Seismic Design of Geotechnical Structures for NCTIR

Abstract

This paper outlines key elements and the main findings for seismic design of geotechnical structures, i.e. earth retaining systems as well as natural and man-made slopes, and provides an unabridged roadmap for a streamlined design following the principles of value engineering and performance based design. Although emphasis is placed on the work that was carried out by North Canterbury Transport Infrastructure Recovery (NCTIR) on State Highway 1 following the 14 November 2016 Mw 7.8 Kaikōura Earthquake, the derived conclusions are valid for any other NZ Transport Agency (NZTA) related geo-mechanical Performance Based Design.

NZTA Bridge Manual Third Edition (NZTA BM3), Amendment 2 (2016), AASHTO LRFD Bridge Design Specification (2016), Eurocode 8 Part 5 (2004), FHWA-NHI-11-032 (2011), and MBIE/NZGS Module 6 (2017) are compared and discussed.

1. Introduction

During the 14 November 2016 Mw 7.8 Kaikōura Earthquake, slope and embankment instability was observed at several locations along Northern State Highway 1 of the South Island of New Zealand. Extensive geological and geotechnical investigations were conducted on landslide-affected areas. Parametric slope stability analyses were carried out for the damaged embankments (considering the actual geometry at the time of the instability and that of the new construction) with the objective of realignment and resilience assessment.

NZTA BM3 (2004, 2016), with an emphasis on post-earthquake performance, was the basis of all the aspects of realignment design. NZTA BM3 manual allows for any departures from specified limitations whenever they cannot be practical or are uneconomical to satisfy as long as they are suitably established, internationally recognized and widely used.

According to NZTA BM3, soil structures are categorized into two main groups, namely slopes and retaining structures, with their own specific seismic performance criteria that relate to their level of importance, height, association with bridges and protective effect to adjacent properties. The Author believes that due to the many adjustments and departures applied frequently and by engineers with different levels of expertise, structures that belong to the same class are often treated differently. This creates uncertainties on how to properly follow the regulations.

In this paper an attempt is made to fill the gap in the knowledge and minimize uncertainties in NZTA BM3 arising from high seismic demand and/or cost consideration using technically detailed bases that are widely and internationally acceptable for geotechnical earthquake engineering and Performance Based Design.

2. Theoretical Background

Earthquake-induced ground accelerations can result in significant inertial forces in slopes, embankments, and retaining structures and these forces may lead to instability (i.e. failure) or permanent deformation. Current practice for the analysis of the performance of slopes, embankments, and retaining structures during earthquake loading is to use any or a combination of the related methods:

• Limit Equilibrium using a pseudo-static representation of the seismic forces;
• Displacement-Based Analysis using the Newmark sliding block concept for preliminary design and more rigorous, stress-strain, numerical modelling methods for advanced and detail design;

The selection between the two approaches would normally be made on the basis of the complexity of the slope geometry and soil conditions within the slope, the level of ground shaking, and the performance based issues for earthworks design.

2.1. Limit Equilibrium Pseudo-static Stability Analysis

In this approach induced seismic loads are modelled as a static horizontal force in conventional limit equilibrium analysis to either verify that the capacity (C) is greater than the demand (D) or to evaluate the capacity/demand (C/D) ratio (or factor of safety, FoS) for comparison to an acceptable value. The seismic load is defined by means of seismic coefficients k_h and k_v (horizontal and vertical component of acceleration, respectively), which are determined on the basis of the peak ground acceleration (α_max or PGA), the earthquake magnitude (Mw), the geometry of the soil mass being loaded, and a performance criterion (i.e. the allowable displacement). This type of analysis is generally referred to as a pseudo-static stability analysis.

2.1.1 Selection of seismic coefficient

The results of pseudo-static analyses are critically dependent on the value of the seismic coefficient, kh. Selection of an appropriate pseudo-static coefficient is the most important, and most difficult, aspect of a pseudo-static stability analysis. The seismic coefficient controls the pseudo-static force on the failure mass, so its value should be related to some measure of the amplitude of the inertial force induced in the potentially unstable material.

