THEK Research Institute · Ingeniería sísmica

SeSDA — Sequential Seismic Degradation Analysis

Sequential seismic degradation analysis method

SeSDA analyzes how the load-bearing capacity of a structure decreases under multiple earthquakes. It applies the Ductility Degradation Law (DuDeL) after each inelastic excursion and retains the structural state for subsequent events. This case study uses inelastic hPIM (2PIM) for step-by-step integration of the dynamic response.

Explore case study 1 ↓Read the papers ↗Request a license ↗

Author: M.Sc. (TUM) Marcelo Moncayo Theurer · Guayaquil, Ecuador · 2026

SEQUENCES AND DEGRADATION

2PIM TIME INTEGRATION

01 · Fundamentos

From a single earthquake to the full seismic history

A structure does not start each earthquake from an undamaged state: earlier plastic excursions change its remaining strength and produce residual displacements.

01 · SeSDA

Earthquake sequence

Applies multiple ground-motion records over the service life, carrying the deformed and degraded state forward between events.

02 · DuDeL

Ductility-based degradation

Quantifies the loss of yield strength based on the ductility reached during each inelastic excursion.

03 · hPIM / 2PIM

Inelastic time integration

Computes displacements, forces and dynamic response step by step. The hPIM paper reports preliminary accuracy comparisons with Newmark.

04 · Verificación

Residual strength

The paper proposes the acceptance threshold Fᵧ,final / Fᵧ,0 ≥ 0.55. The system reports whether the condition is met.

02 · Formulación de los papers

DuDeL and dynamic response using 2PIM

SeSDA defines an explicit law to update strength after ductile excursions and uses a numerical time integrator to compute structural response to each acceleration record.

Ductility-based lifetime law · DuDeL

N_f(μ) = 34.63 × [(15 − μ) / (μ − 1)]^2.6

Nf is the equivalent number of excursions at ductility μ, defined for 1 < μ < 15. Ductility is calculated as μ = umax/uy.

Update at each plastic excursion

F_y,i = F_y,i−1 − F_y,0 / N_f(μ_i)

Each plastic excursion reduces the available yield strength relative to the initial Fy,0. The remaining strength is retained when the next earthquake begins.

Equation of motion and final criterion

mü(t) + ců(t) + f_s(u,ů) = −m a_g(t)

R = F_y,final / F_y,0 ≥ 0.55

Earthquake 1→Inelastic 2PIM→μ → DuDeL→Residual strength→Earthquake 2 → … → Earthquake n

The hPIM paper presents preliminary validation for linear systems; the case study shown here is an inelastic 2PIM application within SeSDA.

03 · Caso de estudio

Case study 1: sequence of three real earthquakes

The first available case study includes New Zealand (2010), Türkiye (2023) and Myanmar (2025). It evaluates inelastic excursions, strength, residual displacement and energy balance. Additional examples will be added in later versions.

FINAL CASE-STUDY RESULT

PASSED

Fᵧ,final/Fᵧ,0 = 0.9334 · mínimo propuesto ≥ 0.55

1 226.25 → 1 144.63 kN

Capacidad at yield initial → final

Reducción total: 6.656 % · strength retenida: 93.34 %

32Total inelastic excursions

3Consecutive ground-motion records

0.601Cumulative Eₕ/Eᵢ

−149.52 mmAccumulated residual displacement

Table 1. Step-by-step strength degradation

Earthquake / station	Component	PGA (m/s²)	Fᵧ before (kN)	Cᵧ before	uᵧ (mm)	Initial u (mm)	u max (mm)	Ductility μ	Excursions	Excursion μ: min / mean / max	Loss (kN)	Strength loss (%)	Fᵧ after (kN)
New Zealand · 2010-09-03 · M7.0 — Greendale (NZ GDLC)	Horizontal N55W · 305°	7.575	1 226.25	0.5000	31.06	0.00	101.79	3.28	8	0.84 / 1.87 / 3.28	1.19	0.097 %	1 225.06
Türkiye · 2023-02-06 · M7.8 — Sağlık Ocağı (TU 2708)	Este–Oeste	10.364	1 225.06	0.4995	31.03	−67.46	208.51	6.72	23	0.69 / 3.80 / 6.73	71.98	5.870 %	1 153.08
Myanmar · 2025-03-28 · M7.7 — Naypyitaw (GE NPW), DMH/GEOFON	Este–Oeste	5.617	1 153.08	0.4702	29.21	−106.42	178.71	6.12	1	6.12 / 6.12 / 6.12	8.45	0.689 %	1 144.63

PGA: peak ground acceleration · μ = umax/uy · excursion ductility listed as minimum / mean / maximum · percentage loss relative to the yield strength at the beginning of the event.

