Section 5 Underwater explosion (shock)

5.1.1 There are two principal loading mechanisms associated with the underwater detonation of a conventional high explosive ordnance:

• shock wave loading;
• bubble flow loading.

5.1.2 The energy released is in general, equally divided between shock wave energy and the energy contained within the superheated high pressure bubble of gaseous explosion products.

5.1.3 The shock wave generated as the detonation wave passes into the water is a highly non-linear pressure pulse which propagates at a speed well in excess of the speed of sound in water (approximately 1500 m/s). However, within a few charge radii of the detonation point, it can be mathematically defined as an acoustic pressure pulse travelling at the speed of sound. Its amplitude falls off inversely with distance and its profile can be characterised by a pulse which has an infinite rise to a peak pressure followed by an exponential decay. The peak value and decay rate at a given field point are given by the similitude equations/coefficients for the explosive material.

5.1.4 In the meantime, the gas bubble begins to expand against the ambient hydrostatic pressure displacing water radially outward as incompressible flow. As it expands, it loses pressure and temperature but the inertia of the outwardly flowing water leads to an overshoot of the equilibrium state so that at maximum bubble radius, the gas pressure is well below the ambient. This initiates the collapse sequence, the gas bubble is recompressed, slowly at first but then rapidly, to a minimum volume by the hydrostatic forces. Because of the generation of a large pressure in the bubble during this stage the bubble begins to expand again and several other cycles may follow. The gas bubble and water interaction can be thought of as a gas spring - mass system. It has a periodicity associated with it but because of energy losses during the process, the spring constant and mass changes over each cycle leading to a change in the periodicity. At each minimum, that is, each recompression, additional pressure pulses are emitted which become weaker with each oscillation as shown in Figure 2.5.1 Shock wave bubble pulse.

Figure 2.5.1 Shock wave bubble pulse

5.1.5 The bubble is pulsating in a gravitational field and will have a tendency to migrate to the water/air boundary (the free surface). However, this bodily motion of the bubble centre may be influenced by the proximity of other boundaries such as the seabed or a nearby ship structure. The rate at which a bubble will migrate to the free surface is a function of the buoyancy forces generated when it is at its maxima and of the drag forces it experiences as it moves through the water. Because these drag forces are small when the bubble is at its minima, it tends to migrate vertically upwards more rapidly when at its smallest volume.

5.1.6 The fluid flow generated by the bubble dynamics is an important loading mechanism for a structure, within its sphere of influence. Normally bubble loading can be ignored if the bubble never approaches within a distance of around ten times the maximum bubble radius. The important feature of the bubble loading is its low frequency which is ideally suited to induce ship hull girder flexural motion. This flexural motion is commonly referred to as hull girder whipping. This loading mechanism is dealt with in Vol 1, Pt 4, Ch 2, 6 Whipping. If the bubble is within one bubble radius of the ship structure, it is likely to form a jet which will impact on the structure. This bubble collapse mechanism will cause extensive local damage. It is generally not possible to efficiently design against this loading event for a NS2 or NS3 ship. For a NS1 ship there may be sufficient residual strength to withstand such damage, but the extent of the damage will need to be determined by a specialist calculation and the capability of the hull using a residual strength assessment, see Vol 1, Pt 4, Ch 2, 7 Residual strength.

5.1.7  The shock wave loading is greatest at a point on the structure nearest to the detonation event and because of the fall-off with distance and the narrowness of the pulse width, it can be thought of as a local loading event. (In contrast, the bubble induced whipping of the hull girder is considered a global loading event.) The remainder of this section will focus on the shock loading event only.

5.1.8 There are no simple analytical or numerical techniques for reliably determining the shock resistance of a structure. A measure of the resistance to shock loading can be achieved by good design of the details of the structure to avoid stress concentrations which may lead to rupture. It is also possible to ensure that the plating thickness is matched to the assumed performance of the joints using a simple damage law. The inertial loads on the ship's structure caused by the equipment and its seatings can be determined by time domain analysis.