If the slope was rigid, the inertial force induced on a potential slide would be equal to the product of the actual horizontal acceleration and the mass of the unstable material. This inertial force would reach its maximum value when the horizontal acceleration reached its maximum value.

The seismic coefficient is typically assumed to be some function of the site-specific Horizontal Peak Ground Acceleration (α_max). Seed and Martin (1966) and Dakoulas and Gazetas (1986), using shear beam models, showed that the value of k_h for earth dams depends on the size of the failure mass.

In recognition of the fact that actual slopes and many retaining structures are not a rigid body and that the peak acceleration exists for only a short time, the pseudo-static coefficients used in practice generally correspond to acceleration values well below α_max.

The seismic coefficient can range from significantly less than 50% of the α_max to the full α_max, depending on the slope/retaining structure height, the magnitude of the earthquake, performance requirements, and the designer’s views. The α_max can be height-adjusted. This adjustment depends upon the seismic environment, and increases with slope/retaining structure height.

The design seismic coefficient and associated minimum required C/D ratio are selected such that behaviour of the slope or retaining structure, in terms of permanent deformation, is within a range considered acceptable. A C/D ratio of less than 1.0 when using the height-adjusted α_max as the seismic coefficient implies some permanent movement of the slope or retaining structure.

2.2.2 Maximum seismic coefficient

Madabhushi et al. (2009) explain that the maximum acceleration, α_lim, which can be transmitted through a soil stratum in a seismic event is limited by the shear strength of the soil. This limiting acceleration can be estimated using the below relationships.

• For dry granular soil (cohesionless) the peak limiting acceleration is given by

where φ’ is the effective friction angle

• For fine grained soil (cohesive) the equivalent relationship is given by

where s_u is the undrained shear strength at depth h, and γ is the average bulk unit weight of the soil mass.

Application of these relationships indicates limiting horizontal accelerations of between 0.5g and 0.8g for dry granular soils, and 0.5g for depths approximately greater than 5m for fine grained soils. Consequently, the horizontal coefficient of acceleration (k_h=0.5α_max for slopes or k_h=0.5α_max or 0.67α_max for earth retaining structures) should not be selected to be greater than 0.4g.

When a design α_max greater than 0.8g is required then soil mass failures are expected. To complete the design and to assess the site response and performance, time history analyses, using finite element or finite difference based methods, or the advanced method discussed in the NZTA BM3 Section 5.4.2 should be employed.

2.2. Displacement-Based Seismic Stability Analysis

In contrast to the limit equilibrium approach, the displacement-based approach involves the explicit calculation of cumulative seismic deformation. The potential failure mass is treated as either a rigid body or deformable body, depending on whether a simplified Newmark sliding block approach or more advanced numerical modelling is used.

The purpose of the Newmark (1965) method is to estimate the slope deformation for those cases where the pseudo-static FoS is less than 1.0 (i.e. the failure condition). The Newmark (1965) method assumes that the slope will deform only during those portions of the earthquake when the out-of-slope earthquake forces cause the pseudo-static FoS to drop below 1.0. When this occurs, the slope will no longer be stable, and it will be accelerated downslope. The longer that the slope is subjected to a pseudo-static FoS below 1.0, the greater the slope deformation. On the other hand, if the pseudo-static FoS drops below 1.0 for a mere fraction of a second, then the slope deformation will be limited.

A limitation of the Newmark (1965) method is that it may prove unreliable for those slopes that do not tend to deform as a single block. An example is a slope composed of dry and loose granular soil (i.e. sands and gravels). The individual soil grains that compose a dry and loose granular soil will tend to individually deform, rather than the entire slope deforming as one single block. In a sloping environment, the individual soil particles not only will settle, but also will deform laterally in response to the unconfined slope face.

Bray et al. (2018) state that the pseudo-static slope stability procedures and Newmark sliding block analyses form the basis for a preliminary estimate of the expected seismic displacement of the earth system. However, for critical earth systems, or when liquefaction may occur, dynamic nonlinear effective stress analyses using finite-element or finite-difference methods with robust soil constitutive models may be employed.

It is important to note that the following methods may be employed depending on the design stage, the project’s complexity, and the level of associated risk.

