infrastructure resilience under climate change. Q_flow remains stable at ~45.5 over 80 years, suggesting consistent drainage capacity but no dynamic adaptation to changing rainfall patterns. ΔL increases linearly from slightly negative to ~0.05, indicating gradual thermal expansion of materials and potential long-term deformation if not addressed in design. FS stays slightly above 3.0, implying stable slopes, though the model may underestimate impacts from rainfall, seismic events, or soil saturation. The most concerning is R, which rises exponentially from <10 to >60, signaling escalating erosion risks that could undermine road foundations. Erosion (R) and thermal expansion (ΔL) emerge as the most time-sensitive threats, highlighting the need for climate-responsive road designs prioritizing erosion control and material resilience to ensure long-term functionality. Figure 3 presents resilience score over the study duration.

Figure 3 shows a steady increase in the road infrastructure’s resilience score from ~9 to ~30 over an 80-year simulation, indicating escalating vulnerability as cumulative stressors intensify. Lower scores therefore represent greater resilience, while higher scores signal declining performance under climate stress. This growth reflects the combined effects of hydrological capacity, material thermal response, frost heave resistance, landslide stability, and drainage line performance, evaluated under SSP 4.5 and SSP 8.5 scenarios. Enhanced drainage design, including optimized slope, width, and depth, plays a key role in mitigating flood risks. The results suggest a declining risk profile if adaptive measures are maintained, though the outcome remains model-dependent. Simulation of resilience score against time and thermal expansion is presented in Figure 4 .

Figure 4 presents a 3D plot showing the relationship between thermal expansion (ΔL) and road infrastructure resilience over time. Initially, ΔL is near zero, indicating minimal heat-induced deformation. Over time, ΔL increases due to rising temperature anomalies, paralleled by a rise in the resilience score, used here as a composite indicator of climatic stress impacts rather than resistance. The non-linear escalation suggests that beyond certain thresholds, small thermal changes could cause disproportionately large damage, accelerating deterioration. This highlights the need for heat-resistant materials and thermally adaptive designs, ensuring road performance accounts for long-term thermal trends and anticipated climate-driven stresses. Figure 5 shows simulation of resilience score against drainage deterioration against time.

Figure 5 shows that resilience scores rise with increasing drainage deterioration (R), confirming that higher scores reflect greater vulnerability caused by declining drainage efficiency. Over time, R rises non-linearly, driven by erosion, storm surges, and reduced sediment replenishment, causing resilience scores to escalate sharply. The concave curve suggests a tipping point where small increases in R trigger disproportionately high risk, particularly in coastal or low-lying areas. This non-linear behavior underscores the urgency of early mitigation to prevent rapid transitions from stability to critical risk. Figure 6 shows the combined effects of time and thermal stress (ΔL) on road infrastructure resilience.

Figure 6 shows that as thermal expansion (ΔL) increases over time, the resilience score also rises, reflecting steadily compounding vulnerability due to material fatigue. The near-linear gradient suggests continuous risk accumulation from thermal expansion, driven by gradual material fatigue rather than sudden failures. The color shift from blue (low stress) to yellow (high stress) visually emphasizes growing thermal risk. These findings highlight the need for heat-resistant materials and designs to address persistent, long-term degradation under projected climate warming. Figure 7 presents simulation of resilience score vs time and R (drainage deterioration).

Figure 7 illustrates how shoreline retreat or drainage deterioration (R) and time combine to influence road infrastructure resilience. The resilience score represents cumulative risk from prolonged environmental exposure rather than structural strength. At early times and low R, scores remain modest, reflecting limited stress. Figure 7 and Figure 8 illustrate that combined increases in drainage deterioration (R) and thermal expansion (ΔL) escalate resilience scores rapidly, confirming that higher scores signal compounding vulnerability under multiple simultaneous stressors. The non-linear surface gradient and color shift from blue (low risk) to yellow (high cumulative risk) underscore how long-term deterioration compounds vulnerability. This pattern emphasizes the need for proactive drainage design and timely interventions to prevent escalating climate-related risks.

Figure 8 illustrates the combined effects of thermal expansion (ΔL) and drainage deterioration (R) on road infrastructure resilience. Both factors individually increase the resilience score, indicating escalating vulnerability due to compounding stressors, but their simultaneous rise produces a compounding effect, sharply elevating risk. The surface gradient shows that moderate increases in either factor raise vulnerability, while high ΔL and R together push the system into a critical risk zone, as highlighted by the upper-bound color shift. This underscores that roads facing both heat stress and poor drainage are most prone to failure. The results stress the need for integrated adaptation strategies addressing both thermal and hydrological stressors.

Adaptation and resilience design in grey and green engineering is essential for integrating climate risk into road design and ensuring long-term infrastructure resilience. With escalating threats from extreme heat, intensified rainfall, flooding, and sea-level rise, proactive responses to vulnerabilities are critical. Grey measures, such as reinforced drainage, elevated embankments, and thermally resistant pavements, offer robust, immediate protection. Embedding these within a climate-integrated design framework enables balanced decisions on performance, cost, and sustainability. This objective bridges the gap between risk assessment and actionable design, ensuring that climate-informed evaluations translate into resilient infrastructure capable of safeguarding road networks against future climate uncertainties. Figure 9 presents absolute impact of component exclusion on resilience score.