Table 2. Energy, residual strength and displacements

Earthquake	R = Fᵧ/Fᵧ₀	Residual displacement (mm)	Eₕ hysteretic (kJ)	Eᵢ input (kJ)	Damping energy (kJ)	Eₕ/Eᵢ	Balance error	DuDeL excursions
Earthquake 1	0.9990	−67.46	194.3	344.2	149.9	0.565	1.9 × 10⁻⁵	8
Earthquake 2	0.9403	−106.42	595.7	935.0	339.2	0.637	1.8 × 10⁻⁴	23
Earthquake 3	0.9334	−149.52	49.7	118.1	68.4	0.421	1.2 × 10⁻⁴	1

Values transcribed from the original case-study screenshots. The table gives energy values for individual earthquakes; sequence totals follow.

1 397.4 kJEᵢ: total input energy

839.7 kJEₕ: total hysteretic energy

557.5 kJTotal damping energy

60.1 %Overall Eₕ/Eᵢ

04 · Results visualization

Figures from case study 1

All figures preserve the supplied original results. They appear in THEK-framed panels with institutional branding, site URL and bibliographic identifiers.

Figure 1: Tabla original: degradation paso a paso — Ground-motion records, PGA, ductility, excursions and residual strength.

Figure 2: Tabla original: balance energético — Input, hysteretic and damping energy for each earthquake.

Figure 3: Evolución de la strength residual — Successive reduction of Fᵧ/Fᵧ₀ using DuDeL, including within individual earthquakes.

Figure 4: Ductilidad a lo largo de la sequence — Ductility histories for New Zealand, Türkiye and Myanmar.

Figure 5: Balance y disipación de energy — Accumulated input, hysteretic and damping energy across the sequence.

Figure 6: Desplazamiento de la estructura — Displacement time history; the residual state persists between events.

Figure 7: Earthquake 1: displacement e hysteresis — Displacement time history and force–displacement hysteresis loops for the New Zealand earthquake.

Figure 8: Earthquake 2: displacement e hysteresis — Calculated response and inelastic loops for the Türkiye earthquake.

Figure 9: Evaluación final: PASSED — The remaining strength exceeds the initial acceptance threshold of 55%.

Figures 1 and 2 preserve the original table panels, while the HTML tables above allow users to read and copy the values.

Note: the nine original technical figure images contain Spanish labels; the accompanying captions, data tables and explanations are provided in English.

04 · Second worked example

Case study 2: one building subjected to five earthquakes

A single structural model is subjected successively to five recorded ground motions. After each earthquake, SeSDA transfers the remaining yield capacity and structural state to the next analysis, applying the DuDeL law at inelastic excursions and the inelastic 2PIM/hPIM time integrator. The event records are a numerical loading sequence; their geographic locations are not the location of the same building, and the dates do not represent a chronological history of the building.

Five-event loading sequence

01Mexico · 2010 · M7.2

02Türkiye · 2023 · M7.8

03New Zealand · 2016 · M7.8

04Japan · 2011 · M6.6

05Japan · 2011 · M7.1

5Earthquakes

116Inelastic excursions

1,226.25 kNInitial strength

991.98 kNFinal strength

80.90%Residual capacity

19.10%Total strength loss

Step-by-step results for the five earthquakes

Step	Earthquake and station	PGA (m/s²)	Maximum ductility μ	Inelastic excursions	Strength loss (kN)	Strength loss (% of Fᵧ,₀)	Fᵧ remaining (kN)	Residual ratio	Eₕ (kJ)	Eᵢ (kJ)	Damping energy (kJ)	Eₕ/Eᵢ
1	Mexico · 2010-04-04 · M7.2 · El Centro; Array 11, McCabe School (NP 5058)	5.763	2.06	16	0.20	0.017	1226.05	0.9998	211.3	451.3	240.0	0.468
2	Türkiye · 2023-02-06 · M7.8 · Sağlık Ocağı (TU 2708)	10.364	3.83	21	3.42	0.279	1222.63	0.9970	593.4	939.3	345.8	0.632
3	New Zealand · 2016-11-13 · M7.8 · Kekerengu Valley Road (NZ KEKS)	11.881	6.21	55	155.30	12.665	1067.33	0.8704	1005.1	1685.5	680.3	0.596
4	Japan · 2011-04-11 · M6.6 · HOKOTA (JP IBR013)	5.847	5.54	0	0.00	0.000	1067.33	0.8704	0.0	51.5	51.5	0.000
5	Japan · 2011-04-07 · M7.1 · Shiogama (JP MYG012)	14.471	6.42	24	75.35	6.145	991.98	0.8090	425.5	712.8	287.0	0.597