Preliminary- Concept Design Stage

• Newmark sliding block; and
• Pseudo-static slope stability procedures;

Detailed Design Stage, Critical Earth Systems, and Liquefaction

• Dynamic nonlinear effective stress analyses using finite-element or finite-difference methods with robust soil constitutive models; and
• Advanced quasi-static effective stress analyses (not appropriate for liquefaction) using finite-element or finite-difference methods with robust soil constitutive models.

3. Codes and Guidances

3.1 NZTA Bridge Manual Third Edition, Amendment 2 (2016)

According to NZTA BM3, earth retaining systems cover the following elements:

• Non-integral bridge abutments and independent retaining walls associated with bridges;
• Retaining walls not associated with bridges;
• Earth retaining structures (including mechanically stabilised walls and slopes); and
• Slopes designed on the basis of undergoing displacement.

These are classified into the following categories:

• Gravity (concrete, gabion, crib) and reinforced concrete cantilever walls;
• Anchored gravity, cantilever, and soldier pile walls; and
• Mechanically stabilised earth (MSE) walls including soil-nailed walls, reinforced soil walls (inextensible and extensible reinforcement).

The designer shall derive the design loads on the structure in accordance with NZTA BM3 Section 6.2, taking into consideration the flexibility and likely deformation of the structure, and the allowable displacement or deformation of the system. Careful consideration shall be given to the interaction between the structure, the ground and foundations, under static, dynamic, earthquake and construction conditions. The deformation and displacement of the structure shall be compatible with the performance requirements for the structure and its interaction with adjacent or supported structures and facilities. However, due to high seismic demand and/or cost considerations various departures are frequently lodged. Because these changes are introduced by designers with various levels of expertise and experience, in many cases similar structures located in similar settings are treated differently. The main features with respect to geotechnical design stipulated in NZTA BM3 are outlined below;

• Section 6.1.2 Table 6.1 stipulates the maximum acceptable limits of settlements (total and differential) and total horizontal displacements. These requirements are provided without a direct link to a referenced methodology that relates them with a range of seismic coefficients used in pseudo-static stability analysis.
• Section 6.2.2 stipulates that the design earthquake loads to be applied to soils, rock and independent soil structures shall be derived as set out in the same section. The peak horizontal ground acceleration to be applied shall be unweighted and derived for the relevant return period.
• Section 6.2.3 stipulates that for the structural design of earth retaining structures the design horizontal ground acceleration to be used in computing seismic inertia forces of non-integral abutments and independent walls and of the soil acting against them shall be weighted and derived for the relevant return period and hazard factor.
• Section 6.3.2 stipulates that the factor of safety against instability shall be assessed using conventional slope stability analysis with load and strength reduction factors of one, and the seismic coefficient, k_h, associated with the relevant earthquake accelerations as set out in 6.2.2. If the factor of safety is less than 1 and the failure mechanism is not brittle (such as in rocks where the initiation of failure could substantially reduce the strength of the materials), then the critical seismic coefficient associated with the ground acceleration at which the factor of safety is one, k_γ shall be assessed using large strain soil parameters consistent with the likely displacements due to earthquake shaking.
• When k_γ< k_h the displacement likely at the design ultimate limit state seismic response, and under the Major Event (ME) associated with bridge collapse avoidance, shall be assessed using moderately conservative soil strengths consistent with the anticipated stress-strain behaviour and relevant strain levels and a Newmark sliding block displacement approach. Displacements may be assessed using the methods described by Ambraseys and Srbulov, Jibson, Bray and Travasarou.
• Section 6.4.1 specifies that for the assessment of the stability of embankments using pseudo-static seismic analysis, the peak ground acceleration to be applied shall be derived in accordance with 6.2 for the annual probability of exceedance associated with the importance of the slope as defined in 2.1.3. In applying the pseudo-static analysis, the α_max shall not be factored down by a structural performance factor or any other factor. However, slopes designed on the basis of undergoing displacement are discussed in Section 6.6.1, where it is specified that embankments designed on the basis of permitting displacement under earthquake response, the requirements of 6.6.9 shall also be satisfied.
• Section 6.6.9 stipulates that vertical accelerations shall be taken into consideration in the design of retaining structures, and that earth retaining structures and slopes may be designed to remain elastic under the design earthquake load specified in 6.2.2 or to allow limited controlled permanent outward horizontal displacement under strong earthquake shaking.