Figure 9 shows sensitivity analysis in assessing how removing key stressors affects road infrastructure resilience. Excluding landslide susceptibility (FS) yields both positive and negative changes, showing complex interactions and variability in its influence. In contrast, removing drainage deterioration (R) consistently reduces resilience, confirming it as a dominant stressor. Frost-heave (h_f) has a smaller but noticeable effect, reflecting its secondary role. The differing magnitudes highlight that R and FS are the most critical factors, while Q_flow and ΔL would also contribute meaningfully if included. The analysis shows resilience is stressor-dependent, with drainage and landslide risks requiring the highest priority in adaptation strategies. The analysis indicates that without effective drainage, the road’s capacity to withstand disruptions falls sharply. Grey engineering responses include larger culverts, lined channels, and improved cross-drainage, while green measures, such as bio-retention systems, vegetated swales, and rain gardens ( Figure 10 ) enhance infiltration, reduce surface runoff, and complement structural drainage upgrades.

The exclusion of frost-heave effects results in a moderate drop in resilience score, indicating that temperature-induced ground movements remain relevant under extreme heat or cold. Grey engineering could address this through structural reinforcements, while green measures, such as increased vegetation cover, can stabilize surface temperatures and retain soil moisture, reducing freeze-thaw vulnerability. Landslide susceptibility (FS) also shows notable influence, with resilience declining when excluded, underscoring the need for slope stability in hilly areas. Solutions range from retaining walls and slope drainage (grey) to reforestation and terracing (green). Figure 11 confirms drainage management as the most critical factor, and integrating both engineering and ecological strategies offers the strongest pathway to climate-resilient, sustainable road infrastructure.

Figure 11 shows the percentage reduction in resilience score when key factors are excluded. Removing frost-heave causes the largest reduction, exceeding 80% in some cases, confirming drainage as the most critical resilience determinant. Grey measures like reinforced channels and culverts, and green solutions such as bioswales and permeable pavements, are vital under intense rainfall. Excluding hf yields the smallest drop, though its importance rises in freeze-thaw climates. FS exclusion shows substantial impact, highlighting slope vulnerability in steep or unstable terrain. Compared to Figure 9 , absolute reductions, Figure 12 presents a relative perspective for prioritizing cost-effective, targeted interventions, combining grey and green strategies.

Figure 12 quantifies the impact of key variables on road infrastructure resilience. Excluding Q_flow (hydrological flow) causes the largest reduction, nearly 55%, underscoring the importance of stormwater management through grey measures like engineered channels, culverts, and retention basins. R (drainage deterioration) follows, with about a 30% reduction, reflecting the need for hybrid green-grey strategies such as bioswales, buffer strips, and permeable pavements to counter intensified rainfall and flooding. ΔL (thermal expansion), h_f (frost-heave), and FS (landslide safety) have smaller impacts (<10%), indicating localized or secondary importance in this setting. Together with Figure 9 and Figure 11 , the results highlight that prioritizing drainage, hydrological capacity, and thermal resilience through integrated grey and green engineering is crucial to maintaining road performance under climate stress.

The simulation results quantitatively reinforce the conceptual and empirical foundations outlined in the literature review, particularly regarding the dominant role of hydrological stressors and the complementary value of hybrid grey-green engineering approaches. The weight analysis ( Table 3 ) indicates that ${\alpha }_{\text{Sea level}}$, used as a proxy for cumulative rainfall and drainage deterioration, exerts the greatest influence (0.9967) on resilience, while ${\alpha }_{\text{Temperature}}$ and ${\alpha }_{\text{Extreme events}}$ have minimal values. This finding aligns with evidence that flood-related hazards dominate road infrastructure vulnerability in tropical contexts [22] [34] . For Kangundo Road, this confirms the need to prioritize water-related hazard mitigation, consistent with the adaptation planning perspectives in [12] [30] . The practical implication is that climate adaptation budgets and infrastructure upgrade programmes should allocate proportionately greater resources toward drainage system design, expansion, and maintenance, rather than heavily investing in temperature-specific mitigations.

Temporal simulations show that while Q_flow remains stable, R (drainage deterioration) increases exponentially, signaling escalating erosion and drainage inefficiency, trends consistent with projected increases in extreme rainfall for sub-Saharan Africa [5] [6] . Without intervention, this trajectory implies a transition from manageable wear to accelerated functional degradation, shortening asset lifespan and increasing life-cycle costs. Thermal expansion (ΔL) displays steady growth, supporting the argument that even small temperature variations can accumulate to cause long-term material fatigue [17] . This implies that thermally adaptive designs should be incorporated during new road construction, even if temperature is not the dominant hazard, to avoid compounded maintenance burdens in the future.

The combined hazard plots ( Figures 4-8 ) reveal non-linear risk escalations when ΔL and R interact, emphasizing the necessity for integrated strategies that address both thermal and hydrological stressors through reinforced drainage and thermally adaptive designs [31] [35] . Such patterns suggest that single-hazard adaptation approaches are insufficient, as combined stresses can push the system past critical thresholds much earlier than individual hazards would. Sensitivity analyses ( Figures 9-12 ) highlight drainage deterioration and hydrological flow as the most critical resilience determinants, aligning with identified empirical gaps that call for drainage-focused interventions in African high-use road corridors [32] .

While frost-heave and slope stability rank lower in this context, their significance in other climatic or topographic conditions underscores the value of the flexible, context-specific resilience planning framework outlined in [27] . The implication is that resilience frameworks should be locally calibrated but still maintain modularity to incorporate emerging risks. The results operationalize the engineering resilience principles by demonstrating that Kangundo Road’s resilience is most threatened by water-related stressors, and that hybrid grey-green engineering offers the most robust pathway to sustainable, climate-resilient performance. The findings also support the need for integrated infrastructure-climate planning policies that mandate multi-hazard risk assessment at the design stage, link maintenance cycles to climate projections, and promote nature-based solutions alongside structural upgrades to ensure both robustness and sustainability.