PASSES THE PROPOSED CRITERION

Residual yield capacity Fᵧ,final / Fᵧ,₀ = 0.8090 ≥ 0.55

991.98 kN

Fᵧ,final

This result assesses only the proposed SeSDA residual-strength threshold for the supplied numerical example; it is not an independent verification of a real building or of all code requirements. Earthquake 4 had zero degrading excursions. The original screenshots are retained without fabricated time-history points.

Original numerical results: five-earthquake sequence

Original calculation output in Spanish; English titles, descriptions, and a complete readable results table are provided.

Step-by-step degradation: event details and demand.

Step-by-step degradation: energy and residual capacity.

Residual yield-capacity ratio during the five earthquakes.

Ductility time histories for the five records.

Cumulative input, damping and hysteretic energies.

Cumulative displacement over the full sequence.

Earthquake 1: displacement and hysteresis.

Earthquake 2: displacement and hysteresis.

Earthquake 3: displacement and hysteresis.

Earthquake 5: displacement and hysteresis.

05 · Third worked example

Case study 3: one building subjected to another five-earthquake sequence

This third numerical example applies a different sequence of five recorded ground motions to the same structural model. SeSDA transfers the residual yield capacity and structural state from one analysis to the next, using DuDeL for degradation and the inelastic 2PIM/hPIM time integration strategy. As in the other examples, the listed earthquakes define a numerical loading sequence; they do not mean that a real building physically traveled among those regions.

Five-event loading sequence

01New Zealand · 2010 · M7.0

02Japan · 2011 · M7.1

03Chile · 2017 · M6.9

04Türkiye · 2023 · M7.8

05Chile · 2015 · M8.3

5Earthquakes

56Inelastic excursions

1,226.25 kNInitial strength

1,215.98 kNFinal strength

99.16%Residual capacity

0.84%Total strength loss

Step-by-step results for the five earthquakes

Step	Earthquake and station	Channel	PGA (m/s²)	Maximum ductility μ	Inelastic excursions	Strength loss (kN)	Strength loss (% of Fᵧ,₀)	Fᵧ remaining (kN)	Residual ratio	Residual displacement (mm)	Eₕ (kJ)
1	New Zealand · 2010-09-03 · M7.0 · Greendale (NZ GDLC)	Horizontal N55W · 305°	7.575	3.28	8	1.19	0.097	1225.06	0.9990	-67.46	194.3
2	Japan · 2011-04-07 · M7.1 · Shiogama (JP MYG012)	East-West	14.471	3.60	23	2.89	0.235	1222.18	0.9967	6.35	445.0
3	Chile · 2017-04-24 · M6.9 · Torpederas, Chile (C1 VA01)	East-West	8.889	0.71	0	0.00	0.000	1222.18	0.9967	6.35	0.0
4	Türkiye · 2023-02-06 · M7.8 · Sağlık Ocağı (TU 2708)	East-West	10.364	4.38	21	5.96	0.486	1216.22	0.9918	-35.68	595.7
5	Chile · 2015-09-16 · M8.3	East-West	6.771	2.27	4	0.25	0.020	1215.98	0.9916	-37.75	6.2

PASSES THE PROPOSED CRITERION

Residual yield capacity Fᵧ,final / Fᵧ,₀ = 0.9916 ≥ 0.55

1,215.98 kN

Fᵧ,final

This example shows a comparatively mild cumulative degradation over five earthquakes. The third earthquake remained elastic and therefore produced no degradation, while the fourth earthquake generated the largest hysteretic demand among the supplied event-specific figures. Only the original screenshots provided for this example are included; no missing time-history plots were fabricated.

Original numerical results: five-earthquake sequence

Original calculation output in Spanish; English titles, descriptions, and a complete readable results table are provided.

Step-by-step degradation: residual capacity and hysteretic energy.