3.2 Supplementary Codes and Guidance

NZTA BM3 Section 6.6.2 and 6.6.9 (in the specific case of mechanically stabilized earth walls and slopes) set out a comprehensive list of design standards and codes of practice that provide guidance on the design of retaining structures, including Road Research Unit Bulletin 84 (RRUB84), NZTA Research Report 239 (RR239), Eurocode 8 – Part 5 and AASHTO LRFD Bridge Design Specifications 2014 which can be used as supplementary documents to clarify any ambiguities. AASHTO and Eurocode are recommended to provide guidance on the design of retaining structures. FHWA-NHI-11-032, LRFD Seismic Analysis and Design of Seismic Design of Transportation Geotechnical Features and Structural Foundations, Reference Manual, (2011) along with Eurocode can provide design methods for both slope (and embankment) and retaining structures.

RRUB84 is stipulated in the NZTA BM3 Sections 6.6.2 and 6.2.4 as the basic document to be used to distinguish the wall elements among rigid/elastic, stiff, and flexible depending on the wall movements. RRUB84 defines three types of walls with different displacement characteristics, retained soil behaviour, and associated seismic coefficients. RR239 identifies the difference between MSE Walls and MSE Slopes based on their face inclination from the vertical. Different types and associated design horizontal seismic coefficients are presented in Table 1 below.

Table 1: Road Research Unit Bulletin 84 and Research Report 239 Retaining wall types

* MSE Walls have faces that are less than 30° inclination from the vertical, while MSE Slopes have faces that are more than 30° from the vertical.

3.3. AASHTO LRFD Bridge Design Specifications (2016)

AASHTO 2016, Section 11.6.5 stipulates that the seismic horizontal acceleration coefficient (k_h) for computation of seismic lateral earth pressures and loads shall be determined on the basis of the α_max at the ground surface (i.e., k_h0 = F_αmax α_max = As, where k_h0 is the seismic horizontal acceleration coefficient assuming zero wall displacement occurs).

The seismic vertical acceleration coefficient, k_γ, should be assumed to be zero for the purpose of calculating lateral earth pressures, unless the wall is significantly affected by near fault effects, or if relatively high vertical accelerations are likely to be acting concurrently with the horizontal acceleration.

If the wall is free to move laterally under the influence of seismic loading, and if lateral wall movement during the design seismic event is acceptable to the Owner, k_h0 should be reduced to account for the allowed lateral wall deformation. The selection of a maximum acceptable lateral deformation should take into consideration the effect that deformation will have on the stability of the wall under consideration, the desired seismic performance level, and the effect that deformation could have on any facilities or structures supported by the wall.

Where the wall is capable of displacements of 25mm to 50mm or more during the design seismic event, k_h may be reduced to 0.5k_h0 without conducting a deformation analysis using the Newmark method (Newmark, 1965) or a simplified version of it. This reduction in k_h shall also be considered applicable to the investigation of overall stability of the wall and slope.

A Newmark sliding block analysis or a simplified form of that type of analysis should be used to estimate lateral deformation effects, unless the Owner approves the use of more sophisticated numerical analysis methods to establish the relationship between k_h and the wall displacement. Simplified Newmark analyses should only be used if the assumptions used to develop them are valid for the wall under consideration.

Three recommended methods to estimate wall seismic acceleration considering wave scattering and wall displacement are given in Section A11.5 of AASHTO 2016.

a) Kavazanjian et al. (1997): It does not directly address wave scattering and, since wave scattering tends to reduce the acceleration, the first method is likely conservative.
b) NCHRP Report 611—Anderson et al. (2008): It uses a simplified model that considers the effect of the soil mass, but not specifically the effect of the wall as a structure.
c) Bray et al. (2017), Bray et al. (2010), and Bray and Travasarou (2009): It provides a simplified response spectra for the wall, considering the wall to be a structure with a fundamental period. It estimates the value of k_h applied to the wall mass considering both the wave scattering and lateral deformation of the wall.

The three alternative design procedures should not be mixed together in any way.