5.1.9 The shock performance of a ship's hull structure can be assessed solely by conducting shock tests (usually at scale). However, cost usually precludes this approach and a better strategy is to combine tests to determine failure criteria with numerical modelling using Finite Element methods. This complementary experiment /numerical simulation approach reduces the amount of testing required and also provides a method for extrapolating to full scale from scaled experiments.

5.1.10 Generally, for a normal ship structure, the explosion required to cause uncontrollable flooding or total loss of propulsive power or loss of mission system effectiveness (radars, electronics, etc.) is much less than that required to cause failure of a hull designed for normal sea loads.

5.1.11 Due to operational requirements, some vessel types, such as minesweepers, will be required to resist repeated shock loading at a specified level without degradation of the system or structural performance. Such vessels will also be expected to survive a single attack at a considerably higher shock loading level.

5.2.1 The actual threat level used in the calculation of performance and the areas of the ship to be protected by this design method are to be specified by the Owner and will remain confidential to LR.

5.2.2 Loading levels may be specified with varying degrees of structural and system degradation to define the shock performance of the vessel. An important consideration is the balance that has to be achieved between system functionality and structural performance.

5.2.3 Two performance bounds can be considered for the shock response of structure:

• The first performance bound (lower bound) relates to the onset of material yield (assuming that careful design has ensured that no buckling will occur before this state is reached). This level is useful to know as it may have consequences for system functionality. For example, there may be problems associated with equipment mis-alignment because of the permanent set of the supporting structure.
• The second performance bound (upper bound) relates to removal or rupture of material; this being the loading level at which there is no longer sufficient residual hull girder strength to resist normal environmental loading. This is addressed in a separate assessment which is defined by the residual strength notations RSA1, RSA2 or RSA3 in Vol 1, Pt 4, Ch 2, 7 Residual strength. In conventional naval ships, this upper bound will be significantly higher; but there will be little, if any, system functionality.

5.3.1 The shock performance required is to be specified by the Owner and is to include requirements for:

• Local strength assessment;
• Detailed design;
• Seat design, shock mounts and system hangers;
• Hull valve design and integration;
• Global strength assessment;
• Shock qualification/testing of equipment;
• 1st of class shock trial.

It is recommended that seats, valves, piping and equipment are categorised into:

• equipment required to be capable of operation after the specified shock event;
• equipment that is required to be captive, with reduced or no operational capability after the specified shock event;
• equipment which has no requirements after the specified shock event.

See also Vol 2, Pt 1, Ch 1, 3.1 Categories 3.1.1.

5.3.2 Ships that comply with the minimum or enhanced requirements of this Section will be eligible for the shock notation SH.

5.3.3 For ships where the machinery is in class (LMC notation), and shock requirements for machinery and equipment are specified, the requirements of Vol 2, Pt 1, Ch 3, 4.11 Machinery shock arrangements are to be complied with.

5.3.4 For the minimum shock capability, the design emphasis should focus on maintaining a high level of system functionality and reducing the risk of flooding.

5.3.5 For the assignment of the SH notation, the minimum requirement is for the structure to be designed to resist normal environmental loads in accordance with the Rules. For NS1 ships, the inherent ruggedness in the Rules is sufficient for the structure to resist a low level threat. For NS2 and NS3 ships, the integrity of the hull plate and stiffeners is to be verified, using the simple formulae for pressure in Vol 1, Pt 4, Ch 2, 5.4 Local strength assessment 5.4.1, and comparing the response to a specified standard. In addition, the hull valves below the waterline are to comply with the requirements of Vol 1, Pt 4, Ch 2, 5.8 Design guidance for hull valves, piping and seals.

5.3.6 The minimum local assessment required by Vol 1, Pt 4, Ch 2, 5.3 Notation assessment methodology 5.3.5 can be enhanced by undertaking a more complex assessment as defined in Vol 1, Pt 4, Ch 2, 5.4 Local strength assessment, which accurately models the physics of the rapid, dynamic, fluid structure interaction problem.

5.3.7 In addition to the analysis, the SH notation can be enhanced by selecting detail design requirements to reduce the risk of fracture initiation and structural collapse, based on historical work on shock. Details are provided in Vol 1, Pt 4, Ch 2, 5.5 Detail design guidance.