Earthquake 4: displacement and hysteresis.

05 · Scientific publications

Research papers and DOI links

Complete documentation of the SeSDA/DuDeL method and the hPIM integrator. Local PDF copies are included and available directly on this website.

PAPER · SeSDA / DuDeL

SeSDA — Sequential Seismic Degradation Analysis

Structural analysis and design method for earthquake sequences over the service life using the Ductility Degradation Law (DuDeL). Formulation, residual yield strength and the proposed 55% acceptance threshold.

DOI Zenodo SeSDA: to be confirmed. No DOI is attributed until its association with this publication is verified.

Open SeSDA paper (PDF, Spanish) ↗

PAPER · hPIM / 1PIM / 2PIM

hPIM — Higher-order Polynomial Integration Method

Formulation, stabilization and preliminary numerical validation of 1PIM and 2PIM for structural dynamics, compared with central differences and Newmark.

Zenodo: 10.5281/zenodo.22746001 ↗

SSRN: 10.2139/ssrn.7568078 ↗

Open hPIM paper (PDF, Spanish) ↗

Paper editions

The SeSDA/DuDeL paper is available in English and Spanish; the hPIM paper is supplied in Spanish. These original PDF files are included in the package.

SeSDA paper · English PDF SeSDA paper · Spanish PDF hPIM paper · Spanish PDF

Full PDF papers (original Spanish editions)

The SeSDA paper is included in both English and Spanish; the hPIM paper is included in Spanish.

SeSDA / DuDeL

Open / download PDF

hPIM / 1PIM / 2PIM

Open / download PDF

06 · Use and scientific cooperation

License to use the SeSDA system

System licensed by THEK Research Institute

Use, implementation and commercial exploitation of the software system require a license from THEK Research Institute. This website presents the method and its results; it does not provide public access to the computational engine.

Request a license by email ↗

Research, collaboration and inquiries

THEK Research Institute welcomes inquiries about academic collaboration, method applications, consulting, implementation and its scientific publications.

research@hithek.com

hithek.com ↗ · sesda.hithek.com ↗

SeSDA — Sequential Seismic Degradation Analysis

From a single earthquake to the full seismic history

Earthquake sequence

Ductility-based degradation

Inelastic time integration

Residual strength

DuDeL and dynamic response using 2PIM

Ductility-based lifetime law · DuDeL

Update at each plastic excursion

Equation of motion and final criterion

Case study 1: sequence of three real earthquakes

Table 1. Step-by-step strength degradation

Table 2. Energy, residual strength and displacements

Figures from case study 1

Original step-by-step degradation table

Original energy-balance table

Evolution of residual strength

Ductility throughout the sequence

Energy balance and dissipation

Structural displacement

Earthquake 1: displacement and hysteresis

Earthquake 2: displacement and hysteresis

Final assessment: PASSED

Case study 2: one building subjected to five earthquakes

Five-event loading sequence

Step-by-step results for the five earthquakes

Original numerical results: five-earthquake sequence

Step-by-step degradation: event details and demand.

Step-by-step degradation: energy and residual capacity.

Residual yield-capacity ratio during the five earthquakes.

Ductility time histories for the five records.

Cumulative input, damping and hysteretic energies.

Cumulative displacement over the full sequence.

Earthquake 1: displacement and hysteresis.

Earthquake 2: displacement and hysteresis.

Earthquake 3: displacement and hysteresis.

Earthquake 5: displacement and hysteresis.

Final acceptance decision from SeSDA.

Case study 3: one building subjected to another five-earthquake sequence

Five-event loading sequence

Step-by-step results for the five earthquakes

Original numerical results: five-earthquake sequence

Step-by-step degradation: event details and demand.

Step-by-step degradation: residual capacity and hysteretic energy.

Residual yield-capacity ratio during the five earthquakes.

Ductility time histories for the five records.

Cumulative displacement over the full sequence.

Earthquake 1: displacement and hysteresis.

Earthquake 2: displacement and hysteresis.

Earthquake 4: displacement and hysteresis.

Final acceptance decision from SeSDA.

Research papers and DOI links

SeSDA — Sequential Seismic Degradation Analysis

hPIM — Higher-order Polynomial Integration Method

Paper editions

Full PDF papers (original Spanish editions)

SeSDA / DuDeL

hPIM / 1PIM / 2PIM

License to use the SeSDA system

System licensed by THEK Research Institute

Research, collaboration and inquiries