3.4. Eurocode 8 Design of Structures for Earthquake Resistance, Part 5 (2004, 2013)

3.4.1. Slope Stability

Eurocode 8, Clause 4.1.3, stipulates that a verification of ground stability shall be carried out for structures to be erected on or near natural or artificial slopes, in order to ensure that the safety and/or serviceability of the structures is preserved under the design earthquake. Under earthquake loading conditions, the limit state for slopes is that beyond which unacceptably large permanent displacements of the ground mass take place within a depth that is significant both for the structural and functional effects on the structures.

Clause 4.1.3.2 stipulates that an increase in the design seismic action shall be introduced, through a topographic amplification factor, in the ground stability verifications for structures with importance factor γI greater than 1.0 on or near slopes.

Clause 4.1.3.3 stipulates that the response of ground slopes to the design earthquake shall be calculated either by means of established methods of dynamic analysis, such as finite elements or rigid block models, or by simplified pseudo-static methods.

In modelling the mechanical behaviour of the soil media, the softening of the response with increasing strain level, and the possible effects of pore pressure increase under cyclic loading shall be taken into account. The design seismic inertia forces FH (horizontal) and FV (vertical) acting on the ground mass, for the horizontal and vertical directions, respectively, in pseudo-static analyses shall be taken as:

FH = 0.5α * S * W

FV = ±0.5FH if the ratio a_vg/a_g is greater than 0.6

FV = ±0.33FH if the ratio a_vg/a_g is not greater than 0.6

Where: α is the ratio of the design ground acceleration on type A ground (rock site), a_g, to the acceleration of gravity g (α=a_g/g), a_vg is the design ground acceleration in the vertical direction, a_g is the design ground acceleration for type A ground, S is the soil parameter of EN 1998-1:2004, 3.2.2.2, and W is the weight of the sliding mass.

3.4.2. Earth Retaining Structures

Section 7.1 stipulates that permanent displacements, in the form of combined sliding and tilting, the latter due to irreversible deformations of the foundation soil, may be acceptable if it is shown that they are compatible with functional and/or aesthetic requirements.
Section 7.3.1 stipulates that any established method based on the procedures of structural and soil dynamics, and supported by experience and observations, is in principle acceptable for assessing the safety of an earth-retaining structure.
The following aspects should be accounted for:

a) The generally non-linear behaviour of the soil in the course of its dynamic interaction with the retaining structure;
b) The inertial effects associated with the masses of the soil, of the structure, and of all other gravity loads which might participate in the interaction process;
c) The hydrodynamic effects generated by the presence of water in the soil behind the wall and/or by the water on the outer face of the wall.
d) The compatibility between the deformations of the soil, the wall, and the tiebacks, when present.

Section 7.3.2.2 stipulates that for the purpose of the pseudo-static analysis, the seismic action shall be represented by a set of horizontal and vertical static forces equal to the product of the gravity forces and a seismic coefficient. The vertical seismic action shall be considered as acting upward or downward so as to produce the most unfavourable effect.

The intensity of such equivalent seismic forces depends, for a given seismic zone, on the amount of permanent displacement which is both acceptable and actually permitted by the adopted structural solution. In the absence of specific studies, the horizontal (k_h) and vertical (k_γ) seismic coefficients affecting all the masses shall be taken as:
k_h = α * S / r

k_γ = ±0.5k_h if a_vg/a_g is larger than 0.6

k_γ = ±0.33k_h otherwise

Where, the factor r takes the values listed in Table 2 depending on the type of retaining structure. For walls not higher than 10m, the seismic coefficient shall be taken as being constant along the height.

Table 2: EC8 reduction factor based on type of retaining structure

* Conceptually, the factor r is defined as the ratio between the acceleration value producing the maximum permanent displacement compatible with the existing constraints, and the value corresponding to the state of limit equilibrium (onset of displacements). Hence, r is greater for walls that can tolerate larger displacements.