5.3.8 The SH notation may be further enhanced by undertaking shock trials in accordance with established procedures, on the first ship in the class. The magnitude of the test is normally less than the design value for the hull and at a level that is appropriate for the equipment and systems.

5.3.9 Global assessment may be undertaken for the SH notation, using the residual strength procedures outlined in Vol 1, Pt 4, Ch 2, 7 Residual strength with the extent of damage being defined from the results of the local strength assessment rather than the damage radii. For the RSA1 procedure, the damaged structure is to be removed from the analysis. For the RSA2 or RSA3 procedure, if the damage is limited, the geometry of the damaged structure can be modelled and if the damage is severe, the structure is to be removed from the analysis. The structure is considered acceptable when the hull girder is able to withstand the design loads as specified in Vol 1, Pt 5 Environmental Loads.

5.4.1 For the notation SH, a simple analysis can be performed which allows the motion response at any point in the ship to be determined. This can be derived from experimental results or the Taylor plate equations given below. Once the motion response is known, the damage potential can be determined by comparing the response to a specified standard.

Maximum velocity

V max

=

m/s

Time to maximum velocity

t max

=

seconds

where

z	=
u	=
θ	=	decay constant of explosive charge in seconds
P m	=	peak pressure in N/mm2
ρ	=	density of water in kg/m3
c	=	speed of sound in water in m/s
m	=	structural mass per unit area in kg/m3.

5.4.2 A more complex assessment method can be used to enhance the SH notation. Methods can be used which accurately model the physics of the shock event. At the simplest level, a finite element model of the structure coupled with a suitable boundary element from proprietary software may be used.

5.4.3 For complex ships such as multi-hull designs a boundary element approach may not be suitable and a volume element approach should be used. Also, if non-linear fluid behaviour is important (i.e. hull cavitation or bulk cavitation), then a volume element approach should be used, unless the finite element or boundary element code used has a suitable cavitation model.

5.4.4 The assessment method or analysis used should be validated against shock trial results and the evidence made available. As an alternative to analysis, full or large-scale shock trials of a section of the ship can be used to validate the proposed design. For novel design arrangements or ship types, a combination of trials and analysis may be necessary, the requirements of which will depend on the threat level and type of structure or ship design.

5.4.5 Any finite element analysis performed for local strength assessment is to be in accordance with the requirement of this Section for assignment of the SH notation.

5.4.6 The extent of the analysis model is to be from about 0,35L _R to 0,55L _R and encompass at least two major compartments and three watertight bulkheads. It is to be sufficiently large to avoid reflections within the structure from the boundaries, for the threats considered. For the assessment of structural strength, the structure need only be modelled to 1,0 m above the design water line. If the model is to be used to determine equipment response, all structure within that section should be modelled.

5.4.7 The model, or versions of the model, should encompass representative integral tank arrangements and hull penetrations, stabiliser inserts, hull valves, the failure of which could lead to uncontrollable flooding. Penetrations, the failure of which will not lead to significant flooding or damage, need not be considered. The tanks and penetrations need not actually be in the section under consideration but should be sufficiently similar to represent structure outside the region modelled.

5.4.8 All masses above 100 kg should be included in the model together with an approximation of the mounting system if applicable.

5.4.9 The model should include at least one major machinery item or raft.

5.4.10 The response of hull panels depends upon a large number of variables which are both design and attack geometry dependent. To simplify the task, the following assumptions can be made:

• The charge detonates in the worst location, perpendicular to the structure under consideration.
• All welding is continuous and there are no manufacturing or material defects in the panels.

5.4.11 During the analysis, appropriate elements are to be used to couple the fluid medium and the structural model.

5.4.12 The shock wave can be represented by an exponentially decaying, infinite rise time pressure pulse which sweeps across the structure at the speed of sound.

5.4.13 Non-linear structural modelling can be used in finite element analyses. If used, stiffeners should be modelled explicitly using shell elements of the appropriate thickness. Stiffener flanges should be modelled with at least two elements per half width or flange. Initial imperfections in the hull plating are to be taken into account prior to the dynamic loading analysis.

