Honda CRV is a compact-sized crossover SUV. It wae designed mainly for street driving. Its AWD system is not for serious off-road use. But it does have certain all-wheel drive capabilities. The CRV basically is a front-wheel-drive vehicle. Its road manner will be more like a FWD vehicle, even it does have a drive shaft to the rear wheels. The rear wheels will get power only when the front wheels lost traction. The CRV does not have a central differential, so how does it do it? The Honda engineers selected a system called "dual-pump" system.
Here is the description of the system from the Wikipedia.com
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Real Time 4WD system on the CR-V utilizes a Dual hydraulic Pump Rear Differential and 4WD Transfer case. The dual pump system employs two pumps, one driven by the drive shaft (front) and the other driven by the differential. When there is a pressure difference of greater than 3% between these two pumps, a clutch that connects the front and rear axles begins to engage. The greater the difference in axle speeds, the more torque is applied to the rear. This system would most accurately be called, "automatically engaged four wheel drive," because the driver has no control over when the system engages. To allow the ABS braking system to function properly, the 4WD clutch will disengage if the brakes are applied.
Later Model CR-Vs equipped with automatic transmissions also have a lockup torque converter and Grade Logic program which aids the CR-V when climbing steep inclines by keeping the transmission in the lower gear. The 2007 and later Model 4WD system was improved and sends an additional 20% more torque to the rear tires than earlier models.
When driven off road, CR-Vs with the 4WD System are typically used in the Green Laning or "Two-tracking" type of off roading. The CR-V is surprisingly capable when driven off the pavement. It can successfully navigate mud, sand, hills steep enough to scare some people, and ten or more inches of snow, depending on how dense or wet the snow is, as well as the dirt roads and light trails it was designed for.
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Now the important question is: what if the dual-pump system failed?
Let me give you an example.
If the pump on the rear differential failed but the pump on the drive shaft from the front engine still generates pressure, the system will engage the clutch because the system thinks the rear wheels are not moving and the front wheels must be slipping(although that is not what happened). If the clutch is fully engaged (similar to a locked central differential), that will be very dangerous. First, the mechanical components(differential, drive shafts, gears...) will be under excess force when the vehicle makes turns. Second, it will change the vehicle's road manner which could lead the vehicle to lost control. So the engineer must limit the power to the rear wheels and not allow the cluch fully engaged. This is a design compromise.
So when you take CRV to a off-road test, don't expect it to do the things that a real off-road vehicle can do, like climbing a steep hill while the surface is slippery. That is not what the CRV was designed for.