3.5. FHWA-NHI-11-032, LRFD Seismic Analysis and Design of Transportation Geotechnical Features and Structural Foundations, Reference Manual (2011)

Section 6.2.2 states that most slopes can accommodate at least a limited amount of seismically-induced movement. Therefore, the seismic coefficient is always equal to less than the height-adjusted α_max and typically is on the order of 50% of the height-adjusted α_max for allowable seismic slope deformations on the order of 25mm to 50mm. Therefore, the seismic coefficient will never be more than the site-specific α_max. It is typically equal to or less than 50% of the site-specific α_max, and in some cases it can be equal to or less than 25% of the site-specific α_max.

Section 6.2.3 states that in contrast to the limit equilibrium approach, the displacement-based approach involves the explicit calculation of cumulative seismic deformation. The potential failure mass is treated as either a rigid body or deformable body, depending on whether a simplified Newmark sliding block approach or more advanced numerical modelling is used.

The values of k_max are the maximum possible values and only apply to walls of less than 6m in height that cannot accommodate lateral displacement on the order of 25mm to 50mm in the design earthquake. For walls 6m tall or higher, the value of k_max can be reduced to account for spatial incoherence (also referred to as wave scattering), or averaging of the ground acceleration over the active (or passive) wedge. For walls that can accommodate at least 25mm to 50mm of lateral displacement in the design earthquake, another reduction for system ductility (allowable lateral displacement) can be applied. These adjustments can be applied to the maximum seismic coefficient to evaluate the design seismic coefficient, k_h.

If the earth retention system can be allowed to translate laterally, the seismic coefficient can be reduced to account for the ductility of the wall system. As discussed in the Newmark method permanent seismic displacement is a function of the yield acceleration, the acceleration at which seismic displacement is initiated. For a retaining wall, the yield acceleration is the seismic coefficient at which the horizontal forces (the demand) on the wall system equal the lateral resisting forces (its capacity).

3.6 Earthquake Geotechnical Engineering Practice, Module 6: Earthquake Resistant Retaining Wall Design (2017)

Module 6 is part of a series of guidance modules developed jointly by the Ministry of Business, Innovation & Employment (MBIE) and the New Zealand Geotechnical Society (NZGS). This document deals with earthquake resistant retaining wall design only. The New Zealand Building Act considers the retaining structures as buildings which are as a consequence subject to the requirements of the New Zealand Building Code.

The module discusses in Section 5 the limit equilibrium pseudo-static analysis method and stipulates the derivation of the horizontal coefficient of acceleration, k_h, from the unweighted horizontal peak ground acceleration, α_max. In Clause 5.1, k_h is calculated by the following equation:

Where, α_max is the unweighted horizontal peak ground acceleration, A_topo is the topographic amplification factor, and W_d is the wall displacement factor used to reduce the α_max

The topographic amplification factor, A_max, is adapted from Eurocode 8, Part 5: Part 5: BS EN 1998-5: 2004 (Annex A) and is further refined.

In Section 5.3 it is recognised that designing flexible retaining walls to resist the full ULS peak ground acceleration (α_max) is unnecessary and uneconomical in most cases. Most retaining wall systems are sufficiently flexible to be able to absorb high transient ground acceleration pulses without damage because the inertia and damping of the retained soil limits deformations. Wave scattering effects also reduce the accelerations in the backfill to values less than the peak ground motions adjacent to retaining walls. Also, in most cases, some permanent wall deformation is acceptable for the ULS case (refer to Table 4.1).

A non-exhaustive list of performance requirements is provided in Section 4.2 Table 4.1. The wall displacement factor, Wd, is selected according to the amount of permanent displacement that can be tolerated for the particular design case. Reducing the design acceleration by W_d implies that permanent movement of the structure and retained ground is likely to occur. Several other assumptions are implied, including that:

a) The retaining structure is sufficiently resilient or ductile to withstand the movement;
b) The supporting soils are not susceptible to strength loss with straining; and
c) Any supported structures or services can tolerate the movement.

The intent of that table is to give guidance on selecting seismic design parameters for retaining structures. The movements indicated are for typical cases and represent permanent movement from a single design earthquake for selecting appropriate design acceleration coefficients. Instantaneous dynamic movements during an earthquake will be greater and there may be additional movements from gravity loads prior to an earthquake. Some buildings will be more sensitive to movement than others and it is the designer’s responsibility to ensure that movements can be tolerated.

4. Discussion and Recommendation

The five documents presented in the previous sec