5.4.14 The structure is considered acceptable when:

• Elastic deflections are less than the temporary limits of machinery and systems.
• Permanent deflections are less than the limits of machinery and systems.
• Deflections and strain are less than the limits of the structure or applicability of the analysis method.

5.5.1 For enhanced shock performance, any of the following design details can be included in the design, which is based on historical shock testing and experience.

5.5.2 Tank boundaries are to be of equivalent scantlings to the hull boundaries.

5.5.3 Intermittent welding is not to be used on hull girder structure or tank boundaries below the water line or for 1 metre in way of the deck and shell connections.

5.5.4 Structural discontinuities are to be avoided and in general a minimum taper of 1:4 is to be applied to changes of structural section.

5.5.5 Bar keels are not to be fitted.

5.5.6 Tanks are to be integral with the ship's structure. For free standing tanks greater than 100 litres, calculations demonstrating the capability of the tank and supporting structure are to be submitted.

5.5.7 Main machinery mounts or raft mounts are to be supported on transverse web frames or floors forming part of the transverse ring structure. See Vol 1, Pt 3, Ch 2, 3.2 Primary members 3.2.2

5.5.8 The size of longitudinal members passing through, or ending on, bulkheads are to be as small as possible, though still complying with the appropriate scantling requirements of Vol 1, Pt 6, Ch 3 Scantling Determination. Bulkhead stiffeners are to be fitted perpendicular to the shell plating.

5.5.9 Where deep longitudinal members are unavoidable, their connection to the bulkhead will be specially considered.

5.5.10 Bottom longitudinals are to be of a uniform size. Alternate large and small longitudinals are to be avoided as they may lead to high shear forces in the bulkhead.

5.5.11 Access holes in all primary framing members are to be avoided in areas of high shear stress. Where they are essential to the operation of the ship they are to be circular and fitted with appropriate stiffening or compensation.

5.5.12 Frames on the bilge are to be provided with adequate lateral support, consideration should be given to the fitting of a shock stringer.

5.5.13 Lapped connections are not to be used to connect frames to floors.

5.5.14 All bulkhead stiffeners are to end on longitudinals, see Figure 2.5.2 Bulkhead stiffening.

Figure 2.5.2 Bulkhead stiffening

5.5.15 In transversely framed ships, bulkhead stiffeners are to be terminated on a shock stiffener welded to the bulkhead, parallel to, and spaced 500 mm from the shell. The bulkhead plating thickness is to be suitably increased in way. The shock stringer and bulkhead plate may be replaced by a web frame of suitable scantlings.

5.5.16 Bulkhead penetrations are to be grouped, away from the side shell and kept above the water line as far as is practicable.

5.5.17 Shell frames and deck beams are to be fitted in such a way as to minimise misalignment. Brackets where fitted are to be radiused and fitted with soft toes.

5.5.18 Where the vessel is to be subjected to very high levels of shock, the following details can be included in the design.

5.5.19 Pillar bulkheads are to be used below the waterline in place of pillars.

5.5.20 It is recommended that symmetric stiffeners should be fitted to the to the underwater portion of the shell envelope.

5.5.21 Where a transverse framing system is used, the shock capability of the structure will be specially considered. Calculations supporting the use of particular design details are to be submitted.

5.5.22 All bulkhead stiffeners are to end on longitudinals, see Figure 2.5.2 Bulkhead stiffening. An increased thickness margin strake on bulkheads of thickness not less than 80 per cent of the adjacent shell plate thickness, the thickness of the adjacent shell stiffener or 6,5 mm. The margin plate is to have a width not less than 1,5 times the adjacent stiffener spacing or four times the depth of adjacent shell stiffeners.

5.5.23 Shell frames and deck beams are to be fitted in such a way as to minimise misalignment. The frames are to be fitted within a tolerance of 0,3 median line up to a maximum of 3,0 mm where is the greater thickness of the frames being connected. Where this is not possible, the frame is to be released over 20 and realigned.

5.5.24 Where brackets are fitted, similar tolerances to Vol 1, Pt 4, Ch 2, 5.6 Seat design 5.6.5 are to be applied subject to a suitable area being provided for weld fillet, see Figure 2.5.3 Bracket connections. Tripping brackets or intercostal stiffeners should be used to stabilise the frame at the bracket toes. Brackets are to be radiused and fitted with soft toes.

Figure 2.5.3 Bracket connections

5.5.25 The cross-sectional area of the bulkhead stiffeners at their outer ends in way of the margin plate should not be less than 60 per cent of the area of the web of the hull longitudinals to which they are attached. To achieve this requirement, the bulkhead stiffeners may be tapered between the outer end and the point at which the size is the minimum required to withstand lateral pressure. The slope of the taper is to be such that:

A_x > 0,6A_L- 2t_x/3

5.5.26 The short stiffeners above the turn of bilge should be on the same side of the bulkhead as the main bulkhead stiffeners and should end on such a stiffener, see Figure 2.5.2 Bulkhead stiffening. Where necessary, an additional diagonal stiffener may be worked to facilitate the arrangement.

5.6.1 The shock notation may be enhanced by specifying that some or all of the equipment seating is to be designed to resist shock loading. Seat design should take account of the acceleration and deceleration from the shock wave; the magnitude of the shock acceleration will depend on the equipment mass, position in the ship and mounting arrangements. The seat design methodology is to be in accordance with a specified standard. The selection of seats to be assessed will depend on the equipment supported and the compartment in which it is situated.

5.6.2 Minor seats should be assessed to ensure that equipment remains captive. Detail design requirements such as minimum thickness, alignment, and free edge support can be specified to improve shock performance. In the absence of information, minor seats can be considered as those with equipment mass below 100 kg.

5.6.3 Seats which are not classed as minor are to be assessed for shock loads using acceleration values appropriate to the region of the ship in which the equipment is installed. Large items of equipment where the seat is integrated into the ship’s structure will normally require a finite element analysis to assess the strength of the seat. Where these seats are adjacent to the hull or an integrated tank, the fluid structure interaction may need to be modelled. See Vol 1, Pt 4, Ch 2, 5.4 Local strength assessment.

5.6.4 The shock accelerations are to be specified by the Owner. In general, accelerations will be specified for the following regions of the ship:

1. within 2,0 m of the wetted hull;

2. main transverse bulkheads and decks below the strength deck;

3. above strength deck and superstructures.

Shock accelerations can be scaled using a factor for different equipment based on its category of use.

5.6.5 For each equipment seat to be assessed, a report is to be provided containing the following information:

1. equipment mass and centre of gravity;

2. location in vessel;

3. mounting system;

4. spatial clearances around the mounted equipment;

5. captivity requirements;

6. relevant excitation frequencies from mounted equipment in the case of reciprocating or rotational machinery;

7. calculations demonstrating maximum stress and displacement, under vertical acceleration, vertical deceleration and athwartships accelerations. For non-linear analyses, strain rates are to be provided;

8. equipment alignment requirements, as appropriate.

5.6.6 As a minimum, the following seat load cases are to be assessed:

1. bolts; pull through, tensile, shear and bearing strength;

2. seat flange; flange bending and top plate weld area;

3. seat web; buckling and overturning;

4. deck; seat weld area if less than flange.

5.6.7 Stress and strain are to be assessed against criteria appropriate for the seat material and loading rate. The first fundamental mode of vibration of the seat including equipment is to be greater than 10 times the shock mount rated natural frequency to provide a sufficiently rigid base for the shock mount. In the absence of specific information, for steel, the data in Table 2.5.1 Allowable stresses for seat design may be used:

5.7.1 All shock mounts are to be of an approved type. Approval is to be undertaken by organisations approved by the Naval Administration. Approval documentation should contain the following information in accordance with NATO document ANEP63:

1. nature and application of the mount, including generic type, application, load range, shock displacement, environmental constraints and frequency range;

2. description of the mount assembly, including the complete assembly, the mount and the associated components;

3. details of the mount standard assembly and installation;

4. physical size, mass and dimensions;

5. performance data as listed in Table 2.5.2 Shock mount characterisation;

6. details of the mount testing process, including method of force generation, number of mounts used/shots used, mount supplier, validation, mount permanent deflection, details of test facility and date of testing;

7. mount specific protection, installation, inspection and maintenance requirements;

8. any applicable historic data, i.e. changes to the mount details over time. For example, changes of material, etc.

5.8.1 Hull valves below the waterline are to be of an approved type. Approval is to be undertaken by organisations approved by the Naval Administration. Approval documentation should contain the following:

1. details of the valve body, main components and securing arrangement to the hull, including bolt material grade and tightening torque;

2. details of the valve testing process, including method of force generation, number of tests, validation, details of test facility and date of testing.

5.8.2 Only materials with sufficient ductility to avoid fracture under shock conditions are to be used. Materials should be able to withstand high stresses for very short periods without exhibiting brittleness. Valve bodies are not to be made from materials with an elongation of less than 10 per cent. There should be adequate material in way of the valve seat to prevent distortion.

5.8.3 In general, the valve body should be as symmetrical as possible with no rapid changes in section; web stiffeners should not be incorporated. Spindles should be as short as possible. Square threads or sharp thread run-outs are to be avoided. Handwheels should be as light and small as possible.

5.8.4 The weight of the actuator is to be considered in the design of the valve and its connection to the hull. The actuator can form a considerable proportion of the overall weight of the valve.

5.8.5 Consideration should be given to the attached piping and its capacity to withstand shock:

1. Detachable pipe connections should be kept to the minimum necessary for installation and maintenance requirements;

2. Flanged and welded connections are to be used adjacent to the hull valve. Adjacent piping is to be designed to allow the valve and hull to flex under shock with limited restraint;

3. Where necessary, piping shall be supported with shock resistant mounts at a sufficient number of locations commensurate with the design shock level. The selection of shock mounts should consider displacement capability, see Vol 1, Pt 4, Ch 2, 5.7 Shock mounts. The response of the piping relative to equipment should be considered. Sufficient space between equipment and piping should be provided to ensure they do not contact each other in a shock scenario;

4. The routing of piping should be developed to minimise the number and size of penetrations through bulkheads, see Vol 1, Pt 4, Ch 2, 5.8 Design guidance for hull valves, piping and seals 5.8.11;

5. The consequences of leakage from piping and fittings should be investigated;

6. Brackets should not be welded direct to steel piping;

7. Adequate division of vital piping systems to isolate damage should be considered;

8. The shock resistance of flanged connections should consider bolt preload, anti-rotational locking devices where appropriate and performance of gaskets.

5.8.6 The sealing arrangement between the valve and the hull insert is to be suitable for shock loading and able to accommodate elongation of the securing studs.

5.8.7 Hull valve designs can be approved by the following methods:

1. physical testing;

2. semi-empirical methods;

3. direct calculation.

5.8.8 Physical shock testing may be used to assess the valve. Physical testing is to take account of the attachment to the hull and possible combinations of hull scantlings, stiffener spacing, materials, etc.

5.8.9 Recognised semi-empirical methods may be used to assess the valve.

5.8.10 Validated numerical methods may be used to assess the valve. Where used, they are to take account of the following criteria:

1. asymmetry in the valve and piping assembly;

2. dimensions of the hull insert/pad;

3. use of sea tube between the valve and hull insert;

4. hull scantlings and stiffener/frame spacing;

5. plasticity in the hull and valve assembly;

6. the effective mass of the valve, actuator and piping;

7. the valve to hull securing arrangement, taking into account fit and pre-stress effects;

8. dynamic properties of materials;

9. the effect of any surrounding equipment or masses.

Sea tubes of unusual material, GRE for example, or unusual configuration are to be assessed by physical shock testing and not assessed by numerical simulation.

5.8.11 The potential for leakage from seals/glands under shock loading, and the consequences of leakage, are to be considered. The shock resistance of vital seals/glands, including stern-tube seals, is to be validated by shock qualification testing. The sealing efficiency of stern-tube seals should not be compromised by the anticipated axial, radial and angular shaft movements commensurate with the design shock level.